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* stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition . | i | 0911.0791 | * stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition . the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . the disagreement between the model predictions and observations of cluster colours and magnitudes may indicate problems with or deficiencies in the modelling , and dioes not necessarily tell us that star clusters do not behave like ssps . matching the photometric properties of star clusters using ssp models is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . composite models , characterized by complex star - formation histories , also match the observed cluster colours . [ firstpage ] | simple stellar populations ( ssps ) , defined as groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition certainly exist in nature . a priori , we can not say that all stellar groups , associations or star clusters are ssps , however . most galaxies certainly are not . conceptually , ssps are appealing because they are easy to model theoretically and their temporal evolution can be followed accurately . all stars of an ssp should have the same initial metal content . at any given time , the stars composing an ssp describe an isochrone in the theoretical hertzsprung russell ( hr ) diagram , which can easily be transformed to an observational colour magnitude diagram ( cmd ) . detailed observations of this kind are available only for resolved stellar populations , either galactic clusters or star clusters in nearby galaxies , or the stars making up the satellites of the milky way . only in these few cases can we reliably establish the simplicity of a stellar population by inspection of its cmd . integrated properties of stellar populations , such as their colours or spectral - energy distributions , are subject to degeneracies ( e.g. , old , metal - poor populations resemble younger , metal - richer ones ) and statistical ( stochastic ) uncertainties ( due to the small number of stars present in low - mass systems ) which , in most cases , prevent us from establishing with certainty if we are observing an ssp . of course , the question as to whether or not star clusters can be described by ssps does not apply to those clusters which have been shown explicitly to host stellar populations of a composite nature , e.g. , resolved clusters where a double or triple main sequence ( ms ) has been detected such as ngc 2808 ( piotto _ et al . _ 2007 ; see also kalirai & richer 2010 ; van loon 2010 ) , or clusters showing evidence of prolonged star formation like @xmath0 centauri ( villanova _ et al . _ 2007 ) , nor to dwarf galaxies like leo a ( cole _ et al . _ 2007 ) or other galaxies in the local group with well - established multiple episodes of star formation ( gallart _ et al . _ 2007 ) . |
the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . [ firstpage ] | c | 0911.0791 | * stellar evolution ; population synthesis ; spectral evolution ; simple stellar populations ; tp agb stars * in this paper , i review to what extent we can understand the photometric properties of star clusters , and of low - mass , unresolved galaxies , in terms of population synthesis models designed to describe ` simple stellar populations ' ( ssps ) , i.e. , groups of stars born at the same time , in the same volume of space , and from a gas cloud of homogeneous chemical composition . the photometric properties predicted by these models do not readily match the observations of most star clusters , unless we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the stellar initial mass function . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . the disagreement between the model predictions and observations of cluster colours and magnitudes may indicate problems with or deficiencies in the modelling , and dioes not necessarily tell us that star clusters do not behave like ssps . matching the photometric properties of star clusters using ssp models is a necessary ( but not sufficient ) condition for clusters to be considered simple stellar populations . composite models , characterized by complex star - formation histories , also match the observed cluster colours . [ firstpage ] | the magnitudes and colours predicted by stellar population synthesis models do not readily match observations of unresolved star clusters , which are commonly expected to behave like ideal ssps . this lack of agreement between the model predictions and observations may indicate problems or deficiencies in the modelling , and does not necessarily tell us that star clusters do not behave like ssps . in this review , i have briefly summarized the results of simple simulations which show how the range of colours observed in intermediate - age lmc star clusters can be understood on the basis of current stellar evolution theory , if we properly take into account the expected variation in the number of stars occupying sparsely populated evolutionary stages , due to stochastic fluctuations in the imf . in this case , population synthesis models reproduce remarkably well the full ranges of observed integrated colours and absolute magnitudes of star clusters of various ages and metallicities . some young clusters are described by supersolar - metallicity models , which may not be realistic for the lmc . there is no need to introduce ad hoc assumptions into population synthesis models ( maraston 1998 ; 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15.pt we consider photon radiation in @xmath0 events at the upgraded fermilab tevatron and the cern large hadron collider ( lhc ) as a tool to measure the electric charge of the top quark . , it will be possible to determine the charge of the top quark with an accuracy of about 10% . | i | hep-ph0106341 | 15.pt we consider photon radiation in @xmath0 events at the upgraded fermilab tevatron and the cern large hadron collider ( lhc ) as a tool to measure the electric charge of the top quark . we analyze the contributions of @xmath1 production and radiative top quark decays to @xmath2 , assuming that both @xmath3-quarks are tagged . with 20 fb@xmath4 at the tevatron , the possibility that the `` top quark '' discovered in run i is actually an exotic charge @xmath5 quark can be ruled out at the @xmath6 confidence level . at the lhc , it will be possible to determine the charge of the top quark with an accuracy of about 10% . | like most of its fundamental quantum numbers , the electric charge of the top quark has not been measured so far . alternative interpretations for the particle we believe is the charge @xmath7 isospin partner of the @xmath3-quark are thus not ruled out . for example , since the correlations of the @xmath3-quarks and the @xmath8-bosons in @xmath186 are not determined , it is conceivable that the `` @xmath45-quark '' observed at the tevatron is an exotic quark , @xmath19 , with charge @xmath5 which decays via @xmath187 . this interpretation is consistent with current precision electroweak data @xcite . in order to determine the charge of the top quark , one can either measure the charge of the @xmath3-jet , or investigate photon radiation in @xmath0 events . the latter method actually measures a combination of the em coupling strength and the charge quantum number . combining the results of the two methods will thus make it possible to determine both quantities . in this paper we have explored the possibility of measuring @xmath20 in @xmath188 , assuming that both @xmath3-quarks are tagged . our analysis makes use of both @xmath1 production and radiative top quark decays , and is carried out at the tree level . the em coupling strength is assumed to take its sm value . top quark and @xmath8 boson decays are treated in the narrow width approximation . contributions from radiative @xmath8 decays can be suppressed by simple phase space cuts ( see eq . ( [ eq : radw ] ) ) . the remaining event sample can be separated into a @xmath1 sample , a @xmath25 , @xmath189 sample , and a @xmath25 , @xmath190 sample by imposing invariant mass and cluster transverse mass cuts ( see eqs . ( [ eq : top51 ] ) ( [ eq : top7 ] ) ) . in the phase space region dominated by @xmath1 production , the cross section increases if the magnitude of @xmath20 increases . at the tevatron , @xmath117 annihilation dominates and photon radiation off the incoming quarks constitutes an irreducible background which limits the sensitivity to @xmath20 . in contrast , at the lhc , gluon fusion dominates , and the @xmath1 cross section scales approximately with @xmath118 . in the phase space regions which enhance @xmath0 production with one of the top quarks decaying radiatively ( @xmath78 ) , interference effects between the feynman diagrams where the photon is emitted from the top quark , the @xmath8 boson and the @xmath3-quark line may cause the cross section to either decrease or increase with @xmath191 . for example , for @xmath115 , the @xmath192 cross section via radiative top quark decays is reduced by a factor of @xmath193 to @xmath194 . the changes in the individual cross sections are reflected in the photon transverse momentum distribution in the various phase space regions . we also found that the @xmath143 distribution , where @xmath144 is the @xmath3 or @xmath97-quark with the smaller @xmath105 , is sensitive to the charge of the top quark in the phase space regions dominated by @xmath0 production where one of the top quarks decays radiatively . in order to determine how well one can hope to measure the top quark charge using photon radiation in top quark events in future tevatron and lhc experiments , we have performed @xmath160 tests of the @xmath122 and the @xmath143 distributions in the various phase space regions of interest . at the tevatron , with an integrated luminosity of 20 fb@xmath4 , one will be able to exclude at @xmath6 c.l . the possibility that an exotic quark @xmath19 with charge @xmath5 and not the sm top quark has been found in run i. for smaller integrated luminosities , the number of events expected is very small and it will be difficult to perform a quantitative analysis using differential cross sections . in this case , the ratio of the cross section associated with radiation in top production to the radiative decay cross section may be a useful tool . at the lhc with 10 fb@xmath4 obtained at @xmath175 , it should be possible to measure the electric charge of the top quark with an accuracy of about 10% . for comparison , at a linear collider with @xmath195 gev and @xmath196 fb@xmath4 , one expects that @xmath20 can also be measured with a precision of about 10% @xcite . finally , at a @xmath197 collider it is conceivable that the top quark charge can be determined with an accuracy of better than 1% , if the @xmath24 cross section can be measured with a precision of 2% @xcite . the measurement of the electric charge of the top quark at the tevatron using photon radiation in top quark events is severely limited by statistics . even with an integrated luminosity of 20 fb@xmath4 , @xmath20 can only be determined with a precision of @xmath198 . however , as we pointed out in sec . i , information on the electric charge of the top quark may also be obtained from a measurement of the charge of the @xmath3-jets , and the charge sign of the leptons in semileptonically tagged @xmath3-quarks . this may significantly improve the precision which can be obtained . detailed simulations will be necessary in order to determine how well the top quark charge can be measured using these methods . we would like to thank c. ferreti , h. frisch , b. knuteson , t. lecompte , j. parsons , z. sullivan and j. womersley for stimulating discussions . one of us ( u.b . ) is grateful to the fermilab theory group , where part of this work was carried out , for its generous hospitality . this work has been supported in part by doe grant de - fg02 - 91er40685 , nsf grants phy-9600155 and phy-9970703 , and a nsf graduate student fellowship . f. abe _ et al . _ ( cdf collaboration ) , phys . lett . * 74 * , 2626 ( 1995 ) . s. abachi _ et al . _ ( d collaboration ) , phys . lett . * 74 * , 2632 ( 1995 ) . p. c. bhat , h. prosper and s. s. snyder , int . j. mod . * a13 * , 5113 ( 1998 ) . d. chang , w.f . chang , and e. ma , phys . * d59 * , 091503 ( 1999 ) and phys . * d61 * , 037301 ( 2000 ) . b. grzadkowski and z. hioki , nucl . b585 * , 3 ( 2000 ) and references therein . g. velev , talk given at the top thinkshop@xmath199 , fermilab , november 2000 . t. stelzer and w. f. long , comput . commun . * 81 * , 357 ( 1994 ) . h. murayama , i. watanabe and k. hagiwara , kek-91 - 11 ( 1991 ) . a. denner and t. sack , z. phys . * c46 * , 653 ( 1990 ) . t. affolder _ et al . _ , ( cdf collaboration ) , phys . rev . * d63 * , 032003 ( 2001 ) . b. abbott _ et al . _ ( d collaboration ) , phys . rev . * d58 * , 052001 ( 1998 ) . d. abbaneo _ et al . _ ( the lep electroweak working group ) , cern - ep-2001 - 021 ( february 2001 ) ; hep - ex/0103048 . a. d. martin , r. g. roberts and w. j. stirling , phys . * b387 * , 419 ( 1996 ) . u. baur and e. l. berger , phys . * d47 * , 4889 ( 1993 ) . t. abe _ et al . _ ( american linear collider working group collaboration ) , slac-570 _ resource book for snowmass 2001 , 30 jun - 21 jul 2001 , snowmass , colorado _ , hep - ex/0106055 , hep - ex/0106056 , hep - ex/0106057 and hep - ex/0106058 . e. boos , hep - ph/0009100 , and references therein . ccccc + & @xmath1 & @xmath109 & @xmath121 & + & contribution & contribution & contribution & total + tevatron , @xmath200 & 1.70 fb & 0.12 fb & 0.10 fb & 1.92 fb + tevatron , @xmath201 & 2.37 fb & 0.03 fb & 0.02 fb & 2.42 fb + lhc , @xmath200 & 33.3 fb & 5.78 fb & 4.86 fb & 44.0 fb + lhc , @xmath201 & 111.4 fb & 1.21 fb & 0.97 fb & 113.6 fb + + tevatron , @xmath200 & 0.36 fb & 0.26 fb & 0.13 fb & 0.75 fb + tevatron , @xmath201 & 0.52 fb & 0.07 fb & 0.03 fb & 0.62 fb + lhc , @xmath200 & 0.68 fb & 3.67 fb & 2.26 fb & 6.61 fb + lhc , @xmath201 & 2.25 fb & 0.87 fb & 0.59 fb & 3.71 fb + + tevatron , @xmath200 & 0.11 fb & 0.06 fb & 0.19 fb & 0.36 fb + tevatron , @xmath201 & 0.16 fb & 0.01 fb & 0.05 fb & 0.22 fb + lhc , @xmath200 & 0.15 fb & 1.07 fb & 3.63 fb & 4.85 fb + lhc , @xmath201 & 0.49 fb & 0.26 fb & 0.85 fb & 1.60 fb + .limits achievable at 95% c.l . for @xmath170 in @xmath188 at the tevatron and the lhc . bounds are shown for the photon transverse momentum distribution in the phase space region defined by the @xmath1 selection cuts , and the @xmath122 and @xmath143 distributions of the combined radiative top decay regions . the last row displays the combined limits from the three distributions . the @xmath3-quark charge is given by @xmath162 . the cuts imposed are described in sec . ii . for the @xmath143 distribution , the @xmath122 cut of eq . ( [ eq : top4 ] ) has been replaced by @xmath151 gev . [ cols="^,^,^ " , ] |
observations presented here and previous radio observations of the neutral gas content of this group suggest that the interactions that have taken place in the sextet only redistributed the stars from the member galaxies within the group . we speculate that future interactions may be strong enough to strip the gas from ngc6027d and trigger star cluster formation . | c | astro-ph0208284 | _ hubble space telescope _ wide field planetary camera 2 images of hickson compact group 79 , seyfert s sextet , are presented . both point sources and extended sources detected on the three wf chips were photometered in four filters : f336w , f439w , f555w , and f814w . unlike other hcgs that have been imaged with _ hst _ , there do not appear to be any candidate young star clusters among the detected point sources . the majority of the point sources that may be star clusters associated with the sextet have red colors consistent with stellar populations older than 1 gyr . a similar conclusion is drawn with regard to the extended sources . the majority of these appear to be background galaxies , but a few candidate dwarf galaxies are identified as potentially associated with seyfert s sextet . however , no blue , star forming objects similar to the tidal dwarf galaxy candidates identified in other hcgs are found among the extended objects identified in this study . a redshift for one dwarf galaxy candidate was measured from a spectrum obtained with the hobby - eberly telescope , and this object was found to have a redshift similar to ngc6027e , the discordant spiral formerly identified as a member of this compact group . the _ hst _ observations presented here and previous radio observations of the neutral gas content of this group suggest that the interactions that have taken place in the sextet only redistributed the stars from the member galaxies within the group . we speculate that future interactions may be strong enough to strip the gas from ngc6027d and trigger star cluster formation . | the case study of seyfert s sextet presented here is part of a continuing effort to determine whether dwarf galaxies form during tidal interactions among giant galaxies . the sextet appears to be the most logical choice to search for tidal dwarf formation ; it is the most compact of the hickson compact groups , contains two prominent tidal tails , has a low velocity dispersion , and previous ground - based imaging revealed a number of faint , extended objects within the boundaries of the group . however , the results of the _ hst _ imaging of seyfert s sextet show that , contrary to expectations , there is very little evidence for dwarf galaxy formation or any other strong star formation in this group . a large number of both point sources and extended sources were catalogued and photometered from the three wide field images . we find that very few objects are detected in either of the two blue filters , f336w and f439w , and those that are detected in the two red filters , f555w and f814w , have red colors consistent with those of old stellar populations . the majority of the point sources detected appear to be old ( @xmath118 gyr ) and the majority of the extended sources detected appear to be background galaxies . these photometric results contrast sharply with _ hst _ imaging studies of other hcgs , such as hcg92 ( stephan s quintet ) and hcg31 . in hcg92 , @xcite found a number of bright , blue star cluster candidates in the tidal debris regions of this group . the images of this compact group also show bright , blue extended sources in the `` northern starburst region '' and in the tidal tails of ngc7319 and ngc7318a / b . hcg31 contains a significant number of bright , blue point sources @xcite similar to those seen in hcg92 . star - forming regions are also observed in hcg31 that are `` too small to be called galaxies themselves , but are not clearly associated with either galaxy ac or galaxy e '' @xcite . thus , both hcg92 and hcg31 contain what appear to be young star clusters and tidal dwarf galaxy candidates , while seyfert s sextet does not appear to contain a significant population of either type of object . the star cluster candidates identified in this study have photometric properties consistent with those for models of massive ( @xmath119 ) clusters with ages @xmath120 years . the ages of these objects suggest that they are not entirely a primordial population , but may be the product of an interaction within the compact group at some time within the past few gyr . @xcite argue that the optical tail associated with ngc 6027b and the gas that they associate with ngc 6027d may have resulted from an interaction between these two disk galaxies more than @xmath121 years ago . the ages we derive for many of the cluster candidates are consistent with this hypothesis . while there do not appear to be any young star clusters or tidal dwarf galaxies associated with seyfert s sextet , we did identify several candidate dwarf galaxies in the group . this sample includes a few faint , blue extended sources , and two galaxies with peculiar morphologies : an irregularly shaped galaxy located quite near the disk of ngc6027c and an unusual , `` cometary '' galaxy located within the tidal tail associated with ngc6027c . an additional candidate , galaxy 4.2 , has already been ruled out as a member of the sextet ; the hobby - eberly telescope spectrum of this object instead shows that it is associated with ngc6027e , the discordant redshift member of seyfert s sextet . whether or not the other candidate dwarf galaxies are associated with the sextet , they appear morphologically very different from the clumpy , blue tidal dwarf galaxy candidates in hcg92 and hcg31 . the data suggest that there is some fundamental , physical difference between the sextet and the two hcgs that are known to contain young star clusters and tidal dwarf galaxy candidates . one obvious difference between these groups are the types of galaxies contained in each : seyfert s sextet is primarily made up of early - type ( s0/e ) galaxies , stephan s quintet contains spirals , and hcg31 contains mostly irregular galaxies . based on these morphologies , one initial expectation is that the neutral gas content in seyfert s sextet is likely to be lower than that of either hcg31 or hcg92 . radio observations show that the sextet contains only @xmath122 of neutral hydrogen @xcite , about an order of magnitude less than that of hcg31 and hcg92 @xcite . the most recent observations of the gas content of hcg92 @xcite revise the gas mass of this group downward , however it remains at least five times larger than the gas in seyfert s sextet . what appears to be the more significant difference among these three hcgs , however , is nt the gas mass , but the _ distribution _ of the . @xcite present vla neutral hydrogen observations of seyfert s sextet that indicate that the majority of the mass is retained by the disk of ngc6027d , although some gas is found in a tail extending to the east of this galaxy and also in the optical tidal tail associated with ngc6027b . in hcg31 , the vla neutral hydrogen maps @xcite show that the gas is found both in the galaxies themselves and in a large envelope of gas that is plausibly attributed to tidal interactions between the galaxies . the distribution of in hcg92 is found to lie entirely outside of the galaxies @xcite , however . the is concentrated in clouds and tidal tails that are not coincident with the disks of the member galaxies . @xcite proposed an evolutionary sequence based on their vla observations of the content of hcgs . in their model , `` phase 1 '' hcgs are those where the vast majority of the neutral gas remains bound to the member galaxies . `` phase 2 '' hcgs are more evolved in the sense that the galaxies retain some of the gas , while approximately half of the gas mass is found in tidal features . the final , most evolved phase is broken into two subclasses , `` phase 3a '' and `` phase 3b '' . phase 3a groups are those where the gas is almost completely stripped from the galaxies and is found entirely within tidal features , while phase 3b groups are a few rare cases where the entire group seems to be contained in a single cloud . hcg31 is considered a prototype phase 2 group , and hcg92 is considered an extreme example of phase 3a . both @xcite and @xcite find seyfert s sextet to be anomalous ; its gas distribution suggests that the system has not experienced significant dynamical evolution , while optical observations suggest the opposite . we propose one possible scenario for the history of seyfert s sextet that takes into account the following significant factors : ( 1 ) the tidal tails are evidence for interactions among the accordant redshift members some time in the past , ( 2 ) the interactions that have occurred have not triggered star and/or star cluster formation similar to that seen in other merging galaxies and compact groups , ( 3 ) the relatively small amounts of neutral gas in seyfert s sextet remains bound in the one late type galaxy and does not appear to be distributed among the group environment , and ( 4 ) the low velocity dispersion among the member galaxies and the small distances between the member galaxies suggests that future interactions among the galaxies are likely . this accumulated evidence suggests that a number of gas - poor ( and one gas - rich ) galaxies have interacted beginning perhaps as long as 1 gyr or more in the past ( dated by the colors of the red globular cluster candidates ) . the interactions in the group have created the optical tidal tails and perhaps created the elliptical member of the sextet , ngc6027a , as well . the interactions in the past stripped stars from the progenitor galaxies , redistributing them within the group . the evidence for a red , low surface brightness halo encompassing all of the member galaxies , which is seen in our images as well as deeper ground - based images , is further evidence for a redistribution of the galaxies stars within the group . the only ongoing star formation and most of the neutral gas is found within the disk of ngc6027d , the only late type member of the group , suggesting that any interaction that involved this galaxy must have been minor , although the galaxy disk does appear somewhat irregular and perhaps warped . we speculate that further interactions are probably inevitable , and a major interaction between ngc6027d and the other members of the group may trigger the stripping of its neutral gas and star cluster formation throughout the group in the future . moreover , the low velocity dispersion suggests that none of the four large galaxies are likely to escape the group , and thus the group members may merge into a single galaxy , rather than remaining distinct . thus , we believe that we are seeing seyfert s sextet at the `` beginning of the end '' ; we presume that the future interactions will be the end of this group , transforming it into a single galaxy . we wish to acknowledge the help of m. eracleous with data reduction of our het spectra . we also wish to thank j. hibbard for a number of useful discussions . sz acknowledges support from the national science foundation through a research experiences for undergraduates award . this work was supported by nasa stsci and by the nsf under grants nsf ast 00 - 71223 and stsi hst - go-08717.04-a . lllcc alternate names : & & hcg 79 , vv115 , ngc6027 + equatorial coordinates : & & 15@xmath12359@xmath12412@xmath125 @xmath126 @xmath127 ( j2000.0 ) + mean redshift : & & 0.0145 + radial velocity dispersion : & & 138 km s@xmath0 + + galaxies : & & name & type & @xmath128 ( km s@xmath0 ) + & & ngc6027a & e0 & 4294 + & & ngc6027b & s0 & 4446 + & & ngc6027c & s0 & 4146 + & & ngc6027d & sdm & 4503 + & & ngc6027e & scd & 19809 + lrrrr 2.6 & 22.63@xmath1330.25 & 23.28@xmath1330.19 & @xmath134 & @xmath135 + 3.3 & 20.83@xmath1330.11 & 22.42@xmath1330.19 & @xmath136 & @xmath136 + 3.8 & 22.02@xmath1330.20 & 23.20@xmath1330.25 & @xmath136 & @xmath136 + 3.10 & 21.31@xmath1330.18 & 22.54@xmath1330.23 & @xmath136 & @xmath136 + 3.14 & 19.39@xmath1330.06 & 20.42@xmath1330.06 & 21.39@xmath1330.28 & 21.70@xmath1330.59 + 4.1 & 21.86@xmath1330.22 & 22.71@xmath1330.20 & @xmath137 & @xmath138 + 4.2 & 19.58@xmath1330.15 & 20.30@xmath1330.13 & 21.37@xmath1330.22 & 20.98@xmath1330.42 + 4.3 & 20.95@xmath1330.12 & 21.73@xmath1330.13 & 23.01@xmath1330.27 & 22.21@xmath1330.35 + 4.6 & 20.58@xmath1330.12 & 21.74@xmath1330.15 & @xmath136 & @xmath136 + |
a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/. | i | 1507.03703 | a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , i have developed a method to calculate bpmfs for protein - ligand systems . the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the results demonstrate that the method is promising , but that ligand pose sampling and phase space overlap can sometimes prevent precise bpmf estimation . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/. | fast and accurate predictions of binding free energies between proteins and small organic ligands would have significant impact on designing drugs @xcite and other modulators of biological processes . the clear relevance of protein - ligand binding affinity prediction in chemical biology and drug discovery has inspired a vast array of physics - based methods ( for a broad review , see @xcite ) , each with a different trade - off between computational accuracy and speed . on one extreme , molecular docking focuses on speed . docking algorithms are designed to quickly obtain plausible configurations of a protein - ligand complex . scoring functions are then used to rank one configuration versus another . docking programs are commonly assessed by their ability to redock ligands into crystallographic structures from which they have been removed . comparative studies @xcite and blinded exercises @xcite consistently show that docking methods are adept at generating the native pose but are less competent at giving it the highest rank . in this context , it is not surprising that docking scores are poorly correlated with binding free energies @xcite . in contrast , alchemical pathway methods are based on rigorous statistical mechanics . the methods involve sampling from a series of possibly nonphysical thermodynamic states in between end - states where the receptor and ligand are bound and unbound . in the unbound state , the receptor - ligand nonbonded interaction terms may be switched off or the species may be physically separated . in accordance to the established statistical mechanics of noncovalent binding @xcite , the receptor is usually allowed full flexibility . unfortunately , sampling a fully flexible complex from multiple statistical distributions along an alchemical pathway generally requires substantial computing resources ; it has been suggested that most published studies are not fully converged @xcite ! even sampling the ligand binding pose is challenging @xcite . to bypass this difficulty , most pathway calculations pursue relative binding free energies between similar molecules and assume that the binding mode does not change . in absolute binding free energy calculations , ligand sampling issues are usually alleviated by confining the molecule to a specific pose @xcite . within this restricted range of problems , alchemical pathway calculations are amassing a growing track record of accurate prediction ( e.g. @xcite ) . _ the success of these methods suggests that docking may be substantially improved by incorporating rigorous statistical mechanics . _ implicit ligand theory ( ilt ) @xcite , a recently derived statistical mechanics framework for noncovalent association , has the potential to inspire new methods that combine the speed of docking and the rigor of alchemical pathway methods . ilt formally separates receptor and ligand sampling into two distinct stages . because the first stage of receptor sampling does not require a ligand , receptor conformations can be sampled once and used with many different ligands . in contrast , conventional alchemical pathway methods require thorough receptor sampling for every receptor - ligand pair . the second stage is to calculate the binding potential of mean force ( bpmf ) - the binding free energy between a ligand and a _ rigid _ receptor configuration ( eq . [ eq : bpmf ] ) - for each receptor configuration . finally , the standard binding free energy is an exponential average of bpmfs ( eq . [ eq : fe_ilt ] ) . while multiple bpmfs are required to estimate a standard binding free energy , the overall calculation should require less computer time than conventional methods because bpmfs are easier to estimate than binding free energies with a fully flexible receptor . the key reason for this speedup is that a bpmf calculation only requires sampling of the ligand , which usually has many fewer degrees of freedom than the complex . furthermore , nonbonded interactions between a rigid receptor and ligand can be treated by interpolating precomputed three - dimensional grids , a strategy first developed for docking @xcite . once the grid is stored , calculation time no longer depends on the size of the receptor . in contrast , conventional alchemical pathway methods require frequent force evaluation between flexible receptor atoms . as the number of pairwise interactions scales as @xmath1 with n receptor atoms ( neglecting cutoffs ) , the relative efficiency of ilt - based methods will be more pronounced as receptor size increases . in the first paper on ilt , bpmfs were estimated for simple host - guest systems @xcite . here , the focus is on precise bpmf estimation for protein - ligand systems . @xcite previously computed binding free energies between simple ligands and a rigid protein , t4 lysozyme . in contrast , the present work involves more diverse systems . @xcite were equally rigorous , but did not implement specialized methods to significantly speed their calculations compared to flexible - receptor calculations . @xcite developed a fast method based on a number of approximations . as in other bpmf @xcite and standard binding free energy @xcite calculations , hamiltonian replica exchange is applied . the main methodological differences between the current and previous work are the adaptive initialization of thermodynamic states and the use of linearly - scaled interaction grids @xcite with transformation - based smoothing @xcite ; these will be discussed in detail in the section on _ theory and methods_. the method is demonstrated on the astex diverse set @xcite , a curated database of 85 high - quality protein - ligand complexes of pharmaceutical or agrochemical interest . the algorithm is implemented in a new software package , alchemical grid dock ( algdock ) , a python module based on the molecular modeling toolkit ( mmtk ) 2.7.8 @xcite . algdock is available under the open - source mit license at https://github.com / ccbatiit / algdock/. |
fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t . | m | 1507.03703 | a binding potential of mean force ( bpmf ) is a free energy of noncovalent association in which one binding partner is flexible and the other is rigid . expanding on previous work with host - guest systems , i have developed a method to calculate bpmfs for protein - ligand systems . the method is based on replica exchange sampling from multiple thermodynamic states at different temperatures and protein - ligand interaction strengths . protein - ligand interactions are represented by interpolating precomputed electrostatic and van der waals grids . using a simple estimator for thermodynamic length , thermodynamic states are initialized at approximately equal intervals . the method is demonstrated on the astex diverse set , a database of 85 protein - ligand complexes relevant to pharmacy or agriculture . fifteen independent simulations of each complex were started using poses from crystallography , docking , or the lowest - energy pose observed in the other simulations . benchmark simulations completed within three days on a single processor . overall , protocols initialized using the thermodynamic length estimator were system - specific , robust , and led to approximately even replica exchange acceptance probabilities between neighboring states . in most systems , the standard deviation of the bpmf converges to within 5 k@xmath0 t . even with low variance , however , the mean bpmf was sometimes dependent on starting conditions , implying inadequate sampling . within the thermodynamic cycle , free energies estimated based on multiple intermediate states were more precise , and those estimated by single - step perturbation were less precise . the results demonstrate that the method is promising , but that ligand pose sampling and phase space overlap can sometimes prevent precise bpmf estimation . the software used to perform these calculations , alchemical grid dock ( algdock ) , is available under the open - source mit license at https://github.com / ccbatiit / algdock/. | this section reviews implicit ligand theory , details the algorithms in algdock , and describes the setup of the bpmf calculations on the astex diverse set . for the noncovalent association between a receptor @xmath2 and ligand @xmath3 to form a complex @xmath4 , @xmath5 , the standard binding free energy is , @xmath6 where @xmath7 is the inverse of boltzmann s constant times the temperature , @xmath8 is the standard concentration ( 1 m = 1/1660 @xmath9 ) , and @xmath10 is the equilibrium concentration of species @xmath11 . activities have been assumed to be unity , a reasonable approximation in the limit of low concentrations . coordinates of the complex , @xmath12 , are partitioned into receptor ( @xmath13 ) and ligand internal ( @xmath14 ) and external ( @xmath15 ) coordinates . based on this partitioning , the interaction energy is defined as @xmath16 , where @xmath17 is an effective potential energy that includes the gas - phase potential energy @xmath18 and solvation free energy @xmath19 @xcite . a bpmf is an exponential average of interaction energies over ligand coordinates in the binding site @xcite , @xmath20 where @xmath21 is an indicator function that takes values between 0 and 1 and specifies whether the receptor and ligand are bound or not . according to ilt , the standard binding free energy @xmath22 is related to an exponential average of bpmfs over boltzmann - distributed receptor configurations @xmath13 , @xmath23 } dr_r } { \int e^{-\beta { \mathcal u}(r_{r } ) } dr_r } \right ) - \beta^{-1 } \ln \left ( \frac{\omega c^\circ}{8 \pi^2 } \right ) , \label{eq : fe_ilt}\end{aligned}\ ] ] where @xmath24 is the volume of the binding site . a bpmf can also be expressed as a ratio of partition functions @xcite , @xmath25 } ~ dr_l d\xi_l } \right ) . \label{eq : bpmf_ratio}\end{aligned}\ ] ] in algdock , bpmfs are estimated by completing the thermodynamic cycle shown in figure [ fig : thermo_cycle ] . , width=322 ] mathematical expressions for individual free energy differences within the cycle are given in table [ tab : b_parts ] . the sum of all the free energy components in table [ tab : b_parts ] is @xmath26 . . * thermodynamic cycle for bpmfs : expressions * [ cols="^,^,^,^",options="header " , ] the least precise free energy estimates between adjacent milestones . counts are based on all simulations or the imprecise subset , when the standard deviation of the total bpmf is greater than 5.0 . [ tab : least_precise ] for systems with poor convergence of bpmf estimates , longer sampling is not necessarily an effective way to improve the precision of free energy estimates . while @xmath27 $ ] usually decreases monotonically with sample size , this trend is not universally true ( figure [ fig : std_fe_cycle ] ) . in some systems there are temporary jumps in @xmath27 $ ] due to instability in determining the equilibrated cycle . more importantly , in other systems , @xmath27 $ ] appears flat , with little or no change with increased sampling . $ ] based on 15 independent simulations of ( a ) the ligand or @xmath28 $ ] based on the ligand simulations and 15 independent simulations of the complex starting from the ( b ) crystallographic , ( c ) docked , and ( d ) lowest - energy observed poses . [ fig : std_fe_cycle],width=641 ] + in some systems , the variance is low but free energy estimates are dependent on the starting poses . when results from all simulations between milestones c&d are grouped together , the standard deviation in many systems no longer converges to within 5 @xmath29 . because converged thermodynamic quantities should not depend on initial conditions , this inconsistency implies that some simulations are not fully converged . when free energy estimates contradict , it is not completely clear which result is most consistent with the force field . false convergence is quantified based on the minimum value , using @xmath30 $ ] . a system is considered to be falsely converged when @xmath31 $ ] is less than 5 @xmath29 but @xmath32 $ ] is greater than 15 @xmath29 . based on this definition , false convergence occurs in a nontrivial fraction of systems ( table [ tab : nconverged ] ) . ultimately , poor convergence and false convergence are caused by incomplete sampling . the most straightforward explanation for incomplete sampling is that a simulation starts and remains trapped in a local minimum distinct from the global minimum energy . indeed , between milestones c&d , most falsely converged calculations starting from the crystal structure ( 4/5 ) and docked poses ( 7/11 ) have no starting pose within 1.0 of the lowest - energy observed pose . however , sampling the lowest - energy structure is not a sufficient condition for complete sampling , as other poses may have a lower _ free energy_. for simulations starting from the lowest - energy observed pose , four systems appear falsely converged between milestones c&d ( formatted by pdb identifier ( @xmath31 , \sigma[f , f_{min}]$ ] ) with @xmath33 in units of @xmath29 ) : 1hww ( 0.353 , 16.1 ) , 1r1h ( 3.95 , 15.3 ) , 1hp0 ( 0.496 , 16.7 ) , 1gm8 ( 0.422 , 15.6 ) . for 1hww ( figure [ fig : dock_last](c ) and ( d ) ) and 1gm8 ( figure [ fig : dock_last](g ) and ( h ) ) , starting from the crystallographic pose leads to a lower estimate of @xmath34 than the lowest - energy pose . for 1hp0 ( figure [ fig : dock_last](e ) and ( f ) ) , a docked pose has the lowest estimated @xmath34 . 1r1h does not appear to sample different poses ; the large @xmath32 $ ] is the result of an outlier with a significantly lower @xmath34 estimate than average . |
a discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined . one of the central problems is the criteria used to judge what variation of the parameters describing a set of partons is acceptable within the context of a global fit . various ways of addressing this question are outlined . | i | hep-ph0205233 | a discussion is presented of the manner in which uncertainties in parton distributions and related quantities are determined . one of the central problems is the criteria used to judge what variation of the parameters describing a set of partons is acceptable within the context of a global fit . various ways of addressing this question are outlined . | the procedure of determining parton distributions by so - called global fits to data , mainly structure functions , is long established @xcite-@xcite . however , it is a rather more recent development to try to determine the errors on these distributions at the same time . this has come about for a number of reasons . firstly , the sheer amount of data ( full references in @xcite ) sensitive to various parton distributions , and the precision of this data , has become such that an accurate determination of all parton distributions is possible ( with some problems only in difficult to reach regions of phase space , e.g. @xmath0 very near to 1 ) . secondly , the understanding of the experimental errors on this data has reached a new level of sophistication , with the systematic errors being understood far better in terms of their separate sources and correlations . lastly , the theoretical understanding at nlo in @xmath1 has improved so that subtleties due to e.g. heavy quarks are now understood . there are many issues in the determination of errors on parton distributions , and a discussion of these may be found in @xcite . however , one of the main outstanding problems , and the focus of a discussion session at this meeting , is the manner in which one determines precisely the size of the errors . |
stochastic dynamics , within the markovian regime and ohmic friction , some standard quantum thermodynamics functions such as the energy average and heat capacity can be extracted . in particular , special emphasis is put on the so - called quantum stochastic resonance which is a cooperative effect of friction , noise and periodic driving occurring in a bistable system . | c | 1604.03712 | a langevin canonical framework for a chiral two - level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well - known spin - boson model . from this stochastic dynamics , within the markovian regime and ohmic friction , some standard quantum thermodynamics functions such as the energy average and heat capacity can be extracted . in particular , special emphasis is put on the so - called quantum stochastic resonance which is a cooperative effect of friction , noise and periodic driving occurring in a bistable system . | in previous works , we have succesfully applied a langevin canonical formalism to the stochastic dynamics of a non - isolated chiral tls when reproducing some quantum thermodynamic functions ( such as , the partition function and heat capacity ) . in this paper , as a continuation and extension of our work , we have tackled the dynamics of the qsr . this resonance is considered as a well known cooperative effect of friction , noise and periodic driving occurring in a bistable system . under the presence of the driving field , the heat capacity has also been analyzed at asymptotic times . we have assumed so far that the tunneling rate is a constant value . obviously , this rate could be considered to also be a function of time . this should have important implications in the detection of qsr in chiral molecular systems . due to the fact that this stochastic dynamics is occurring at ultracold regimes , a sort of bose - einstein condensation could take place . moreover , at this regime , the noise is usually colored with a complex time autocorrelation function . all of these ingredients should be incorporated to such a dynamics in order to improve the description of nonisolated chiral tls . work in this direction is now in progress . leggett , a.j . ; chakravarty , s. ; dorsey , a.t . ; fisher , m. p.a . ; garg , a. ; zwerger w. dynamics of the dissipative two - state system . _ rev . phys . _ * 1987 * , _ 59 _ , 1 - 85 ; _ ibid . _ erratum * 1995 * , _ 67 _ , 725 . guijarro , a. , yus , m. _ the origin of chirality in the molecules of life _ , rsc publishing , cambridge , 2009 . bargueo , p. ; de tudela , r. p. constraining long - range parity violation in gravitation using high resolution spectroscopy of chiral molecules . d _ * 2008 * , _ 78 _ , 1002004 - 1,5 . bargueo , p. ; peate rodrguez , h.c . ; gonzalo , i. ; sols f. ; miret artes , s. friction - induced enhancement in the optical activity of interacting chiral molecules . lett . _ * 2011 * , _ 516 _ , 29 - 34 . dorta urra , a. ; peate rodrguez , h.c . ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. dissipative geometric phase and decoherence in parity - violating chiral molecules . _ j. chem . phys . _ * 2012 * , _ 136 _ , 174505 . rodrguez , h.c . ; dorta urra , a. ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. a langevin canonical approach to the dynamics of chiral systems : populations and coherences . _ chirality _ * 2013 * , _ 25 _ , 514 - 520 . rodrguez , h.c . ; dorta urra , a. ; bargueo , p. ; rojas lorenzo , g. ; miret artes , s. a langevin canonical approach to the dynamics of chiral systems : thermal averages and heat capacity . _ chirality _ * 2014 * , _ 26 _ , 319 - 325 . cahn , s.b . ; ammon , j. ; kirilov , e. ; gurevich , y.v . ; murphree , d. ; paolino , r. ; rahmlow , d.a . ; kozlov , m.g . ; demille d. zeeman - tuned rotational level - crossing spectroscopy in a diatomic free radical . * 2014 * , _ 112 _ , 163002 . bargueo , p. ; prez de tudela , r. ; miret arts , s. ; gonzalo , i. an alternative route to detect parity violating energy differences through bose - einstein condensation of chiral molecules . phys . _ * 2011 * , _ 13 _ , 806 - 810 . |
a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . rev . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot . | i | 0810.5642 | a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . the dmc results compare well with an analytic expression derived by one of us [ phys . rev . b * 78 * , 035111 ( 2008 ) ] for the total energy to within @xmath0 over an order of magnitude range of density , which increases with valley degeneracy . for @xmath1 ( six - fold valley degeneracy ) the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot . | good quantum numbers , that describe conserved quantities as a quantum system evolves , derive their significance from their connection to the powerful conservation laws of physics . in addition to the familiar examples of spin and crystal momentum , under some circumstances electrons in solids can have an additional quantum number that distinguishes them , which we call the _ flavor _ ; we denote the total number of flavors by @xmath5 . one example of such a system are semiconductors and semimetals that have degenerate conduction - band valleys , the flavor denotes the electron s valley . examples of multi - valley semiconductors include ge , which as shown in fig . [ fig : gebandstructure ] has four degenerate valleys ( n.b . not eight , as valleys at the brillouin zone vertices overlap ) , si has six degenerate valleys , a ge - si alloy has ten degenerate valleys , and @xmath6 has twelve valleys in the @xmath7 band @xcite . the system has been experimentally realized as an electron - hole liquid that forms in drops @xcite . in these systems the number of flavors ( the number of valleys ) is well defined and there are strong coulomb interactions between particles which motivates the analysis . this is in contrast to several other systems in which the number of flavors is poorly defined such as heavy fermions @xcite , charged domain walls @xcite , a super - strong magnetic field @xcite , and spin instabilities @xcite ; or where the number of flavors is well defined but interactions between particles are weak such as ultracold atoms in optical lattices @xcite . the properties of a many - flavor electron gas ( mfeg ) in a semiconductor were first studied analytically for the normal phase by @xcite , and for the superconducting phase by @xcite . recently one of us @xcite extended the mfeg analysis by finding an energy functional and gradient expansion , which allowed the study of inhomogeneous systems . however , the analytical treatment was limited to consider the same contributions to the energy as in the random phase approximation ( these contributions dominate in the many - flavor limit ) . to go further requires numerical calculations , the only example of which for a mfeg to date @xcite used a self - consistent approach for the local field correction formulated by @xcite ( stls ) , see also ref . the method was later applied to charge impurities by @xcite . the calculations of ref . @xcite were performed for @xmath8 , too few flavors to gauge the applicability of the analytic many - flavor approximation , which is estimated to apply at around six or more flavors @xcite . $ ] direction calculated using a plane - wave pseudopotential method @xcite . the fermi energy is at @xmath9 ; below are valence bands with the holes centered around h , above are conduction bands . the first conduction band valley is highlighted in bold , low - lying conduction - band electrons are centered around c. ] in this paper we follow the suggestion of @xcite , and present the results of what are expected to be more accurate diffusion monte carlo ( dmc ) @xcite calculations on the mfeg for @xmath10 , which should allow us to verify the analytical mfeg approach . we then examine aspects of the many - flavor approximation that have not yet been studied computationally : in sec . [ sec : casinoelectrongasdensityresponse ] we compare the analytical density - density response function derived in sec . [ sec : analyticalpolarisability ] with that predicted using dmc . once verified this allows us in sec . [ sec : quantumdotsqmc ] to employ a gradient expansion within density - functional theory ( dft ) to find the ground state of a quantum dot , we compare results with dmc calculations and examine the validity of the gradient expansion . we adopt the atomic system of units : that is @xmath11 . the mass @xmath12 is defined to be the electron mass , @xmath13 , multiplied by a dimensionless effective mass @xmath14 appropriate for the conduction - band valleys , which when @xmath15 will recover standard atomic units . we assume the valleys all have the same dispersion profile and so the same effective mass , @xcite outlined a method of calculating a scalar effective mass for anisotropic valleys . with the above definitions , energy is given in terms of an exciton @xmath16 , where @xmath17 is the hartree energy , and length @xmath18 in terms of the bohr radius @xmath19 . to denote density we use both the number density of conduction - band electrons @xmath20 and the wigner - seitz radius @xmath21 . before presenting the numerical results , to orient the discussion , we describe the basic physics of the mfeg and review the analytical results of ref . @xcite that will be computationally verified in this paper . in a low temperature mfeg , the number of flavors @xmath5 , number density of conduction - band electrons @xmath20 , and fermi momentum @xmath22 are related through @xmath23 at fixed electron density , the fermi momentum reduces with increasing number of flavors as @xmath24 , so each fermi surface encloses fewer states . the semiconductor hole band - structure often has a single valence - band minimum at the @xmath25 point , such as in ge , see fig . [ fig : gebandstructure ] , hence we assume the holes are heavy and are uniformly distributed , providing a jellium background . for a constant number density of particles , the density of states at the fermi surface , @xmath26 , rises with increasing number of flavors as @xmath27 . therefore , the screening length estimated with the thomas - fermi approximation @xcite is @xmath28 , and the ratio of the screening to fermi momentum length - scale varies with number of flavors as @xmath29 . in the many - flavor limit @xmath30 , the screening length is much smaller than the inverse fermi momentum , @xmath31 , and so the dominant electron - electron interactions have characteristic wave vectors which obey @xmath32 . this is in direct contrast to the random phase approximation ( rpa ) where @xmath33 , although in both the many - flavor and the rpa , the same green function contributions with empty electron loops dominate diagrammatically @xcite . these diagrams contain the greatest number of different flavors of electrons , and as @xmath30 therefore have the largest matrix element . since @xmath32 , the typical length - scales of the mfeg are short , this indicates that a local density approximation ( lda ) could be applied . this motivation is in addition to the usual reasons for the success of the lda in dft @xcite , namely that the lda exchange - correlation hole need only provide a good approximation for the spherical average of the exchange - correlation hole and obey the sum rule @xcite . in the many - flavor limit the exact result for the polarizability of a mfeg at wave vector @xmath34 , and matsubara frequency @xmath35 is @xcite @xmath36{\ , , } \end{aligned}\ ] ] which in the many - flavor limit is approximately @xmath37 this quantity governs the density - density response of the mfeg so is important to verify . since eqn . has a simple form it can be used to calculate further properties of the mfeg @xcite , such as homogeneous energy in sec . [ sec : analyticaluniformenergy ] and the gradient expansion in sec . [ sec : analyticalgradient ] , which further motivates its numerical verification . starting from the approximate expression for polarizability , eqn . , it can be shown that the total energy of a mfeg , including all the exchange and correlation contributions is @xcite @xmath38 where @xmath39 and @xmath40 denotes the interacting energy ( which would be zero if electron - electron interactions were ignored ) . in ref . @xcite it was suggested that this relation for the total energy applies over a density range , at @xmath41 accuracy , @xmath42 , which widens with number of flavors as @xmath43 ( see also ref . @xcite ) . considering the number of flavors where the range of validity vanishes indicates that the many - flavor limit will apply if there are ten or more flavors . an alternative estimate for the density range is found in sec . [ sec : groundstateenergyvariation ] by comparing the analytical result with dmc calculations . the applicability of the lda in a mfeg motivates the search for a gradient expansion to the energy eqn . as a way to analyze inhomogeneous systems such as electron - hole drops and quantum dots . the typical momentum transfer in the mfeg is @xmath44 , which defines the shortest length - scale over which a lda can be made , therefore , the maximum permissible gradient in electron density is @xmath45 . a gradient expansion will break down for phenomena with short length - scales , for example mass enhancement @xcite . if electron density is smoothly varying then starting from eqn . , the gradient correction to the energy for a mfeg is @xcite @xmath46 where @xmath47 is the energy of a homogeneous mfeg with density @xmath20 , see eqn . . as discussed in sec . [ sec : analyticalresults ] , this gradient expansion would be useful for dft calculations and so its computational verification is important . |
the dmc results compare well with an analytic expression derived by one of us [ phys . the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 . | c | 0810.5642 | a many - flavor electron gas ( mfeg ) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion monte carlo ( dmc ) calculations . the dmc results compare well with an analytic expression derived by one of us [ phys . rev . b * 78 * , 035111 ( 2008 ) ] for the total energy to within @xmath0 over an order of magnitude range of density , which increases with valley degeneracy . for @xmath1 ( six - fold valley degeneracy ) the applicable charge carrier densities are between @xmath2 and @xmath3 . dmc calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate mfeg polarizability for wave numbers @xmath4 . the analytical result for the mfeg is generalized to inhomogeneous systems by means of a gradient correction , the validity range of this approach is obtained . employed within a density - functional theory calculation this approximation compares well with dmc results for a quantum dot . | we have computationally verified the theory of the mfeg presented in @xcite using qmc simulations . in a homogeneous system , dmc estimates for the ground state energy are consistent with theory and the theoretically estimated density range over which the theory applies is consistent with numerical results . the applicable density for @xmath1 @xmath147 corresponds to a charge carrier density between @xmath2 and @xmath3 . the density response function for a mfeg with 24 flavors was found using three methods : density modulation predicted by vmc , and the variation in ground state energy predicted by vmc and also by dmc . the two vmc results underestimated the response @xmath148 , but the dmc results agreed with theory and could distinguish between the exact and a useful approximate expression for polarizability . we used a many - flavor functional including a local gradient approximation in dft calculations of large quantum dots . the dft calculation estimated the ground - state energy and wave function , which were verified by a dmc calculation . we found the high gradient breakdown of the expansion was at @xmath149 , the low gradient breakdown was consistent with the homogeneous mfeg lowest applicable density , and that the gradient expansion was applicable in the intermediate regime . the many - flavor functional , used as part of dft calculations , could be a useful tool for analyzing other multi - valley semiconductor systems . g.j.c . acknowledges the financial support of an epsrc studentship , p.d.h . was supported by a royal society university research fellowship . we thank n.d.m . hine for providing the dotdft code , p. lpez ros and n.d . drummond for help modifying and running casino , r. needs for providing computing time , and a.j . morris for careful reading of the manuscript . |
a monte carlo - maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model is presented . we show that the optical conductivity displays the anomalies found in the cuprate superconductors , including a drude width which grows linearly with temperature , a drude weight which grows linearly with doping , and a temperature and doping - dependent mid - ir peak . these anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the fermi energy as @xmath0 , and are a generic property of the strongly correlated hubbard model in all dimensions greater than one . | c | cond-mat9412084 | a monte carlo - maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model is presented . we show that the optical conductivity displays the anomalies found in the cuprate superconductors , including a drude width which grows linearly with temperature , a drude weight which grows linearly with doping , and a temperature and doping - dependent mid - ir peak . these anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the fermi energy as @xmath0 , and are a generic property of the strongly correlated hubbard model in all dimensions greater than one . | a quantum monte carlo and maximum entropy calculation of the optical conductivity of the infinite - dimensional hubbard model has been presented . the mott - insulating character of the ground state at half filling drives many anomalous behaviors in the normal state near half filling that are similar to those observed in the cuprate superconductors . in particular the system is always a fermi liquid away from half filling , but the fermi temperature vanishes , and the quasiparticle renormalization factor diverges as half filling is approached . as a result , the free carriers in the system initially have a hole - like character ( that changes to an electron - like character at approximately quarter filling ) . the drude width for these carriers grows linearly with temperature for temperatures above @xmath31 , the drude weight grows linearly with doping , and there is a doping and temperature dependent mid - ir peak . these anomalies arise naturally from the presence of a strongly temperature - dependent quasiparticle peak , whose origin is a kondo - like screening of the magnetic moments , and which appears to occur in the hubbard model for all dimensions greater than 1 . the anomalous features in the experimentally measured optical conductivity for the cuprates are usually attributed to either polarons or impurities . however , any purely polaronic theory has difficulty in explaining the magnetic insulating character of the ground state at half filling . the hubbard model naturally describes such an insulating state , and appears to also describe many of the anomalous features present in the experimental data . in light of this fact , it is worthwhile to try to incorporate both the effects of strong electron correlation , and the electron - phonon interaction into a comprehensive theory for the normal state of the cuprate materials . work along these lines is in progress . we would like to acknowledge useful conversations with w. chung , j. keller , y. kim , d. scalapino , r. scalettar , d. tanner , and g. thomas . this work was supported by the national science foundation grant number dmr-9107563 , the nato collaborative research grant number crg 931429 and through the nsf nyi program . in addition , we would like to thank the ohio supercomputing center , and the physics department of the ohio state university for providing computer facilities . j.g . bednorz and k.a . mller , z. phys . * 64 * , 189 ( 1986 ) . for reviews of relevant experiments see c. h. pennington and c. p. slichter , in _ physical properties of high temperature superconductors _ edited by d. m. ginsberg vol.2 ; 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a new nonconforming rectangle element with cubic convergence for the energy norm is introduced . the degrees of freedom ( dofs ) are defined by the twelve values at the three gauss points on each of the four edges . due to the existence of one linear relation among the above dofs , it turns out the dofs are eleven . the nonconforming element consists of @xmath0 . we count the corresponding dimension for dirichlet and neumann boundary value problems of second - order elliptic problems . we also present the optimal error estimates in both broken energy and @xmath1 norms . finally , numerical examples match our theoretical results very well . + * keywords : * nonconforming finite element ; optimal error estimates ; quadrilateral mesh | i | 1301.6862 | a new nonconforming rectangle element with cubic convergence for the energy norm is introduced . the degrees of freedom ( dofs ) are defined by the twelve values at the three gauss points on each of the four edges . due to the existence of one linear relation among the above dofs , it turns out the dofs are eleven . the nonconforming element consists of @xmath0 . we count the corresponding dimension for dirichlet and neumann boundary value problems of second - order elliptic problems . we also present the optimal error estimates in both broken energy and @xmath1 norms . finally , numerical examples match our theoretical results very well . + * keywords : * nonconforming finite element ; optimal error estimates ; quadrilateral mesh | it has been well known that the standard lowest order conforming elements can produce numerical locking and checker - board solutions in the approximation of solid and fluid mechanics problems : see for instance @xcite and the references therein . an efficient approach to deal with this case is to employ the nonconforming element method , which has made a great impact on the development of finite element methods @xcite . to approximate pdes using a nonconforming element of order @xmath2 , one needs to impose the continuity of the moments up to order @xmath3 of the functions across all the interfaces of neighboring elements . this condition is known as the patch test @xcite . in two dimensions , the patch test is equivalent to the continuity at the @xmath2 gauss points located on each interface . this implies that a @xmath4-nonconforming element , if exists , must be continuous at the @xmath2 gauss points on each edge . these points ( completed with internal points for @xmath5 ) can be used to define local lagrange degrees of freedom ( dofs ) on the simplex if @xmath2 is odd , but this construction is not possible if @xmath2 is even since there exists a lower - degree polynomial vanishing at all the gauss points @xcite . thus suitable bubble functions are often employed to enrich the finite element space . until now , the triangular nonconforming elements are well studied in the literature ( see , @xcite ) , but the analysis of their quadrilateral counterparts is less complete . even though the triangular or tetrahedral meshes are popular to use , in some cases where the geometry of the problem has a quadrilateral nature , one wishes to use quadrilateral or hexahedral meshes with proper elements . for even @xmath2 , the same trouble exists , that is , there also exists a lower - degree polynomial vanishing at all the gauss points . again , some bubble functions are added to the finite element space @xcite . compared to the triangular case , another trouble for quadrilateral finite element is that the dofs and corresponding polynomial space do not match . usually the number of dofs is bigger than the dimension of @xmath4 . for example , for @xmath6 and @xmath7 , the numbers of dofs are @xmath8 and @xmath9 , respectively , while the corresponding dimensions of @xmath4 are @xmath10 and @xmath11 , respectively . therefore , some additional relations must be imposed or some special functions are added to the finite element space such that unisolvency can be satisfied , see @xcite . the purpose of this paper is to develop a @xmath12-nonconforming element on rectangular meshes . we define the 12 gauss points ( 3 gauss points on every edge ) as the dofs . to obtain an optimal order error estimate , the finite element space must be carefully chosen such that any function in this space is a polynomial of degree no greater than 3 on every edge . meanwhile , we also notice that the values on the 12 gauss points satisfy a linear relation if the degree of a polynomial on every edge is no more 3 , which is a little different from the triangular mesh case . thus we define our finite element space as @xmath13 . therefore , the number of dofs is locally 11 . we prove unisolvency and define three types of local and global bases , one of which is defined associated with vertices and the other two of which are defined associated with edges . then we derive optimal error estimates for second - order elliptic problems in broken energy- and @xmath14-norms . finally , numerical examples are provided , which match our theoretical result very well . this paper is organized as follows . in section 2 the @xmath12 nonconforming element is defined on rectangular meshes . the dimensions and basis functions for dirichlet and neumann problems are given . in section 3 interpolation operators are defined and optimal order error estimates are shown . in section 4 , numerical results for the elliptic problems are presented . |
a polynomial invariant of virtual links , arising from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur , is defined and its properties are investigated . examples are given that the invariant can detect chirality and even non - invertibility of virtual knots and links . + _ keywords : _ virtual knot theory , conway skein relation , alexander invariants + _ ams classification : _ 57m25 * on alexander - conway polynomials + for virtual knots and links * + jrg sawollek + december 21 , 1999 ( revised : january 3 , 2001 ) | i | math9912173 | a polynomial invariant of virtual links , arising from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur , is defined and its properties are investigated . examples are given that the invariant can detect chirality and even non - invertibility of virtual knots and links . furthermore , it is shown that the polynomial satisfies a conway - type skein relation in contrast to the alexander polynomial derived from the virtual link group . + _ keywords : _ virtual knot theory , conway skein relation , alexander invariants + _ ams classification : _ 57m25 * on alexander - conway polynomials + for virtual knots and links * + jrg sawollek + december 21 , 1999 ( revised : january 3 , 2001 ) | in @xcite kauffman defines an extension of classical knot diagrams to virtual knot diagrams , motivated by gauss codes on the one hand and knots in thickened surfaces on the other hand . several classical knot invariants can be generalized to the virtual theory without much effort , e.g. , the knot group and derived invariants such as the alexander polynomial , the bracket and jones polynomials , and vassiliev invariants ( which can be introduced in different ways , see @xcite and @xcite ) . the present paper deals with a polynomial invariant that is derived from an invariant of links in thickened surfaces introduced by jaeger , kauffman , and saleur in @xcite . the determinant formulation of the polynomial immediately generalizes to virtual link diagrams . it is a laurent polynomial in two variables with integral coefficients that vanishes on the class of classical link diagrams but gives non - trivial information for diagrams that represent non - classical virtual links . especially , examples can be given that the invariant is sensitive with respect to changes of orientation of a virtual knot . furthermore , the polynomial fulfills a conway - type skein relation in one variable and thus it is denoted by the term conway polynomial . in the same way as in the classical case , the one - variable alexander polynomial of a virtual link can be derived from the virtual link group , but the skein - relation for ( a normalized version of ) the classical alexander polynomial can not be extended to the class of virtual links . therefore , this alexander polynomial is different from the conway polynomial mentioned above in a non - trivial way in contrast to the classical case ( and certain generalizations to links 3-manifolds , see for example @xcite , theorem 5.2.11 ) . this paper is organized as follows . after , in section [ virtknots ] , a short introduction into the field has been given , the determinant formulation of the conway polynomial for virtual links is described in section [ invariant ] . some properties of the polynomial are deduced , especially , that the invariant fulfills a conway - type skein relation , and several example calculations are given . then , in section [ alex ] , the alexander invariants derived from the link group , namely , alexander matrix , alexander ideal , and alexander polynomial , are defined and it is shown that the alexander polynomial does not fulfill any linear skein relation . finally , in section [ conrem ] , general problems in extending certain invariants of classical links to the virtual category are described and the direction of further investigations is indicated . |
the number of terms which should be taken into account is weakly dependent on @xmath0 and remains @xmath2 even if @xmath3 . the elaborated method makes canonical calculations to be not more complicated than the grand canonical ones and is free from any limitations on @xmath0 and @xmath4 . , canonical vs grand canonical calculations , mesoscopic systems . | i | cond-mat0404299 | a practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of @xmath0 independent electrons . drastic simplification of calculations is attained by means of proper ordering excited states of the system . in consequence the exact canonical partition function can be represented as a series in which the first term corresponds to the ground state whereas successive groups of terms belong to many particle - hole excitations ( one particle - hole two particle - hole and so on ) . at small temperatures ( @xmath1 inter - level spacings near the fermi level ) the number of terms which should be taken into account is weakly dependent on @xmath0 and remains @xmath2 even if @xmath3 . the elaborated method makes canonical calculations to be not more complicated than the grand canonical ones and is free from any limitations on @xmath0 and @xmath4 . , canonical vs grand canonical calculations , mesoscopic systems . 05.30.fk , 02.10.ox | the characteristic feature of the modern stage in studying mesoscopic systems is a possibility to fix individual properties of investigated objects such as chemical composition , size geometric shape and particle number . the well known example of such investigations is the discovery of electronic shells in alkali metal clusters @xcite . the other branch of researches is connected with recent advances in the development of new techniques for fabricating two- or three - dimensional micro- and nano - structures that enables current experiments to investigate variations of both the exact number of electrons on such mesoscopic structures and their geometrical shapes with a precise control in all dimensions . frequently experiments are produced so that investigated systems may exchange energy with surroundings ( they are embedded in heat reservoir ) , i.e. they are kept at an invariable temperature , however the exchange by particle is absent . thus , such systems constitute a canonical ensemble , and the most appropriate theoretical method for their statistical description is the canonical formalism . the papers of denton , mhlschlegel and scalapino @xcite were the first where the canonical description was developed in applying to electrons in small metallic grains . at that time it was impossible to fix the shape and particle number of each grain . therefore for constructing the canonical partition function denton et al made the simplest assumption that the energy spectrum of free electrons in a metallic grain is equidistant ( the equal level spacing model ) and two - fold degenerated if there is no magnetic field . using reasonable approximations ( @xmath5 , @xmath6 is number of single electron levels ) denton et al established an analytical expression for the canonical partition function . they showed that the main differences between the canonical and grand canonical values of the heat capacity ( @xmath7 ) and magnetic susceptibility ( @xmath8 ) lie at small temperatures @xmath9 ( @xmath10 is the mean level spacing ) . besides they found that at @xmath11 the grand canonical heat capacity exceeds the canonical one by @xmath12 ( @xmath13 is the boltzmann constant ) . the partition function of denton et al takes into account energy variations in an applied uniform magnetic field . they manifest themselves in oscillations of @xmath8 and @xmath7 with growth of the field . such oscillations are typical for charged particle systems @xcite however the strong periodicity in the oscillations is a feature of the equal level spacing . it is worthwhile emphasizing the @xmath0-independence of thermodynamic quantities as functions of @xmath14 in the canonical calculations of denton et al at @xmath15 , @xmath16 . it is caused by a relatively narrow layer of single particle levels near the fermi energy , which mainly contributes to the partition function , and by the identical for any @xmath0 structure of the single - particle energy spectrum in this layer . the canonical formalism was also used by brack , genzken and hansen @xcite for calculations of thermal properties of the valence electrons in alkali metal clusters . in this case free electron energy spectra contain considerable gaps that accounts for enhanced stability of clusters with the magic numbers of atoms . brack et al showed that the shell structure reveals itself in the theoretical heat capacity . however , the difference between the canonical and grand canonical shell effects is quite noticeable only at temperatures which are less than or of the same order as the mean level spacing @xmath17 near the fermi . thus , both investigations , @xcite , point out the region of the temperatures , @xmath18 , where the comparison of the canonical and grand canonical calculations is of the most interest . besides , in the center of attention should be magic electron numbers ( if they appear in the system ) since the existence of such @xmath0 is a consequence of the appearance of an energy gap near the fermi level that enhances the difference between canonical and grand canonical results . it is well known that @xmath18 is the best regime for observing size effects in mesoscopic systems @xcite . therefore the canonical approach at these temperatures can give more precise theoretical information than the grand canonical calculations . in order to calculate the partition function @xmath19 , occupation numbers , internal energy and other thermodynamic quantities brack et al used recurrence relations connecting @xmath19 with those for smaller @xmath0 and @xmath6 . following this procedure they found that @xmath20 calculation steps were needed to obtain the final result , i.e. for @xmath21 ( @xmath22 ) . such method is still manageable for @xmath0 up to a few hundreds , however it could be hardly applied to @xmath0 and @xmath23 . thus the constructing of the effectively working canonical formalism without restrictions on the particle number and applicable to arbitrary spacing distributions is a problem that has to be solved . parallel with the exact canonical calculations in ref . @xcite approximate methods have been suggested for constructing the canonical partition function of the normal ( nonsuperconducting ) systems . one of them ref . @xcite replaces the projection integral over the gauge variable @xmath24 ( @xmath25 ) by the discrete sum that involves @xmath26 terms . these terms depend on @xmath27 ( instead of @xmath24 ) where the integer @xmath28 varies from @xmath29 to @xmath30 . as shown in sec.1 this method can be viewed as the partial projection . it is the more precise the higher is the value of @xmath26 . in ref . @xcite this method was employed by frauendorf and pashkevich to calculate sodium cluster shape and free energies . another method suggested by rossignoli consists in the evaluation of projection integral in the saddle - point approximation . such approach turns out to be quite satisfactory in the case of not very small temperatures and particle numbers as was demonstrated by calculations of nuclear level densities in ref . @xcite . our effective version of the canonical approach is based on the polynomial representation of the partition function . last years such representation is discussed in the literature @xcite , however our practical version of polynomial calculations was elaborated many years ago for a projection method applied to the bardin - cooper - schriffer ( @xmath31 ) function for describing the particle number conserving pairing correlations in nuclei @xcite . there is an obvious analogy between the @xmath31 function and grand canonical partition function for the independent electron model ( @xmath32 ) . both can be represented as products @xmath33 , where @xmath34 for the @xmath31 function is @xmath35 ( @xmath36 , @xmath37 are the bogolubov parameters , @xmath38 is the operator of the fermion pair creation in time conjugated states @xmath39 and @xmath40 ) while for the canonical partition function @xmath34 is @xmath41 , @xmath42 and @xmath43 being the energy of a single -particle state @xmath39 and the chemical potential respectively . after projection onto a fixed particle number @xmath0 both functions gain the form of a @xmath0-th order symmetric polynomial @xmath44 $ ] . this polynomial @xmath44 $ ] consists of @xmath45 terms ( as before @xmath6 is the total amount of employed single - particle states ) and each term in it is the production of @xmath0 different @xmath34 , i.e. @xmath44 $ ] includes all distributions of @xmath0 @xmath31 pairs or @xmath0 electrons over @xmath6 states . for large @xmath6 and @xmath0 the total number of terms in @xmath0 may be enormous , however a hierarchy of terms can be established according to their surviving at @xmath46 ( @xmath47 is the pairing strength ) or @xmath48 . the first term of this hierarchy corresponds to the independent fermion ground state in which all single - particle states are occupied up to @xmath49 . the second group of terms corresponds to simplest excitations : in the @xmath31 theory it is a particle pair @xmath50 above @xmath49 and a hole pair @xmath51 beneath @xmath49 , for free electrons in a cluster it is one particle - hole excitations . the third group of terms corresponds to a shift of two @xmath31 particle pairs or two cluster electrons above @xmath49 . this alignment of many particle - hole excitations continues till all pairs or cluster electrons are lifted above @xmath49 . the common property of the projected @xmath31 and the canonical partition functions is mutual independence of probabilities of particle and hole excitations . this probability depends only on the energy of the single - particle level on which a @xmath31 fermion pair or a cluster electron is located . for the @xmath31 case it is @xmath52 for levels with @xmath53 while for levels with @xmath54 it is @xmath55 , for cluster electrons it is @xmath56 if @xmath57 , or @xmath41 if @xmath54 . thus summing over particle and hole excitations can be performed independently . the contribution of each group of @xmath58-particle excitations to @xmath44 $ ] includes a sum running distributions of @xmath58 electrons ( here we mean cluster electrons ) over particle levels ( with energies above @xmath49 ) . these sums can be also represented as symmetric polynomials , now they are of @xmath58-th order ( @xmath59 ) . analogous polynomials arise for hole excitations , but in this case electrons are distributed over hole levels ( below and including @xmath49 ) . though the convergence of appearing series is absolute its rate is determined by @xmath60 . practically for @xmath61 they include not more than 5 components ( i.e. up to 5 particle-5 hole excitations ) . our calculations for the pairing problem have indicated high effectiveness of the polynomial representation of the @xmath0-projected @xmath31-function @xcite and this paper is devoted to the adaptation of the polynomial representation to the canonical partition function of normal mesoscopic systems . the material is arranged as following . in sec.2 separation of the full configuration space into two parts , inside and outside the fermi sphere , is realized to construct the canonical partition function @xmath62 as a symmetrical polynomial of @xmath0-th order . @xmath62 is expanded in polynomials of lower orders . these series are composed of products of particle `` and ' ' hole polynomials , the order of which points out how many particles and holes take part in excitations allowed for in @xmath62 . in sec.3 these polynomials are employed to one- and two - body density matrices and on this base the canonical expressions for the heat capacity and magnetic susceptibility are compared to the grand canonical ones . sec.4 collects recurrent relations for polynomials we apply in calculations . sec.5 shows that in a wide range of temperatures and particle numbers the elaborated method possesses high convergence and can be used for various types of single - electron energy spectra . the conclusion is given in sec.6 . algebraic details for the equal level spacing model and the exact canonical partition function of the model are considered in appendix . |
charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg | i | 0907.3120 | a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg | quenched disorder is obiquitous in condensed - matter systems , sometimes determining entirely new physical properties and phenomena . for the theoretical explanation of many experimental findings , models of classical and quantum spin systems are employed and - typically - disorder is introduced through a spatial variation of the exchange couplings , of the direction of the axial anisotropies , and of the sign of the couplings . theoretical and experimental studies of model and real physical systems with these kinds of disorder have lead to much new physics . much discussed have been the glassy phases in magnetic @xcite , and superconducting materials @xcite . in superconductors , specially with the advent of high-@xmath0 ceramic superconductors , the role of disorder has become central in the discussion of the physical properties of real materials @xcite . many materials are naturally microstructured and granularity characterises the mesoscopic structures of most systems , leading to a phase diagram often displaying a superconductor - insulator transition at zero temperature due to the charging energy of the grains . as first pointed out by abeles @xcite , when the grain charging energy arising from the charge @xmath1 and capacitance @xmath2 of the grain , @xmath3 ( @xmath4 is the grain diameter and @xmath5 the electronic charge ) is larger than the josephson - coupling energy @xmath6 between nearest neighbors grains , phase coherence is destroyed due to zero - point quantum fluctuations of the local phase of the superconducting order parameter @xcite . granularity can also be realized in a controlled manner in artificially fabricated josephson - junction arrays of coupled superconducting grains @xcite , with a space dimensionality @xmath4 less than @xmath7 . such granular systems can be theoretically modelled by pseudo - spin systems , the spins representing with their states the few relevant quantum charge states of the grains at relatively low temperatures . in such models the pseudo - spin size is the same for all grains corresponding to the assumption that the grain - size distribution is very narrow , or alternatively , of negligible charging - energy disorder . a well known model of this type is the pseudo - spin - one model introduced by de gennes and studied in different works @xcite where only charge states @xmath8 are allowed , corresponding to @xmath9 . however , realistic systems may contain different kinds of disorder , such as a spatial distribution of josephson couplings between grains or / and a distribution of grain sizes , which leads to disorder in the grain electrical capacitances and charging energies . studies of the effects of disorder in the electrical capacitance or charging energy of the grains have appeared recently @xcite . within a mean - field approximation @xcite , charging energy disorder widens the extent of the superconducting phase at the expense of the insulating one . this behavior is consistent with results for the superconductor - insulator transition from quantum monte carlo simulations in two - dimensional models of josephson - junction arrays @xcite with disorder in the diagonal capacitance matrix . earlier calculations for the related boson hubbard model with disorder in the onsite coulomb repulsion @xcite are also consistent with a decrease in the phase coherence threshold and moreover suggest a different universality class from the non - disordered case @xcite . in this work , we consider the effects of charging energy disorder in granular superconducting materials within the pseudo - spin approach . by considering a spatial distribution of the grain sizes , which leads to local charging energy disorder , a quantum pseudo - spin model with random on - site spin sizes can be constructed . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . spin - size disorder models have seldom been considered in the literature . in the context of classical spin models , spin - size disorder can be readily turned into exchange - coupling disorder ; the physics of quantum systems with spin - size disorder , however , appears to have not been investigated in such depths . it has been considered mostly within the one - dimensional systems : dilution of a quantum spin-@xmath10 2-ladder was studied by sigrist and furusaki @xcite whilst the general problem of a quantum spin chain with random @xmath11 as well as random @xmath12 was considered by westerberg _ et . @xcite within a real - space renormalization - group method showing that these systems belong to a different universality class of disordered spin systems . |
a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . | c | 0907.3120 | a quantum pseudo - spin model with random spin sizes is introduced to study the effects of charging - energy disorder on the superconducting transition in granular superconducting materials . charging - energy effects result from the small electrical capacitance of the grains when the coulomb charging energy is comparable to the josephson coupling energy . in the pseudo - spin model , randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory is developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . and granular superconductors , josephson - junction arrays , superconductor - insulator transition 74.81.-g , 74.25.dw , 74.40.+k , 64.70.tg | we have introduced a quantum pseudo - spin model with random spin sizes to model the effects of charging - energy disorder in granular superconducting materials . randomness in the spin size is argued to arise from the inhomogeneous grain - size distribution . for a particular bimodal spin - size distribution , the model describes percolating granular superconductors . a mean - field theory has been developed to obtain the phase diagram as a function of temperature , average charging energy and disorder . the results are qualitatively consistent with previous mean - field calculations in the phase - number representation . the pseudo - spin model should provide a useful framework to study the critical behavior and universality classes in presence of strong charging - energy disorder . |
a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs . | i | 0801.3078 | a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs . we obtain oxygen abundances which are comparable to those found in high metallicity disc hii regions from direct measurements of electron temperatures and consistent with solar values within the errors . the region with the highest oxygen abundance is r3+r4 in ngc 3504 , 12+log(o / h ) = 8.85 , about 1.5 solar if the solar oxygen abundance is set at the value derived by @xcite , 12+log(o / h)@xmath5 = 8.66@xmath60.05 . the derived n / o ratios are in average larger than those found in high metallicity disc hii regions and they do not seem to follow the trend of n / o vs o / h which marks the secondary behaviour of nitrogen . on the other hand , the s / o ratios span a very narrow range between 0.6 and 0.8 of the solar value . as compared to high metallicity disc hii regions , cnsfr show values of the o@xmath7 and the n2 parameters whose distributions are shifted to lower and higher values respectively , hence , even though their derived oxygen and sulphur abundances are similar , higher values would in principle be obtained for the cnsfr if pure empirical methods were used to estimate abundances . cnsfr also show lower ionisation parameters than their disc counterparts , as derived from the [ sii]/[siii ] . their ionisation structure also seems to be different with cnsfr showing radiation field properties more similar to hii galaxies than to disc high metallicity hii regions . | the inner ( @xmath8 1kpc ) parts of some spiral galaxies show star formation complexes frequently arranged in an annular pattern around their nuclei . these complexes are sometimes called `` hot spots '' and we will refer to these as circumnuclear starforming regions ( cnsfrs ) . their sizes go from a few tens to a few hundreds of pc ( e.g. * ? ? ? * ) and they seem to be made of an ensamble of hii regions ionised by luminous compact stellar clusters whose sizes , as measured from high spatial resolution hst images , are seen to be of only a few pc . the luminosities of cnsfrs are rather large with absolute visual magnitudes ( m@xmath9 ) between -12 and -17 and h@xmath10 luminosities which are comparable to those shown by 30 dor , the largest hii region in the lmc , and overlap with those shown by hii galaxies ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . in the ultraviolet ( uv ) , massive stars dominate the observed circumnuclear emission even in the presence of an active nucleus @xcite . in many cases , cnsfr show emission line spectra similar to those of disc hii regions . however , they show a higher continuum from background stellar populations as expected from their circumnuclear location . the analysis of these spectra gives us the oportunity to measure the gas abundances close to galactic nuclei which , in the case of early type spirals , are expected to be amongst the highest metallicity regions . the importance of an accurate determination of the abundances of high metallicity hii regions can not be overestimated since they constitute most of the hii regions in early spiral galaxies ( sa to sbc ) and the inner regions of most late type ones ( sc to sd ) @xcite without which our description of the metallicity distribution in galaxies can not be complete . in particular , the effects of the choice of different calibrations on the derivation of abundance gradients can be very important since any abundance profile fit will be strongly biased towards data points at the ends of the distribution . it should be kept in mind that abundance gradients are widely used to constrain chemical evolution models , histories of star formation over galactic discs or galaxy formation scenarios . also , the question of how high is the highest oxygen abundance in the gaseous phase of galaxies is still standing and extrapolation of known radial abundance gradients would point to cnsfr as the most probable sites for these high metallicities . accurate measures of elemental abundances of high metallicity regions are also crucial to obtain reliable calibrations of empirical abundance estimators , widely used but poorly constrained , whose choice can severely bias results obtained for quantities of the highest relevance for the study of galactic evolution like the luminosity - metallicity ( l - z ) relation for galaxies . |
are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes . | i | 0801.3078 | a study of cicumnuclear star - forming regions ( cnsfrs ) in several early type spirals has been made in order to investigate their main properties : stellar and gas kinematics , dynamical masses , ionising stellar masses , chemical abundances and other properties of the ionised gas . both high resolution ( r@xmath020000 ) and moderate resolution ( r @xmath0 5000 ) have been used . in some cases these regions , about 100 to 150pc in size , are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9pc estimated from hubble space telescope ( hst ) images . stellar and gas velocity dispersions are found to differ by about 20 to 30km / s with the h@xmath1 emission lines being narrower than both the stellar lines and the [ oiii]@xmath25007lines . the twice ionized oxygen , on the other hand , shows velocity dispersions comparable to those shown by stars . we have applied the virial theorem to estimate dynamical masses of the clusters , assuming that systems are gravitationally bounded and spherically symmetric , and using previously measured sizes . the measured values of the stellar velocity dispersions yield dynamical masses of the order of 10@xmath3 to 10@xmath4 solar masses for the whole cnsfrs . we obtain oxygen abundances which are comparable to those found in high metallicity disc hii regions from direct measurements of electron temperatures and consistent with solar values within the errors . the region with the highest oxygen abundance is r3+r4 in ngc 3504 , 12+log(o / h ) = 8.85 , about 1.5 solar if the solar oxygen abundance is set at the value derived by @xcite , 12+log(o / h)@xmath5 = 8.66@xmath60.05 . the derived n / o ratios are in average larger than those found in high metallicity disc hii regions and they do not seem to follow the trend of n / o vs o / h which marks the secondary behaviour of nitrogen . on the other hand , the s / o ratios span a very narrow range between 0.6 and 0.8 of the solar value . as compared to high metallicity disc hii regions , cnsfr show values of the o@xmath7 and the n2 parameters whose distributions are shifted to lower and higher values respectively , hence , even though their derived oxygen and sulphur abundances are similar , higher values would in principle be obtained for the cnsfr if pure empirical methods were used to estimate abundances . cnsfr also show lower ionisation parameters than their disc counterparts , as derived from the [ sii]/[siii ] . their ionisation structure also seems to be different with cnsfr showing radiation field properties more similar to hii galaxies than to disc high metallicity hii regions . | gas velocity dispersions were measured by performing gaussian fits to the h@xmath1@xmath24861 and [ oiii ] @xmath2 5007 lines on the high dispersion spectra ( figure [ spectra - kin ] ) . stellar velocity dispersions dispersions were measured using the cat lines at @xmath128494 , 8542 , 8662using the cross - correlation technique described in detail by @xcite . late type giant and supergiant stars that have strong cat absorption lines were used as stellar velocity templates . + for the 5 cnsfr observed in ngc 3351 , stellar velocity dispersions are found to be between 39 and 67kms@xmath11 , about 20kms@xmath11 larger than those measured for the gas , if a single gaussian fit is used . however , the best fits obtained involved two different components for the gas : a broad component " with a velocity dispersion similar to that measured for the stars , and a narrow component " with a dispersion lower than the stellar one by about 30kms@xmath11 . these two components were found both in the hydrogen recombination lines ( balmer and paschen ) and in the [ oiii ] @xmath2 5007 line . the narrow component is dominant in the h recombination lines , while the broad component dominates the [ oiii ] one . figure [ velocities ] shows this effect . cnsfr are seen to consist of several individual star clusters , although some of them seem to have an only knot , at the hst resolution . the derived masses for the individual clusters as derived using the sizes measured on the hst images are between 1.8 and 8.7@xmath1310@xmath14m@xmath15 . these values are between 5.5 and 26 times the mass derived for the ssc a in ngc1569 by @xcite and larger than other kinematically derived ssc masses . values for the dynamical masses of the cnsfrs are in the range between 4.9@xmath1310@xmath14 and 4.3@xmath1310@xmath3m@xmath15 . masses derived from the h@xmath1 velocity dispersion under the assumption of a single component for the gas would have been underestimated by factors between approximately 2 to 4 . the masses of the ionising stellar clusters of the cnsfrs have been derived from their h@xmath10 luminosities under the assumption that the regions are ionisation bound and without taking into account any photon absorption by dust . their values are between 8 - 0@xmath1310@xmath16 and 2.5@xmath1310@xmath14m@xmath15 . therefore , the ratio of the ionising stellar population to the total dynamical mass is between 0.02 and 0.16 . the ssc in the observed cnsfrs seem to contain composite stellar populations . although the youngest one dominates the uv light and is responsible for the gas ionisation , it constitutes only about 10% of the total . this can explain the low equivalent widths of emission lines measured in these regions . this may well apply to the case of other ssc and therefore conclusions drawn from fits of ssp ( single stellar population ) models should be taken with caution ( e.g. * ? ? ? also the composite nature of the cnsfrs means that star formation in the rings is a process that has taken place over time periods much longer than those implied by the properties of the ionised gas . |
accurate measurement of relative distance and orientation of two nearby quantum particles is discussed . thus , unlike in previous studies , we consider the case of an arbitrary relative orientation of the two atoms . for this , we model the atom with complete zeeman manifolds , and include parallel as well as orthogonal dipole - dipole couplings between all states of the two atoms . we find that it is possible to determine the distance of the two atoms independent of the orientation , as long as the particles are sufficiently close to each other . | i | 0909.5608 | accurate measurement of relative distance and orientation of two nearby quantum particles is discussed . we are in particular interested in a realistic description requiring as little prior knowledge about the system as possible . thus , unlike in previous studies , we consider the case of an arbitrary relative orientation of the two atoms . for this , we model the atom with complete zeeman manifolds , and include parallel as well as orthogonal dipole - dipole couplings between all states of the two atoms . we find that it is possible to determine the distance of the two atoms independent of the orientation , as long as the particles are sufficiently close to each other . next , we discuss how in addition the alignment of the atoms can be measured . for this , we focus on the two cases of atoms in a two - dimensional waveguide and of atoms on a surface . | progress in many areas of science and its application is fueled by the ongoing progress to measure and structure small objects . in many cases , light is used as a primary tool for reading or writing . but since light is subject to diffraction , a straightforward implementation is restricted to structures of order of the involved wavelength @xcite . different methods have been invented to surpass this limit , such as near - field imaging @xcite , techniques based on the selective addressing of nearby particles @xcite , resolution enhancement due to non - classical effects @xcite , multiphoton spectroscopy @xcite , quantum lithography with classical fields @xcite , or position - dependent dark states @xcite . among the most fundamental problems in this area is the measurement of the distance between two nearby quantum particles such as atoms . it has been recognized that a precise determination of the interparticle distance is possible down to distances far below the wavelength of the employed light based on their mutual interaction . for small distances , the atoms are coupled by the dipole - dipole interaction , which modifies the optical properties of the system @xcite . this was confirmed in a recent experiment @xcite , and it was found that the resonance fluorescence exhibits characteristic features which enable one to determine the relative distance over a large range of small distances @xcite . the resonance fluorescence has the advantage that it can be observed in the far field , and distance determination via fluorescence is not affected by the usual resolution limitations since the distance information is encoded in the frequency spectrum of the emitted light . similar ideas have also been used for the localization of single particles @xcite . the existing distance measurement techniques based on the dipole - dipole interaction , however , are restricted to two two - level atoms in specific geometries , such as aligned along the propagation direction of the exciting laser field . in most practical cases , however , the relative orientation of the two nearby atoms is unknown , and for similar reasons , it is equally difficult to measure the relative orientation as the distance . thus the question arises , whether the ideas of @xcite can be extended to the case of arbitrary orientation . it turns out that it is not meaningful to study the system of two two - level atoms in the case of arbitrary orientations . the reason for this is the appearance of dipole - dipole couplings between orthogonal transition dipole moments ( ddotdm ) in more general geometries @xcite . the electric field emitted by one of the particles has not only a component corresponding to the emitting transition dipole moment , but also a component along the interparticle distance vector . the projection of the latter field component on a transition dipole moment in the second atom can be non - zero even if it is orthogonal to the emitting dipole @xcite . in a real atom with magnetic level structure , these ddotdm lead to the population of excited states even if they are not driven by the external laser field . thus , the two - level approximation breaks down , and correct predictions can only be expected if the theoretical modelling includes complete zeeman manifolds including all occurring dipole dipole couplings @xcite . motivated by this , here we study the determination of relative distance and orientation of two nearby atoms in arbitrary geometry . the atoms are driven by a single resonant standing - wave laser field , and we make use of the far field resonance fluorescence intensity and spectrum as observables . each atom is modelled as a four - level system with one ground state ( total angular momentum zero ) and three excited states ( total angular momentum one ) , including all relevant dipole - dipole couplings occurring in arbitrary geometries . we start by analyzing the distance determination for the case of a known orientation , and present dressed - state interpretations of the obtained resonance fluorescence spectra in various cases of relevance . next , we describe a method to determine the interparticle distance for arbitrary orientation , which works as long as the particles are sufficiently close to each other . finally , we discuss methods to determine the relative orientation of the two particles , focusing on the two cases of atoms confined in a planar waveguide and atoms on a surface . ( color online ) scheme for the determination of relative distance and orientation of two nearby atoms . the atoms @xmath0 are driven on one transition by a standing wave laser field with rabi frequency @xmath1 and scatter light , which is registered in the far field with a detector . the interatomic distance vector @xmath2 is arbitrary , as shown in the left inset . the right inset shows the level structure of each atom . each atom has a single ground state ( zero angular momentum ) and three excited states ( angular momentum 1 ) . ] |
additive models play an important role in semiparametric statistics . additionally , a concrete example is presented to show that a gaussian function depending only on one variable lies in a reproducing kernel hilbert space generated by an additive gaussian kernel , but does not belong to the reproducing kernel hilbert space generated by the multivariate gaussian kernel of the same variance . * key words and phrases . * additive model , kernel , quantile regression , semiparametric , rate of convergence , support vector machine . | i | 1405.3379 | additive models play an important role in semiparametric statistics . this paper gives learning rates for regularized kernel based methods for additive models . these learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel based quantile regression using the gaussian radial basis function kernel , provided the assumption of an additive model is valid . additionally , a concrete example is presented to show that a gaussian function depending only on one variable lies in a reproducing kernel hilbert space generated by an additive gaussian kernel , but does not belong to the reproducing kernel hilbert space generated by the multivariate gaussian kernel of the same variance . * key words and phrases . * additive model , kernel , quantile regression , semiparametric , rate of convergence , support vector machine . | additive models @xcite provide an important family of models for semiparametric regression or classification . some reasons for the success of additive models are their increased flexibility when compared to linear or generalized linear models and their increased interpretability when compared to fully nonparametric models . it is well - known that good estimators in additive models are in general less prone to the curse of high dimensionality than good estimators in fully nonparametric models . many examples of such estimators belong to the large class of regularized kernel based methods over a reproducing kernel hilbert space @xmath0 , see e.g. @xcite . in the last years many interesting results on learning rates of regularized kernel based models for additive models have been published when the focus is on sparsity and when the classical least squares loss function is used , see e.g. @xcite , @xcite , @xcite , @xcite , @xcite , @xcite and the references therein . of course , the least squares loss function is differentiable and has many nice mathematical properties , but it is only locally lipschitz continuous and therefore regularized kernel based methods based on this loss function typically suffer on bad statistical robustness properties , even if the kernel is bounded . this is in sharp contrast to kernel methods based on a lipschitz continuous loss function and on a bounded loss function , where results on upper bounds for the maxbias bias and on a bounded influence function are known , see e.g. @xcite for the general case and @xcite for additive models . therefore , we will here consider the case of regularized kernel based methods based on a general convex and lipschitz continuous loss function , on a general kernel , and on the classical regularizing term @xmath1 for some @xmath2 which is a smoothness penalty but not a sparsity penalty , see e.g. @xcite . such regularized kernel based methods are now often called support vector machines ( svms ) , although the notation was historically used for such methods based on the special hinge loss function and for special kernels only , we refer to @xcite . in this paper we address the open question , whether an svm with an additive kernel can provide a substantially better learning rate in high dimensions than an svm with a general kernel , say a classical gaussian rbf kernel , if the assumption of an additive model is satisfied . our leading example covers learning rates for quantile regression based on the lipschitz continuous but non - differentiable pinball loss function , which is also called check function in the literature , see e.g. @xcite and @xcite for parametric quantile regression and @xcite , @xcite , and @xcite for kernel based quantile regression . we will not address the question how to check whether the assumption of an additive model is satisfied because this would be a topic of a paper of its own . of course , a practical approach might be to fit both models and compare their risks evaluated for test data . for the same reason we will also not cover sparsity . consistency of support vector machines generated by additive kernels for additive models was considered in @xcite . in this paper we establish learning rates for these algorithms . let us recall the framework with a complete separable metric space @xmath3 as the input space and a closed subset @xmath4 of @xmath5 as the output space . a borel probability measure @xmath6 on @xmath7 is used to model the learning problem and an independent and identically distributed sample @xmath8 is drawn according to @xmath6 for learning . a loss function @xmath9 is used to measure the quality of a prediction function @xmath10 by the local error @xmath11 . _ throughout the paper we assume that @xmath12 is measurable , @xmath13 , convex with respect to the third variable , and uniformly lipschitz continuous satisfying @xmath14 with a finite constant @xmath15 . _ support vector machines ( svms ) considered here are kernel - based regularization schemes in a reproducing kernel hilbert space ( rkhs ) @xmath0 generated by a mercer kernel @xmath16 . with a shifted loss function @xmath17 introduced for dealing even with heavy - tailed distributions as @xmath18 , they take the form @xmath19 where for a general borel measure @xmath20 on @xmath21 , the function @xmath22 is defined by @xmath23 where @xmath24 is a regularization parameter . the idea to shift a loss function has a long history , see e.g. @xcite in the context of m - estimators . it was shown in @xcite that @xmath22 is also a minimizer of the following optimization problem involving the original loss function @xmath12 if a minimizer exists : @xmath25 the additive model we consider consists of the _ input space decomposition _ @xmath26 with each @xmath27 a complete separable metric space and a _ hypothesis space _ @xmath28 where @xmath29 is a set of functions @xmath30 each of which is also identified as a map @xmath31 from @xmath3 to @xmath5 . hence the functions from @xmath32 take the additive form @xmath33 . we mention , that there is strictly speaking a notational problem here , because in the previous formula each quantity @xmath34 is an element of the set @xmath35 which is a subset of the full input space @xmath36 , @xmath37 , whereas in the definition of sample @xmath8 each quantity @xmath38 is an element of the full input space @xmath36 , where @xmath39 . because these notations will only be used in different places and because we do not expect any misunderstandings , we think this notation is easier and more intuitive than specifying these quantities with different symbols . the additive kernel @xmath40 is defined in terms of mercer kernels @xmath41 on @xmath27 as @xmath42 it generates an rkhs @xmath0 which can be written in terms of the rkhs @xmath43 generated by @xmath41 on @xmath27 corresponding to the form ( [ additive ] ) as @xmath44 with norm given by @xmath45 the norm of @xmath46 satisfies @xmath47 to illustrate advantages of additive models , we provide two examples of comparing additive with product kernels . the first example deals with gaussian rbf kernels . all proofs will be given in section [ proofsection ] . [ gaussadd ] let @xmath48 , @xmath49 $ ] and @xmath50 ^ 2.$ ] let @xmath51 and @xmath52.\ ] ] the additive kernel @xmath53 is given by @xmath54 furthermore , the product kernel @xmath55 is the standard gaussian kernel given by @xmath56 define a gaussian function @xmath57 on @xmath58 ^ 2 $ ] depending only on one variable by @xmath59 then @xmath60 but @xmath61 where @xmath62 denotes the rkhs generated by the standard gaussian rbf kernel @xmath63 . the second example is about sobolev kernels . [ sobolvadd ] let @xmath64 , @xmath65 $ ] and @xmath58^s.$ ] let @xmath66 : = \bigl\{u\in l_2([0,1 ] ) ; d^\alpha u \in l_2([0,1 ] ) \mbox{~for~all~}|\alpha|\le 1\bigr\}\ ] ] be the sobolev space consisting of all square integrable univariate functions whose derivative is also square integrable . it is an rkhs with a mercer kernel @xmath67 defined on @xmath68 ^ 2 $ ] . if we take all the mercer kernels @xmath69 to be @xmath67 , then @xmath70 $ ] for each @xmath71 . the additive kernel @xmath72 is also a mercer kernel and defines an rkhs @xmath73\right\}.\ ] ] however , the multivariate sobolev space @xmath74^s)$ ] , consisting of all square integrable functions whose partial derivatives are all square integrable , contains discontinuous functions and is not an rkhs . denote the marginal distribution of @xmath6 on @xmath27 as @xmath75 . under the assumption that @xmath76 for each @xmath71 and that @xmath43 is dense in @xmath29 in the @xmath77-metric , it was proved in @xcite that @xmath78 in probability as long as @xmath79 satisfies @xmath80 and @xmath81 . the rest of the paper has the following structure . section [ ratessection ] contains our main results on learning rates for svms based on additive kernels . learning rates for quantile regression are treated as important special cases . section [ comparisonsection ] contains a comparison of our results with other learning rates published recently . section [ proofsection ] contains all the proofs and some results which can be interesting in their own . |
adopting the framework of the halo occupation distribution ( hod ) , we investigate the ability of galaxy clustering measurements to simultaneously constrain cosmological parameters and galaxy bias . starting with a fiducial cosmological model and galaxy hod , we calculate spatial clustering observables on a range of length and mass scales , dynamical clustering observables that depend on galaxy peculiar velocities , and the galaxy - matter cross - correlation measurable by weak lensing . , the inferred constraints on the galaxy hod provide valuable tests of galaxy formation theory . | i | astro-ph0512071 | adopting the framework of the halo occupation distribution ( hod ) , we investigate the ability of galaxy clustering measurements to simultaneously constrain cosmological parameters and galaxy bias . starting with a fiducial cosmological model and galaxy hod , we calculate spatial clustering observables on a range of length and mass scales , dynamical clustering observables that depend on galaxy peculiar velocities , and the galaxy - matter cross - correlation measurable by weak lensing . we then change one or more cosmological parameters and use @xmath0-minimization to find the galaxy hod that best reproduces the original clustering . our parameterization of the hod incorporates a flexible relation between galaxy occupation numbers and halo mass and allows spatial and velocity bias of galaxies within dark matter halos . despite this flexibility , we find that changes to the hod can not mask substantial changes to the matter density @xmath1 , the matter clustering amplitude @xmath2 , or the shape parameter @xmath3 of the linear matter power spectrum cosmology and bias are not degenerate . with the conservative assumption of 10% fractional errors , the set of observables considered here can provide @xmath4 ( @xmath5 ) constraints on @xmath2 , @xmath1 , and @xmath3 , using galaxy clustering data _ alone_. the combination @xmath6 is constrained to @xmath7 . in combination with traditional methods that focus on large - scale structure in the `` perturbative '' regime , hod modeling can greatly amplify the cosmological power of galaxy redshift surveys by taking advantage of high - precision clustering measurements at small and intermediate scales ( from sub - mpc to @xmath8 ) . at the same time , the inferred constraints on the galaxy hod provide valuable tests of galaxy formation theory . | our analysis shows that hod modeling can substantially increase the cosmological power of galaxy clustering measurements , by breaking degeneracies between the clustering of dark matter and the bias of galaxies with respect to mass . changing the shape or amplitude of the matter power spectrum or the value of @xmath1 alters the mass function , spatial clustering , and velocity statistics of the dark halo population in well - understood ways @xcite . our experiments here , which verify the qualitative arguments of @xcite and @xcite , show that changes to the galaxy hod can not mask these changes in the underlying dark halo population . with our highly flexible parameterization of the hod , the set of observables considered here yields @xmath5 uncertainties of @xmath4 in @xmath2 , @xmath1 , and @xmath3 and @xmath7 uncertainty in the combination @xmath387 with @xmath388 . we expect these forecasts to be conservative , as we have not included observables for which we did not have ready analytic approximations , and our assumption of 10% measurement errors is pessimistic in at least some cases . the physical origin of these cosmological constraints is straightforward to understand for simple changes in @xmath1 , @xmath2 , or @xmath270 , as discussed in [ sec : omegam]-[sec : clnorm ] . the general theme of these discussions is that , for a given cosmological model , the spatial clustering of galaxies largely determines the number of galaxies in halos of a given spatial abundance . dynamically sensitive statistics then reveal the halo mass scale , which depends on @xmath2 and @xmath1 . we allow an arbitrary bias @xmath95 between the galaxy and dark matter velocity dispersions within halos , but this freedom does not eliminate the constraining power of dynamical observables because the space velocities of the halos themselves do not change . the main parameter degeneracy is approximately @xmath389 because fixing this combination roughly fixes the halo velocity scale and the abundance of halos at the mass scale of rich galaxy groups . however , the changing shape of the mass function , the differing sensitivities of different velocity measures , and the different @xmath390 dependence of galaxy - galaxy lensing all serve to break this degeneracy . figures [ fig : chgerr ] and [ fig : matrix ] demonstrate that the cosmological constraints emerge from the full web of clustering observables and are not dominated by one or two statistics on their own . constraints on the galaxy hod will themselves provide valuable tests of galaxy formation models . the cutoff regime of @xmath97 is difficult to pin down with the clustering statistics considered here , but for a known cosmological model the relation between average satellite number and halo mass is well determined , and the satellite distribution width @xmath112 , concentration @xmath118 , and velocity bias @xmath95 are measured to @xmath4 , 30% , and 3% , respectively ( fig . [ fig : mcmc_hodpar ] ) . all of these quantities depend in detail on the physics that governs the evolution of satellites in larger halos ( see , e.g. , @xcite ) , while the relative mass of halos that host central and satellite galaxies depends on the efficiency with which halos feed baryonic mass to their central objects ( see , e.g , discussions by @xcite ) . these galaxy formation constraints will be especially powerful when derived as a function of luminosity , stellar mass , or other observables . the two main assumptions built into our modeling are the central - satellite parameterization and environment independence of the hod . the central - satellite distinction appears well rooted in galaxy formation physics , and it allows us to represent the range of plausible galaxy hods more completely with a moderate number of parameters . however , we have confirmed with other tests that if we model galaxy bias with a flexible hod parameterization that does not impose a central - satellite distinction , but instead introduces a characteristic mass for the narrow - to - wide transition of @xmath96 as in @xcite , then we reach almost identical conclusions about the cosmological constraining power of the clustering observables considered in this paper . recent numerical results imply an environmental dependence of halo formation times that opens the door to environmental variation of the hod , especially in the single - galaxy regime . as discussed in [ sec : environment ] , we expect the quantitative impact of such dependence to be small , but potentially significant at the high level of precision we ultimately hope to attain . investigation of environmental dependence effects and methods of allowing for them in hod modeling are a high priority for future work . the cosmological modeling approach advocated here is closely related to the clf method introduced by @xcite and @xcite , who use clustering data and the global galaxy luminosity function to constrain the dependence of the luminosity function on halo mass . in principle , the clf and hod methods are equivalent they are merely differential and integral forms of one another . one can derive the clf from a series of hod fits to galaxy samples with different luminosity thresholds @xcite . conversely , one can integrate the clf to infer @xmath97 for galaxies above a luminosity threshold @xcite . the principal virtue of our hod - based approach is that by focusing on a single , well - defined class of galaxies , we can parameterize the hod in a way that seems likely to capture the predictions of any reasonable galaxy formation model . this kind of comprehensive parameterization is more difficult to achieve for the full clf , and most analyses to date have assumed , for example , that the clf has a schechter form in halos of fixed mass . nonetheless , it is valuable to pursue both hod and clf approaches and test for consistency of conclusions . hod modeling complements rather than replaces the perturbative approach based on large - scale measures that can be modeled with linear or quadratic bias . hod modeling is more complex , but it can take advantage of high - precision clustering measurements on small and intermediate scales . hod modeling can also amplify the power of the perturbative approach , extending its reach further into the non - linear regime and checking its range of validity at a desired level of precision . for example , @xcite show that an hod - based approach to redshift - space distortions can improve recovery of the perturbative parameter @xmath39 that controls large - scale flows . @xcite show that the linear bias model provides an accurate description of galaxy - galaxy lensing for @xmath391 , and they show how to accurately model this phenomenon on smaller scales ( see also @xcite ) . j. yoo et al . ( 2007 , in preparation ) show that the scale - dependent bias factors derived by fitting the projected galaxy correlation function can extend recovery of the shape of the linear matter power spectrum into the mildly non - linear regime . clf and hod analyses of the 2dfgrs and sdss redshift surveys have already produced a number of interesting results , even though they have considered only a fraction of the potential clustering observables . these results confirm , at least qualitatively , many of the basic predictions of current galaxy formation models , including the general form of the mean occupation function , the dependence of this function on luminosity , the existence of a minimum mass - to - light ratio in the halos of @xmath392 galaxies where galaxy formation is most efficient , the large gap between the minimum halo mass for central and satellite galaxies above a luminosity threshold , the sub - poisson fluctuations of @xmath96 that are a consequence of this gap , and the strong preference of galaxies with older stellar populations for higher mass halos @xcite . in combination with cmb data , the cosmological constraints from hod modeling of the sdss projected galaxy correlation function are almost as tight as those from the large - scale galaxy power spectrum , and the two analyses are consistent within their statistical uncertainties @xcite . for the most part , the cosmological inferences from clf / hod modeling of galaxy clustering agree with those from other methods , but matching the mass - to - light ratios of galaxy clusters simultaneously with other clustering data appears to require values of @xmath1 and/or @xmath2 that are substantially lower than the commonly adopted values of 0.3 and 0.9 @xcite . if this conclusion is correct , then the evidence for it should become much stronger as more clustering observables are brought into play and the sdss data set itself moves to completion . we have focused in this paper on the cosmological parameter constraints that can be derived from galaxy clustering alone , using external data only to guide the choice of power spectrum shape and motivate the assumption of gaussian initial conditions . as with perturbative analyses of large - scale structure , the long - term interest lies in combining these constraints with those from the cmb , the ly@xmath11 forest , type ia supernovae , and other cosmological observables . the complementary sensitivities of these observables lead to much tighter parameter constraints . more importantly , conflicts among them could point the way to physics beyond the simplest versions of @xmath43cdm , such as evolving dark energy , a gravitational wave contribution to cmb anisotropy , departures from scale invariance in the primordial power spectrum , non - zero space curvature , cosmologically significant neutrino masses , and so forth . by sharpening the constraints from large - scale structure in the new generation of galaxy redshift surveys , hod modeling can play a critical role in efforts to test the standard cosmological model and , perhaps , discover its breaking points . we thank andreas berlind , jeremy tinker , and jaiyul yoo for valuable discussions on these topics . we thank barth netterfield for suggesting a cubic spline parameterization of the mean occupation function , sandy faber for suggesting the influence matrix investigation , and andy gould for advice on the @xmath0 minimization method . this work was supported by nsf grants ast 00 - 98584 and ast 04 - 07125 . z. z. acknowledges the support of nasa through hubble fellowship grant hf-01181.01-a awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . z. z. was also supported by a presidential fellowship from the graduate school of the ohio state university at an early stage of the project . |
, astrosat will provide unprecendented opportunity for simultaneous multi - wavelength observations , which is of immense value in study of highly variable sources , especially x - ray binaries and active galactic nuclei . the large area x - ray proportional counters ( laxpc ) of astrosat , which has the largest effective area in the hard x - ray band compared to all previous x - ray missions , will enable high time resolution x - ray measurements in the 2 - 80 kev band with moderate energy resolution . here we give a brief summary of the payload characteristics of astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects . | i | 1307.5637 | astrosat is an astronomy satellite designed for simultaneous multi - wavelength studies in the optical / uv and a broad x - ray energy range . with four x - ray instruments and a pair of uv - optical telescopes , astrosat will provide unprecendented opportunity for simultaneous multi - wavelength observations , which is of immense value in study of highly variable sources , especially x - ray binaries and active galactic nuclei . the large area x - ray proportional counters ( laxpc ) of astrosat , which has the largest effective area in the hard x - ray band compared to all previous x - ray missions , will enable high time resolution x - ray measurements in the 2 - 80 kev band with moderate energy resolution . here we give a brief summary of the payload characteristics of astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects . the possibility of aiding gravitational wave experiments is also briefly mentioned . | almost all astrophysical objects have significant non - thermal processes that result in emission across a broad energy band . even stars exhibit flares which are non - thermal processes . multi - wavelength observations are therefore key to have complete understanding of a variety of astrophysical objects and astrophysical processes . x - ray binaries and active galactic nuclei ( agn ) are prime examples of objects with emission over a wide band . often the most dominant part of the electromagnetic emission is within the optical to hard x - ray band . moreover , these accretion powered sources show intensity variation over a wide range of timescales , from milliseconds which is the time scale for material to go around a low magnetic field neutron star , to years which is the time scale around supermassive black holes in the most powerful of agns . the x - ray variation can be periodic , quasi - periodic , random with flares , bursts and outbursts , and often a mixture of two or more of these patterns . the optical and uv emission also show intensity variations , though not quite as sharp and strong as x - rays . while in some sources one type of emission is known to be reprocessed into another type and therefore , the causal relation between the multiple components are understood to some extent , there are types of sources in which the source of variations , their causes and effects on the other components are not yet understood very well . simultaneous multi - wavelength observations are therefore key to our understanding of the broadband emission mechanism and interrelation between multiple emission processes in x - ray binaries and agns . simultaneous multi - wavelength x - ray and uv - optical observations are however very difficult to carry out . apart from the requirement of coordination between the space - based x - ray observatories and ground - based ( or on a different space telescope like the hst ) optical telescopes , the typical duty cycle for simultaneous multi - wavelength data from such observations is very low , owing to the different nature of good time interval ( gti ) of space and ground based observatories . simultaneous x - ray and uv - optical observations from the same satellite platform can mitigate many of these problems and yield rich dataset . astrosat , with its three co - aligned x - ray instruments and two uv - optical telescopes with a total of three bands is designed to bring in this new capability of quality simultaneous multi - wavelength observation capability . two other space observatories , the xmm - newton@xcite and swift@xcite have limited optical and uv capabilities along with very powerful x - ray telescopes and the new potential of single platform simultaneous multi - wavelength observations have been demonstrated to quite a large extent with these instruments . in addition to the multi - wavelength aspect , the three co - aligned x - ray instruments will also provide very good capability for broadband x - ray measurements , with particular improvement in capabilities in the hard x - ray band of 15 - 80 kev . the large area x - ray proportional counter ( laxpc ) instrument of astrosat has an effective area that is in this range several times larger than any other x - ray instrument , which will enable certain unique measurements like quasi periodic oscillations ( qpo ) in the hard x - ray band , pulse phase - resolved study of the cyclotron resonance scattering fearure ( crsf ) in accretion - powered high magnetic field pulsars etc . the astrosat@xcite is being developed under a large collaboration including several indian organisations and some participation from the united kingdom and canada . though the mission has been delayed , it is expected to be launched in 2013 . in the following sections we give a brief description of the instruments onboard astrosat and discuss some of the main science topics that will be addressed with the laxpc , and with simultaneous observations with the uvit telescopes , with particular emphasis on x - ray binaries and compact objects . |
background : : : models based on using perturbative polarization corrections and mean - field blocking approximation give conflicting results for masses of odd nuclei . purpose : : : systematically investigate the polarization and mean - field models , implemented within self - consistent approaches that use identical interactions and model spaces , so as to find reasons for the conflicts between them . methods : : : for density - dependent interactions and with pairing correlations included , we derive and study links between the mean - field and polarization results obtained for energies of odd nuclei . we also identify and discuss differences between the polarization - correction and full particle - vibration - coupling ( pvc ) models . results : : : we have identified and numerically evaluated self - interaction ( si ) energies that are at the origin of different results obtained within the mean - field and polarization - correction approaches . the simplest deformed mean - field approach that does not break parity symmetry is unable to reproduce full pvc effects . | i | 1310.0435 | background : : : models based on using perturbative polarization corrections and mean - field blocking approximation give conflicting results for masses of odd nuclei . purpose : : : systematically investigate the polarization and mean - field models , implemented within self - consistent approaches that use identical interactions and model spaces , so as to find reasons for the conflicts between them . methods : : : for density - dependent interactions and with pairing correlations included , we derive and study links between the mean - field and polarization results obtained for energies of odd nuclei . we also identify and discuss differences between the polarization - correction and full particle - vibration - coupling ( pvc ) models . numerical calculations are performed for the mean - field ground - state properties of deformed odd nuclei and then compared to the polarization corrections determined by using the approach that conserves spherical symmetry . results : : : we have identified and numerically evaluated self - interaction ( si ) energies that are at the origin of different results obtained within the mean - field and polarization - correction approaches . conclusions : : : mean - field energies of odd nuclei are polluted by the si energies , and this makes them different from those obtained by using polarization - correction methods . a comparison of both approaches allows for the identification and determination of the si terms , which then can be calculated and removed from the mean - field results , giving the self - interaction - free energies . the simplest deformed mean - field approach that does not break parity symmetry is unable to reproduce full pvc effects . | the perturbative particle - vibration - coupling ( pvc ) model for odd - particle - number nuclei emerges naturally from the self - consistent green s function theory @xcite . it describes the polarization of the nucleus when one particle is added or removed @xcite , and its results can , in principle , be directly compared against experimental data . as used in nuclear physics , the perturbative pvc method employs one - particle or one - hole states ( or one - quasiparticle states ) coupled with the rpa or qrpa excitations of an even - even reference nucleus , and the residual nucleon - nucleon interaction that mixes these states at second - order perturbation theory . numerous pvc calculations of increasing level of sophistication have already been performed , see , e.g. , refs . @xcite and excellent recent reviews thereof available in refs . @xcite . an alternative to describing odd nuclei within the perturbative pvc calculations are the energy - density - functional ( edf ) methods , see , e.g. , refs . @xcite , which use blocking of single - particle ( s.p . ) or quasiparticle orbitals . to distinguish these methods from the full pvc approach , in the present study we call them mean - field polarizations or polarization corrections . the advantage of blocked mean - field calculations is that they are non - perturbative and variational . as it turns out , the effects obtained within the blocked mean - field methods are substantially different and , in general , weaker than those obtained from the perturbative pvc @xcite . this discrepancy between models , even when using exactly the same interactions and model spaces , needs to be solved , and this is the main purpose of the present work . the link between the mean - field and perturbative methods has been proposed long time ago @xcite . here , we identify several approximations that are required to firmly establish such a link , and we also extend the derivations to edfs based on density - dependent interactions and to those that include pairing correlations . since the determination of mean - field polarizations requires breaking symmetries , no numerical comparison of the two approaches , such as given here , is available up to now . as required by a thorough comparison , both in the mean - field and ( q)rpa calculations we use full self - consistency and exactly the same particle - hole edfs , pairing interactions , and model spaces . the paper is built around two main chapters presenting theoretical derivations in sec . [ sec2 ] and appendix [ sec5 ] , and numerical results in sec . [ sec3 ] . for theory , we present results pertaining to the hartree - fock ( hf ) approximation ( sec . [ sec2.2 ] ) , density functionals ( sec . [ sec2.4 ] ) , and pairing correlations treated within the hartree - fock - bogoliubov ( hfb ) framework ( sec . [ sec2.3 ] ) . then , results of calculations are discussed for the density - independent ( sec . [ sec3.1 ] ) and density - dependent ( sec . [ sec3.2 ] ) particle - hole interactions , and for paired systems ( sec . [ sec3.3 ] ) . conclusions are given in sec . |
based on non - equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two - phase flow in porous media . these equations together with the conservation of saturation reduces the immiscible two - phase flow problem to a single - phase flow problem of a complex fluid . | c | 1605.02874 | based on non - equilibrium thermodynamics we derive a set of general equations relating the partial volumetric flow rates to each other and to the total volumetric flow rate in immiscible two - phase flow in porous media . these equations together with the conservation of saturation reduces the immiscible two - phase flow problem to a single - phase flow problem of a complex fluid . we discuss the new equation in terms of the relative permeability equations . we test the equations on model systems , both analytically and numerically . | we have in this paper constructed a theory based on non - equilibrium thermodynamics that reduces the immiscible _ two - phase flow _ in porous media to a _ one - phase _ flow problem . let us now consider a three - dimensional isotropic porous medium . let @xmath215 be a point somewhere in this porous medium . the theory that we have developed can then be summarized by the following set of equations , @xmath216 @xmath217 and @xmath218 here ( [ conc-1 ] ) is the conservation law for the wetting saturation . this expression becomes the buckley - leverett equation @xcite if we set @xmath219 , see equation ( [ eqn21 ] ) and take the incompressibility of the fluids into account . the non - wetting saturation @xmath220 has been eliminated by using the incompressibility of the two fluids . this implies that @xmath221 is build into the equation set . equation ( [ conc-6 ] ) is the three - dimensional version of equation ( [ eqn20 ] ) . the three - dimensional version of equation ( [ eqn18 ] ) is @xmath222 . this equation follows by taking the derivative of ( [ conc-5 ] ) with respect to @xmath32 and using ( [ conc-6 ] ) . hence , this equation is also contained in ( [ conc-1 ] ) to ( [ conc-6 ] ) . it may replace either of the equations ( [ conc-5 ] ) or ( [ conc-6 ] ) . these equations are all conservation laws , the last two express power input equals dissipation . thus , they transcend the details of the porous medium . equations ( [ conc-1 ] ) to ( [ conc-6 ] ) are 7 equations . there are ten variables @xmath32 , @xmath223 , @xmath224 and @xmath225 . the three equations that close the system of equations are the _ constitutive equations _ @xmath226\;,\ ] ] containing the detailed physics of the system . we see that the constitutive equation does not contain the seepage velocities of the immiscible fluids , @xmath224 and @xmath225 , explicitly . only the saturation @xmath32 enters . hence , the constitutive equation ( [ conc-7 ] ) can be interpreted as that of a single fluid depending on one extra variable , @xmath227 . hence , the equation set ( [ conc-1 ] ) ( [ conc-7 ] ) reduces the immiscible two - phase flow problem in porous media to a one - phase flow problem involving a complex fluid . this viewpoint permeates recent work on the effective permeability of immicible two - phase systems where it is suggested that two fluids behave as if they were a single bingham plastic @xcite . we may clarify this point even further by eliminating the two fluid velocities @xmath224 and @xmath225 in equations ( [ conc-1 ] ) to ( [ conc-6 ] ) . the equation set then reduces to a single equation @xmath228 together with the constitutive equation ( [ conc-7 ] ) , we now have a closed set describing effectively a single fluid with a velocity field @xmath223 which transports an active scalar @xmath32 . in this manuscript we have considered a single driving force that induces the flow : the pressure gradient . other forces such as buoyancy , temperature gradients and chemical driving forces can be incorporated in the non - equil - ibrium thermodynamics formalism used in section [ diss ] . the same is true for the introduction of more immiscible fluids than two . hence , equations ( [ conc-1 ] ) to ( [ conc-6 ] ) may be generalized to include these additional complications . the authors thank eirik grude flekky , knut jrgen mly , thomas ramstad , per arne slotte and marios valavanides for interesting discussions on this topic . ah , sk and is thank vista , a collaboration between statoil and the norwegian academy of sciences , for financial support . ss thanks the norwegian research council , nfr and the beijing computational science research center csrc for financial support . k. t. tallakstad , h. a. knudsen , t. ramstad , g. lvoll , k. j. mly , r. toussaint and e. g. flekky , steady - state two - phase flow in porous media : statistics and transport properties , phys . rev . lett . * 102 * , 074502 ( 2009 ) . k. t. tallakstad , g. lvoll , h. a. knudsen , t. ramstad , e. g. flekky and k. j. mly , steady - state simultaneous two - phase flow in porous media : an experimental study , phys . e * 80 * , 036308 ( 2009 ) . e. m. rassi , s. l. codd and j. d. seymour , nuclear magnetic resonance characterization of the stationary dynamics of partially saturated media during steady - state infiltration flow , n. j. phys . * 13 * , 015007 ( 2011 ) . s. sinha , a. t. bender , m. danczyk , k. keepseagle , c. a. prather , j. m. bray , l. w. thrane , j. d. seymor , s. l. codd and a. hansen , effective rheology of two - phase flow in three - dimensional porous media : experiment and simulation , submitted to trans . ( 2016 ) . r. g. bentsen and j. trivedi , on the construction of an experimentally based set of equations to describe cocurrent or countercurrent , two - phase flow of immiscible fluids through porous media , transp . in por . media , * 99 * , 251 ( 2013 ) . m. moura , e. -a . florentino , k. j. mly , g. schfer and r. toussaint , impact of sample geometry on the measurement of pressure - saturation curves : experiments and simulations , water res . 51 * , 8900 ( 2015 ) . |
the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _ | i | nucl-th0512022 | by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . v.a . kuzmin@xmath1 and t.v . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _ | to discuss the problem of missing strength of gamow - teller ( gt ) transitions , one needs to study the distribution of transition strength over the excitation energy . a convenient tool for that purpose is the strength function of gt transitions @xmath3 where @xmath4 is the energy of the @xmath5 state reckoned from the ground state of a target nucleus , @xmath6 . usually , it is assumed that the effect of missing strength can be explained ( reproduced ) by including 2p2h admixtures into the wave functions of nuclear states involved . in order to check this assumption , we consider the energy - weighted moments of the gt strength function @xmath7 for positive integer @xmath8 . in the first section , we calculate the moments in the random phase approximation , the second random phase approximation and within the fragmentation problem . in the second section , we argue that the explanation of missing strength requires that the particle - hole residual interaction has a specific feature , it should intensively mix the @xmath9 and @xmath10 particle - hole configurations . the example of such an interaction is presented and the strength function of @xmath11 transitions in @xmath12 is demonstrated . in the third section , the calculations of total muon capture rates by complex nuclei are discussed . the fourth section contains the analysis of spin - isospin transitions in @xmath13 nuclei observed in muon capture , and in @xmath14 and @xmath15 reactions . the main results are collected in conclusion . |
by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . kuzmin@xmath1 and t.v . | c | nucl-th0512022 | by analyzing the energy - weighted moments of the strength function calculated in rpa and beyond it is shown that the explanation of the effect of missing strength of gamow - teller transitions requires that residual interaction produce high - excited @xmath0 particle - hole collective states . the example of this interaction is presented . the manifestations of spin - isospin nuclear response in nuclear muon capture are discussed . v.a . kuzmin@xmath1 and t.v . tetereva@xmath2 + _ @xmath1 joint institute for nuclear research , dubna , moscow region , 141980 , russia + @xmath2 skobeltsyn institute of nuclear physics , lomonosov moscow state university , moscow , 119992 , russia _ | the energy weighted moments of strength function of gt transition , @xmath170 , are calculated in the rpa , srpa and within the fragmentation problem . considering @xmath171 and @xmath172 we have shown that the effect of missing gt strength should be reproduced as the result of interaction among the particle - hole excitations , without including the 2p2h configurations . hence , the residual interaction in the spin - isospin channel must intensively mix the @xmath173 and @xmath10 particle - hole states . the example of this interaction is presented . it is shown that the experimental strength function of @xmath11 transition in @xmath12 can be reproduced rather well in the whole region of excitation energy . total muon capture rates were calculated for several nuclei using two variants of residual interaction . theoretical total rates of muon capture by medium nuclei practically do not depend on the residual interaction used in calculation . in heavy nuclei theoretical rates are higher than experimental ones . the excess depends on the residual interaction , and the difference between theory and experiment is the largest when the residual interaction , which forms the high - excited collective states , is used in the calculation . the existence of these states is assumed by the effect of missing gt strength . it is shown that the distributions of transition strength over the excitation energy in @xmath13 nuclei extracted from weak and electromagnetic processes are in conflict with the ones obtained from charge - exchange nuclear reactions . in particular , no quenching of spin - isospin transitions is found in the rates of partial allowed muon capture @xmath174 . rowe , rev . phys . , * 40 , * 153 , ( 1968 ) a.m. lane and j. martorell , ann . phys . , * 129 , * 273 , ( 1980 ) f. gantmacher , theory of matrices , vol . 2 , ams publishing , 2000 s. drod , s. nishizaki , j. speth and j. wambach , phys . rep . , * 197 , * 1 , ( 1990 ) a. bohr and b.r . mottelson , nuclear structure , vol . 1 , new york , amsterdam , 1969 v.v . voronov and v.g . soloviev , fiz . chast . at . yadra , * 14 , * 1380 , ( 1983 ) [ sov . j. part . nucl . , * 14 , * 583 ( 1983 ) ] v.a . kuzmin , theoret . i matemat . fiz . , * 70 , * 315 ( 1987 ) [ theor . and math . phys . , * 70 , * 223 ( 1987 ) ] g.f . bertsch , p. f. bortignon and r.a . broglia , rev . phys . , * 55 , * 287 ( 1983 ) g.j . mathews , s.d . bloom and r.f . hausman , jr . c , * 28 , * 1367 ( 1983 ) s. drod , v. klempt , j. speth , and j. wambach , phys . b , * 166 , * 18 ( 1986 ) s. drod , f. osterfeld , j. speth , j. wambach , phys . b , * 189 , * 271 ( 1987 ) a.i . vdovin and v.g . soloviev , fiz . chast . at . yadra , * 14 , * 237 , ( 1983 ) [ sov . j. part . nucl . , * 14 , * 99 ( 1983 ) ] t. wakasa _ et al . _ , phys . c , * 56 , * 2909 , ( 1997 ) v.a . kuzmin , yad . * 58 , * 418 , ( 1995 ) [ phys . atom . nucl .. * 58 , * 368 , ( 1995 ) ] ; 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by means of one - step model calculations the strong in - plane anisotropy seen in angle - resolved photoemission of the well - known iron pnictide prototype compounds and in their low - temperature antiferromagnetic phases is investigated . the fully - relativistic calculations are based on the korringa - kohn - rostoker - green function approach combined with the coherent potential approximation alloy theory to account for the disorder induced by co substitution on fe sites in a reliable way . the results of the calculations can be compared directly to experimental spectra of detwinned single crystals . in particular the local density approximation can capture most of the correlation effects for the investigated system without the need for more advanced techniques . the results are also used to discuss surface effects and it is possible to identify clear signatures to conclude about different types of surface termination . | i | 1602.05027 | by means of one - step model calculations the strong in - plane anisotropy seen in angle - resolved photoemission of the well - known iron pnictide prototype compounds and in their low - temperature antiferromagnetic phases is investigated . the fully - relativistic calculations are based on the korringa - kohn - rostoker - green function approach combined with the coherent potential approximation alloy theory to account for the disorder induced by co substitution on fe sites in a reliable way . the results of the calculations can be compared directly to experimental spectra of detwinned single crystals . one finds very good agreement with experiment and can reveal all features of the electronic structure contributing to the in - plane anisotropy . in particular the local density approximation can capture most of the correlation effects for the investigated system without the need for more advanced techniques . in addition , the evolution of the anisotropy for increasing co concentration @xmath0 in can be tracked almost continuously . the results are also used to discuss surface effects and it is possible to identify clear signatures to conclude about different types of surface termination . | nowadays the family of iron pnictides is a well - established and important prototype system for unconventional high - temperature superconductivity . starting with the first famous compound @xcite in 2008 , today several different sub - families with a wide structural variety are known . all different groups of iron pnictides share some common physical properties , such as their interesting and sometimes puzzling magnetic behavior . most compounds show a phase transition at low temperatures from a tetragonal to an orthorhombic crystal symmetry which is typically accompanied by the formation of long - range antiferromagnetic order.@xcite it is common believe that the suppression of these phase transitions for example by chemical substitution is crucial for the emergence of unconventional superconductivity.@xcite although it is obvious that an understanding of the magnetic fluctuations in the iron pnictides is mandatory to unveil the physics underlying the superconductivity , this task has proven to be more complex than anticipated.@xcite for example , there was discussion in the literature whether the magnetic moments are better described by an itinerant@xcite or a localized@xcite model and there is up to now no consensus concerning the role of correlation effects@xcite . furthermore , the magnitude of the magnetic moments is difficult to reproduce within density functional theory ( dft ) and it is known to be quite sensitive to computational parameters.@xcite one of the most important experimental tools to get insight into the electronic structure of the iron pnictides is angle - resolved photoemission spectroscopy ( arpes ) . there are numerous publications on this topic , although it was shown that dft calculations have typically problems to reproduce all features of the arpes spectra correctly.@xcite this is often ascribed to strong correlation effects , although this question is still under discussion.@xcite another important difficulty which so far is often ignored is the connection between the magnetic phase of the iron pnictides and the resulting consequences for arpes . this is due to the formation of twinned crystals during the phase transition from tetragonal to orthorhombic and it results in mixed magnetic domains which are orthogonal to each other . macroscopic tools like arpes or transport measurements can so only see the averaged information , while information on the anisotropy is lost.@xcite this is a huge drawback considering a comprehensive study of the electronic structure in the iron pnictides , as it is known that the in - plane anisotropy plays a significant role.@xcite in experiment it is possible to effectively detwin the crystals by applying uniaxial stress during the measurement . this was already done successfully for the 122-prototype in the undoped and in the co - doped case . however , such measurements are connected with several technical difficulties and consequently they are rarely done.@xcite yet , to fully understand the electronic properties of the iron pnictide superconductors in a comprehensive way and to get a deeper insight concerning the influence of the in - plane anisotropy in the magnetic phase such studies are absolutely mandatory . although there is nowadays experimental data on detwinned crystals showing clearly the anisotropy in the fermi surface there is hardly any theoretical work focusing on this problem of magnetic anisotropy in arpes data . in this work this issue is addressed by a comprehensive dft study on the magnetic phase of and on the corresponding arpes spectra . the computational results can be directly compared to the available experimental arpes data on detwinned crystals.@xcite in order to deal with this complex situation the korringa - kohn - rostoker - green function ( kkr - gf ) approach is used , which was already shown to be indeed a very useful and accurate tool to deal with the iron pnictides.@xcite the impact of disorder due to substitution is dealt with by means of the coherent potential approximation ( cpa ) , giving results fully compatible to supercell calculations and more reliable than those based on the virtual crystal approximation ( vca).@xcite |
the occurrence of this minimum as a function of @xmath1 depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry , on the lattice dimensionality or on the position of the ising - like transition . in one - space dimension , the spatial correlation length associated with magnitude fluctuations and the length @xmath0 are approximately equal , with both varying linearly with the radius of the lattice coupling . | r | chao-dyn9506009 | by simulating a nonequilibrium coupled map lattice that undergoes an ising - like phase transition , we show that the lyapunov spectrum and related dynamical quantities such as the dimension correlation length @xmath0 are insensitive to the onset of long - range ferromagnetic order . as a function of lattice coupling constant @xmath1 and for certain lattice maps , the lyapunov dimension density and other dynamical order parameters go through a minimum . the occurrence of this minimum as a function of @xmath1 depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry , on the lattice dimensionality or on the position of the ising - like transition . in one - space dimension , the spatial correlation length associated with magnitude fluctuations and the length @xmath0 are approximately equal , with both varying linearly with the radius of the lattice coupling . | in this section , we discuss our calculations of the lyapunov spectrum and of correlation lengths . our goal is to explore how spatial disorder ( as characterized by the two - point correlation length or by the mutual information correlation length ) is related to dynamical complexity ( as measured by the intensive dimension density and by the dimension correlation length eq . ( [ xi - delta - defn ] ) ) and to investigate how these order parameters vary near the nonequilibrium transition point @xmath12 at which the magnetization bifurcates to nonzero values ( fig . [ fig : m - for - square - lattice ] ) . results for the 2d square lattice are given first , followed by results for lattices with different symmetries and dimensionalities . we do not address issues related to critical exponents of these different models which have been discussed by miller and huse @xcite and more recently by marcq and chat @xcite . related interesting results on similar cmls have also recently been reported by boldrighini et al @xcite . for the two - dimensional periodic square lattice with map eq . ( [ eq : miller - huse - map ] ) , fig . [ fig : m - for - square - lattice ] shows that there is a bifurcation at @xmath108 . this bifurcation corresponds to the onset of long - range order of the lattice variables @xmath86 as demonstrated by the divergence of the two - point correlation length @xmath13 as @xmath1 approaches @xmath92 ( fig . [ fig : divergence - of - xi_2](a ) ) . over this same parameter range , the dimension correlation length @xmath0 varies smoothly ( fig . [ fig : divergence - of - xi_2](b ) ) , deviating by less than four percent from a value of one lattice spacing and attaining a maximum value close to where the correlation length diverges . the lyapunov spectrum of exponents also varies smoothly from one side of the transition to the other as shown in fig . [ fig : lyapunov - spectra ] . we conclude that chaotic fluctuations have a short range , are decoupled from the onset of long - range order measured by @xmath13 , and that the spectrum of exponents is at most weakly dependent on the onset of long - range spatial order . to understand further how various dynamical quantities change near the transition point , we have plotted in fig . [ fig : d - h - l1-vs - g-2d - square ] the variation of the lyapunov fractal dimension density @xmath19 , of the metric entropy density @xmath20 , and of the largest lyapunov exponent @xmath17 across the ferromagnetic transition for a lattice of size @xmath68 , which is already extensively chaotic according to fig . [ fig : ext - chaos ] . as was the case for the length @xmath0 in fig . [ fig : divergence - of - xi_2](b ) , these quantities change by only a small amount through the transition ( at most by 20% ) and all go through a minimum close to , but distinct from , the ferromagnetic transition at @xmath109 . this result was surprising to us since one consequence of coupling neighboring maps more strongly ( increasing the parameter @xmath1 ) would intuitively be to increase correlations between their dynamics , which should decrease both @xmath19 and @xmath20 . [ fig : d - h - l1-vs - g-2d - square](a ) indicates that roughly one quarter of the maximum number of degrees of freedom disappear when the lattice attains its minimum dimension density of @xmath110 . ( an upper bound of @xmath111 is set by the integer lattice spacing . ) it is not clear why the fractal dimension density and other dynamical quantities have extrema near @xmath112 . for an equilibrium non - dissipative cml of ising dynamics on a two - dimensional square lattice , sakaguchi @xcite did not find a local minimum in the entropy @xmath66 but instead found a monotonic decrease consistent with the analytical solution of the spin-@xmath113 ising model on a square lattice @xcite . one explanation for the extrema may be that the dissipative linear coupling in eq . ( [ eq : the - cml ] ) becomes antidiffusive for @xmath114 , enhancing rather than damping short - wavelength fluctuations and so decorrelating nearby lattice variables . the issue is somewhat more subtle than this because the existence of the minimum depends also on details of the local map @xmath25 in eq . ( [ eq : the - cml ] ) . for the less chaotic lattice map eq . ( [ eq : slope-1.1-map ] ) with slope of constant magnitude 1.1 , an ising - like transition still occurs as shown by the bifurcation of the magnetization near @xmath115 in fig . [ fig : m - for - square - lattice - map2 ] . fig . [ fig : d - h - l1-for - square - lattice - map2 ] now shows that the lyapunov dimension density @xmath19 and entropy density @xmath20 decrease monotonically as the parameter @xmath1 is increased , with the largest exponent @xmath17 remaining constant . figures [ fig : m - for - square - lattice ] , [ fig : divergence - of - xi_2](a ) , and [ fig : d - h - l1-vs - g-2d - square ] suggest that the extrema of dynamical quantities may be related to the ferromagnetic transition . on the other hand , the short dimension correlation length in fig . [ fig : divergence - of - xi_2](b ) contradicts this by implying that chaotic fluctuations occur over a length scale that is short compared to the ferromagnetic ordering . to understand this further , we have explored cmls of different symmetry and dimensionality and found that the near - proximity of the extrema with the transition is a coincidence for the two - dimensional lattice with square symmetry . more generally , the positions of extrema seem to be determined simply by the number of nearest neighbors @xmath22 , and not by the symmetry or dimensionality of the cml or by the position of the magnetization bifurcation point . [ fig : m - for - hexagonal - lattice - map1 ] summarizes calculations for a two - dimensional periodic hexagonal lattice by plotting the dependence of magnetization @xmath88 and of dimension correlation length @xmath0 on the coupling constant @xmath1 . the magnetization bifurcates to a nonzero value at @xmath116 which is a smaller value than that for the square lattice since the larger number of nearest neighbors ( six versus four ) increases the effective strength of the diffusive coupling . the relative difference between the transition at @xmath12 and the positions of the extrema in @xmath0 and in related dynamical quantities is substantially larger than was the case for the 2d square lattice . for the hexagonal lattice , extrema in quantities like the length @xmath0 occur at a value close to @xmath117 where @xmath24 is the number of nearest neighbors . a similar result is found for the same cml on a 3d cubic lattice , as shown in fig . [ fig : m - for - cubic - lattice - map1 ] . the transition at @xmath118 occurs at a value close to but smaller than the value on the hexagonal lattice . extrema in the dynamical quantities like @xmath0 again occur at a value close to @xmath119 with @xmath24 . that the positions of the extrema of dynamical quantities is dependent primarily on the number of nearest neighbors is a consequence of the nearest - neighbor diffusive coupling in eq . ( [ eq : the - cml ] ) and of the fact that , for the local map eq . ( [ eq : miller - huse - map ] ) , the chaos is sufficiently strong to make the dimension correlation length @xmath0 quite small , about one lattice length . that the positions of the extrema seem to be given quantitatively by the specific formula @xmath120 is more delicate to understand but may be related to the fact that the discrete laplacian operator changes from diffusive to antidiffusive behavior at this value . the value @xmath120 is the value for which the weight of each of the neighbors is equal to the weight of the central lattice site to be updated . for all cmls that we studied , the dimension correlation length @xmath0 was about one lattice spacing in size and this was also the `` radius '' of the diffusive coupling in eq . ( [ eq : the - cml ] ) . this suggests that the length @xmath0 may be determined by the spatial extent of the diffusive coupling , becoming larger as more sites are coupled to a given site . this conjecture was tested in one - space dimension by coupling together , with equal weight @xmath1 , all lattice variables within a radius @xmath15 of a given site @xmath28 : @xmath121 for this one - dimensional periodic cml with the lattice map eq . ( [ eq : miller - huse - map ] ) , the dynamics varies in a complicated way with radius @xmath15 . for most initial conditions , chaos was found for smaller radii ( @xmath122 ) . for larger radii @xmath123 , the transients lasted much longer and the asymptotic dynamics was periodic . as an example , for @xmath124 the dimension as a function of time initially reached a value @xmath125 even after @xmath126 transient iterations were skipped ; however , the dimension then decreased steadily to zero over the next 30,000 iterations . we believe that this asymptotic periodic behavior is a finite - size effect . for a sufficiently large system size @xmath5 , with the crossover length increasing with the radius @xmath15 , the asymptotic state should be chaotic . for dimensionality @xmath101 , the dimension correlation length @xmath0 varies more strongly with increasing radius @xmath15 than with coupling constant @xmath1 , which allows several different length scales to be compared . [ fig:1d - cml - results ] shows that the two - point correlation length @xmath100 obtained using the magnitudes @xmath127 of the field values has approximately the same linear dependence on the coupling radius @xmath15 as the dimension correlation length @xmath0 . in addition , these two length scales are the same order of magnitude . the two - point correlation length @xmath13 obtained using the actual field values is larger than @xmath0 and does not have the same simple linear dependence on @xmath15 . the situation is then similar to results found for spatiotemporal chaotic solutions of the 1d periodic cgle @xcite in that the spatial correlation length of fluctuations in the magnitude of a field provides a way of estimating the length @xmath0 . |
by simulating a nonequilibrium coupled map lattice that undergoes an ising - like phase transition , we show that the lyapunov spectrum and related dynamical quantities such as the dimension correlation length @xmath0 are insensitive to the onset of long - range ferromagnetic order . as a function of lattice coupling constant @xmath1 and for certain lattice maps , the lyapunov dimension density and other dynamical order parameters go through a minimum . | c | chao-dyn9506009 | by simulating a nonequilibrium coupled map lattice that undergoes an ising - like phase transition , we show that the lyapunov spectrum and related dynamical quantities such as the dimension correlation length @xmath0 are insensitive to the onset of long - range ferromagnetic order . as a function of lattice coupling constant @xmath1 and for certain lattice maps , the lyapunov dimension density and other dynamical order parameters go through a minimum . the occurrence of this minimum as a function of @xmath1 depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry , on the lattice dimensionality or on the position of the ising - like transition . in one - space dimension , the spatial correlation length associated with magnitude fluctuations and the length @xmath0 are approximately equal , with both varying linearly with the radius of the lattice coupling . | in this paper , we have extended recent calculations @xcite concerning the relation between spatial disorder and dynamical complexity of a sustained homogeneous nonequilibrium system from dimensionality @xmath101 to dimensionalities @xmath10 and @xmath11 . this was accomplished by choosing a coupled map lattice , eq . ( [ eq : the - cml ] ) , that underwent an ising - like transition with diverging two - point correlation length as a parameter @xmath1 was varied @xcite . by comparing various length scales such as the two - point correlation length @xmath13 , the dimension correlation length @xmath0 , and the two - point correlation length of magnitude fluctuations @xmath14 near the transition point , we were able to show that the lengths @xmath0 and @xmath14 were short , of order one lattice spacing , even as the length @xmath13 diverged to infinity . in agreement with previous work @xcite , the chaotic fluctuations are decoupled from the average long - range spatial order . the correlation length of magnitude fluctuations seems to provide an effective way to estimate the size of the length @xmath0 . our calculations of the lyapunov spectrum and related quantities such as the lyapunov dimension density @xmath19 , metric entropy density @xmath20 , and the largest lyapunov exponent @xmath17 show that the onset of long - range spatial order ( diverging @xmath13 ) does not affect dynamical invariants , which vary smoothly and weakly through the transition point @xmath12 . thus the average spatial disorder ( measured by @xmath13 ) does not determine dynamical complexity ( measured by @xmath0 ) . rather surprisingly , the intensive densities @xmath19 and @xmath20 go through a minimum near the transition point so that the onset of long - range order does not correspond to a decrease in complexity . by examining cmls of different symmetry and of different dimensionality @xmath6 , we showed that the positions @xmath1 of the extrema were determined by the number @xmath22 of neighbors nearest to a given lattice site ( with @xmath128 ) but not by the symmetry or by @xmath6 . this result can be understood as a consequence of the extremely short dimension correlation length @xmath0 , about one lattice size , so that lattice variables are independent except when they are nearest neighbors . we believe that the minima in @xmath19 and in @xmath20 occur approximately when the discrete laplacian in eq . ( [ eq : the - cml ] ) becomes antidiffusive with increasing parameter @xmath1 . short - wavelength fluctuations are then magnified instead of damped , decreasing correlations between neighboring sites . some of our results concerning extrema in dynamical quantities have been independently obtained by boldrighini et al @xcite although these authors worked with extensive , rather than intensive , quantities and they did not determine whether their calculations corresponded to extensively chaotic regimes . boldrighini et al investigated cmls of the form eq . ( [ eq : the - cml ] ) for dimensionalities @xmath101 and @xmath10 but with some new local maps @xmath25 . besides also finding extrema in the lyapunov fractal dimension , boldrighini et al showed that the odd symmetry of the map @xmath25 was not a sufficient condition for the magnetization to bifurcate to a nonzero value . using a strongly chaotic local map with slope of constant magnitude equal to 5 , they also showed that the magnetization @xmath88 did not bifurcate to a nonzero value if the local map were made sufficiently chaotic compared to the ordering caused by diffusion . in section [ other - lattices ] , we used the less - chaotic local map eq . ( [ eq : slope-1.1-map ] ) with slope of constant magnitude 1.1 to show that the dimension density @xmath19 can decrease monotonically without a minimum even when the magnetization @xmath88 bifurcates to a nonzero value . the dependence of these minima on details of the local map is not yet understood and should be pursued with further studies . the small values of @xmath0 in the present cmls , in the 1d cgle @xcite , and in a nonequilibrium cml with algebraic decay of spatial correlations @xcite have several interesting implications . one is that many previous laboratory experiments @xcite and numerical simulations @xcite concerning spatiotemporal chaos are likely already extensive so that it is meaningful to talk about dimension and entropy densities ( see also the earlier paper by bohr @xcite . ) a second implication is that the dimension correlation length @xmath0 may not be a useful order parameter for future studies of spatiotemporal chaos since it depends only weakly on parameters . a third implication is that the short value of @xmath0 suggests the nonexistence of macroscopic chaotic states for dynamics with local interactions , a point already made by several researchers @xcite . finally , we speculate that @xmath0 is the length scale below which one can replace chaotic fluctuations by a white noise source when trying to develop a hydrodynamic ( long wavelength ) description of spatiotemporal chaos ( see the discussion on pages 953 - 954 in ref . @xcite ) . the short values of @xmath0 raise the question of what determines this length scale . our calculations on the 1d cml eq . ( [ eq : radius - r - cml ] ) with a variable radius of coupling @xmath15 suggest that the length @xmath0 is determined partly by the length @xmath14 characterizing magnitude fluctuations although the reason for and the generality of this correspondence is not understood @xcite . the length @xmath0 is also related to the radius @xmath15 over which nearby lattice sites are coupled together ( fig . [ fig:1d - cml - results ] ) . further calculations with different kinds local maps and of diffusive operators and for different values of @xmath15 should provide further insight . it is appropriate to finish with a discussion about the relevance of these results for laboratory experiments . as discussed at the end of section [ exponents ] , it does not seem possible in the near future to calculate the lyapunov spectrum , the fractal dimension , or the fractal dimension density of a high - dimensional extensively chaotic experimental system for which only time series measurements are available @xcite . our success in calculating these quantities was a result of having explicit knowledge of the dynamical equations which could then be integrated numerically on a powerful parallel computer using algorithms whose complexity only grew algebraically with the dimension @xmath3 @xcite . for many laboratory experiments , a quantitative mathematical description is either lacking ( e.g. , for chemical reactions ) or , if known , is too difficult to work with numerically ( e.g. , the five three - dimensional boussinesq equations describing buoyancy - induced convection in a large - aspect - ratio container @xcite ) . our calculations in section [ results ] suggest that one possible way to estimate the dimension correlation length @xmath0 may be to calculate the correlation length of some function of the physical fields , e.g. , the field magnitude . another possibility will be to discover and to validate algorithms that can calculate the intensive dimension density eq . ( [ delta - defn ] ) directly from time - series measurements that are localized in space @xcite , in lieu of calculating a large extensive fractal dimension @xmath3 and then dividing by the extensive system volume @xmath87 . several steps have been taken in this direction @xcite , but a theoretical foundation has not yet been established nor have the numerical algorithms been adequately tested . |
if a tau lepton , produced by a tau neutrino , escapes from the earth or a mountain , it will decay and initiate a shower in the air which can be detected by an air shower fluorescence or cherenkov telescope . in this paper , we present detailed monte carlo simulations of corresponding event rates for the veritas and two proposed cherenkov telescope array sites : meteor crater and yavapai ranch , which use representative agn neutrino flux models and take into account topographic conditions of the detector sites . the calculated neutrino sensitivities depend on the observation time and the shape of the energy spectrum , but in some cases are comparable or even better than corresponding neutrino sensitivities of the icecube detector . for veritas and the considered cherenkov telescope array sites the expected neutrino sensitivities are up to factor 3 higher than for the magic site because of the presence of surrounding mountains . | i | 1402.4243 | cherenkov telescopes have the capability of detecting high energy tau neutrinos in the energy range of 11000pev by searching for very inclined showers . if a tau lepton , produced by a tau neutrino , escapes from the earth or a mountain , it will decay and initiate a shower in the air which can be detected by an air shower fluorescence or cherenkov telescope . in this paper , we present detailed monte carlo simulations of corresponding event rates for the veritas and two proposed cherenkov telescope array sites : meteor crater and yavapai ranch , which use representative agn neutrino flux models and take into account topographic conditions of the detector sites . the calculated neutrino sensitivities depend on the observation time and the shape of the energy spectrum , but in some cases are comparable or even better than corresponding neutrino sensitivities of the icecube detector . for veritas and the considered cherenkov telescope array sites the expected neutrino sensitivities are up to factor 3 higher than for the magic site because of the presence of surrounding mountains . | in this paper , detailed monte carlo simulations have been employed to evaluate the sensitivity of air cherenkov telescopes to high - energy cosmic tau neutrinos in the pev to eev energy range coming from the horizon . the simulations use recent predictions for neutrino fluxes in agn flares to calculate expected event rates at the veritas site and two future locations of cherenkov instruments : meteor crater and yavapai ranch , taking into account the local topographic conditions . the calculated neutrino rates are comparable to what has been estimated for the icecube neutrino telescope assuming realistic observation times for cherenkov telescopes of a few hours . for models with significant neutrino fluxes at energies above @xmath46ev , the sensitivity of cherenkov telescopes actually surpasses that of icecube . for the sites considered , the expected event rates are up to factor three higher compared to what is expected for the la palma site ( magic ) . 201 t.k gaisser and t.stanev , astropart . 39 - 40 ( 2012 ) 120 . k. koyama et al . , nature 378 ( 1995 ) 255 . a.m. atoyan , c.dermer , new astron . 48 ( 2004 ) 381 . a.neronov , m.ribordy , phys . d 80 ( 2009 ) 083008 . a.mucke , et al . , astropart . . 18 ( 6 ) ( 2003 ) 593 . aartsen et al.,science 342 ( 2013 ) 1242856 . i. cholis and d. hooper jcap 06 ( 2013 ) 030 ; w. winter , phys . rev . d 88 , ( 2013 ) 083007 ; o. kalashev , et al . lett . 111 ( 2013 ) 041103 ; e. roulet et al . ; jcap 01 ( 2013 ) 028 ; f.w . stecker , phys . d 88 ( 2013 ) 047301 ; h.n ha et al . , phys . rev . d 87 ( 2013 ) 063011 ; k. murase et al . d 88 ( 2013 ) 121301 ; l. anchordoqui et al . , d 89 ( 2014).083003 ; m.c . gonzalez - garcia et al . , astropar . 57 ( 2014 ) 39 ; s. razzaque , phys . d , 88 ( 2013 ) 081302 . d. fargion , astro - ph/9704205 ; astro - ph/0002453 ; the astrophysical journal 570 ( 2002 ) 909925 . d. fargion et al . , report no he.6.1.10 ; icrc ( 1999),he 6.1.09 , p.396 - 398.1999 . kieda , m. salamon , b. dingus(usa ) ; d. fargion et al . , the astrophysical journal 613 ( 2004 ) 1285 - 1301 . h. athar , g. parente , e. zas , phys . d62 ( 2000 ) 093010 . a. letessier - selvon , aip conf . 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cold fronts sharp discontinuities recently discovered by chandra in many clusters of galaxies are believed to be due to a hot gas flow over a colder gravitationally bound gas cloud . epsf # 1= # 1#2=.99 = .99 # 1#2#3=.31 = .31 = .31 [ firstpage ] galaxies : clusters : individual : a3667 , x - rays : galaxies : clusters | i | astro-ph0403440 | cold fronts sharp discontinuities recently discovered by chandra in many clusters of galaxies are believed to be due to a hot gas flow over a colder gravitationally bound gas cloud . we analyze the stability of the fronts with respect to kelvin - helmholtz instability and show that an intrinsic width of the interface of the order of a few per cent of the curvature radius strongly limits the growth of perturbation . for the best studied case of a front in the cluster abell 3667 we conclude that current observational data on the width and extent of the front can be explained even in the absence of dynamically important magnetic fields . epsf # 1= # 1#2=.99 = .99 # 1#2#3=.31 = .31 = .31 [ firstpage ] galaxies : clusters : individual : a3667 , x - rays : galaxies : clusters | cold fronts were discovered as sharp features in the x - ray surface brightness distribution in chandra observations of the clusters a2142 and a3667 ( markevitch et al . , 2000 , vikhlinin , markevitch & murray , 2001a ) , see also markevitch et al . similar features have now been found in several other clusters ( e.g. sun et al . , 2002 , kempner , sarazin & ricker , 2002 ) . unlike shocks , these features have lower gas temperature on the x - ray brighter side of the discontinuity . for that reason they are called `` cold fronts '' . it is believed that some cold fronts are formed when a subcluster merges with another cluster and the ram pressure of gas flowing outside the subcluster gives the contact discontinuity the characteristic curved shape . indeed , features resembling cold fronts are found in numerical simulations of cluster formation ( bialek , evrard & mohr , 2002 , nagai & kravtsov , 2003 ) . ablation of the gaseous cloud by the hot gas causes characteristic differential motion of the gas inside the subcluster , which transports the low entropy gas from the subcluster core towards the contact discontinuity , thus enhancing the jump in temperature and surface brightness across the discontinuity ( heinz et al . 2003 ) . here we address the question of the front stability . as was pointed out by vikhlinin et al . ( 2001a , b ) , vikhlinin and markevitch ( 2002 ) the observed fronts are narrow and could be unstable to the kelvin - helmholtz ( kh ) instability . for a3667 however the front appears to be narrow ( less than @xmath05 kpc in width ) up to @xmath030from the stagnation point . magnetic fields can act as a stabilizing agent thus allowing indirect estimates of the field strength near the front ( vikhlinin , markevitch & murray,2001b ) . on the other hand numerical simulations without magnetic field ( and in particular relatively high resolution simulations by heinz et al . 2003 ) do not show instability of the front within 20 - 30 . while this discrepancy could be due to numerical effects , we revisit the question of the front stability below and show that the characteristic convex geometry and finite ( small ) intrinsic width of the interface may help to stabilize the discontinuity with respect to kh instability . the structure of the paper is as follows . in section 2 we derive a simple expression for the growth of the kh instability along the curved interface . in section 3 we argue that diffusion processes are likely to set an approximately constant width for the interface . in section 4 we discuss astrophysical applications . the last section summarizes our findings . |
colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced . we consider the latter case here . small - angle scattering prevails at all energies . some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms . the steep gaussian peak at small angles is followed by the exponential ( orear ) regime with some shoulders and dips , and then by a power - law drop . results from various theoretical approaches are compared with experimental data . * 4.1 the diffraction cone and geometrical approach . * * 4.1.4 reggeon exchanges . * * 4.1.5 the qcd - inspired models . * * 4.4 the hard scattering at large angles . * * 4.4.1 the dimensional counting . | i | 1206.5474 | colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced . we consider the latter case here . although inelastic processes dominate at high energies , elastic scattering contributes considerably ( 18 - 25@xmath0 ) to the total cross section . its share first decreases and then increases at higher energies . small - angle scattering prevails at all energies . some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms . the steep gaussian peak at small angles is followed by the exponential ( orear ) regime with some shoulders and dips , and then by a power - law drop . results from various theoretical approaches are compared with experimental data . phenomenological models claiming to describe this process are reviewed . the unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power - law , hard parton scattering regime under high momentum transfer . data on the interference of the coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude . the real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude ( the so - called overlap function ) at nonforward transferred momenta are also discussed . problems related to the scaling behavior of the differential cross section are considered . the power - law regime at highest momentum transfer is briefly described . * elastic scattering of hadrons * if only you knew what trash gives rise + to verses that are nt ashamed uprise + a. akhmatova + @xmath1 * 1 introduction . * * 2 the main relations . * * 3 where do we stand now ? * * 4 experimental data and phenomenological models . * * 4.1 the diffraction cone and geometrical approach . * * 4.1.1 the geometry of the internal hadron structure . * * 4.1.2 the modified fraunhofer diffraction . * * 4.1.3 electromagnetic analogies . * * 4.1.4 reggeon exchanges . * * 4.1.5 the qcd - inspired models . * * 4.2 the intermediate angles : the dip and the orear regime . * * 4.2.1 the gaussian fits . * * 4.2.2 the phenomenological models . * * 4.2.3 the unitarity condition . * * 4.2.4 the overlap function and the eikonal . * * 4.2.5 the real part of the elastic scattering amplitude at nonzero transferred momenta . * * 4.3 scaling laws . * * 4.4 the hard scattering at large angles . * * 4.4.1 the dimensional counting . * * 4.4.2 coherent scattering . * * 5 discussion and conclusions . * * references . * pacs numbers : 13.85.dz elastic scattering ; 13.75.cs nucleon - nucleon interactions key words : cross section , amplitude , slope , diffraction , orear regime , partons | hadron interactions are strong and , in principle , should be described by quantum chromodynamics ( qcd ) . however , experimental data show that their main features originate from the non - perturbative sector of qcd . only comparatively rare processes with large transferred momenta can be treated theoretically rather successfully by perturbative methods due to the well - known property of the asymptotical freedom of qcd . hence , in the absence of methods for a rigorous solution of qcd equations , our understanding of the dynamics of the main bulk of strong interactions is severely limited by model building or some rare rigorous relations . in fact , our approach to high - energy hadronic processes at present is at best still in its infancy . as has been learned from experiment , strong interactions of colliding high - energy particles give rise to inelastic and elastic processes . some new particles ( mostly pions ) are produced in inelastic processes , which are the most probable ones , comprising 75@xmath0 to 80@xmath0 of all processes at high energies . most created particles have comparatively small transverse momenta . at the same time , in 25@xmath0 to 20@xmath0 of events , the colliding particles do not change their nature and scatter elastically , declining at some angle from their initial trajectories . the only information about this process available from experiment is obtained by the measurement of the differential cross section ( proportional to the probability ) of elastic scattering at some angle at a given energy . in a very tiny range of extremely small angles , the charged particles scatter due to electromagnetic forces . but the dominant process of elastic scattering due to strong interactions proceeds at somewhat larger angles in the so - called diffraction cone . the differential cross sections are heavily weighted toward small transferred momenta exhibiting a huge peak . the scattering angle is still rather small there and becomes smaller and smaller as the energy increases . the probability of scattering at a given angle in this region decreases steeply , similarly to a gaussian exponential . noticeably less than one percent of particles are elastically scattered to larger angles outside this diffraction cone . the gaussian behavior is replaced there by a simple exponential one with some shoulders and ( or ) dips . at ever larger angles ( or transferred momenta ) , a power - like decrease has been observed . at angles close to @xmath2 , some additional flattening is seen . the elastic cross section ( the integral of the differential distribution over angles or transverse momentum ) depends on the energy of the colliding partners . at high energies , it shows a steady tendency to become larger with an increase in energy . we note that the inelastic cross section also increases , such that their sum ( the total cross section ) increases as well . the process of elastic scattering of hadrons has been studied experimentally in a wide energy region with different initial particles . at high energies of colliding partners , the most detailed results are available for the scattering of protons ( @xmath3 ) and antiprotons ( @xmath4 ) on protons . we mainly discuss these data , sometimes referring to other colliding partners of protons such as pions and kaons . some surprises in the behavior of the differential cross sections appeared in the 1960s when the very first experimental data on elastic @xmath3 and @xmath5 scattering were obtained at energies between 6.8 and 19.2 gev in the laboratory system @xcite ( the total energy in the center - of - mass system ( cms ) is only @xmath6 4 - 6 gev ! ) . the diffraction cone behavior changed at larger transferred momenta @xmath7 to a slower @xmath8-dependence . somewhat later , the energy range was extended to 50 gev @xcite . with the advent of new accelerators , the data for @xmath3 scattering at energies @xmath9 19 , 20 , 23 , 28 , 31 , 45 , 53 , 62 gev were published @xcite and the data for @xmath4 at 31 , 53 , 62 , 546 , 630 , 1800 , 1980 gev @xcite appeared . the early results are reviewed in refs @xcite . the compilation of the data can be found in @xcite . only recently , the results of the totem collaboration at the lhc on elastic @xmath3 scattering processes at @xmath10 = 7 tev were published @xcite . surely , these results asked for their understanding and theoretical interpretation . the most important task is to acquire some knowledge about the internal structure of colliding particles by deciphering the information supplied by experimental data about the dependence on energy and transferred momentum . the transferred momentum is directly related to the size and the structure of those regions inside the hadron that participate in the interaction . many phenomenological models have been proposed . most of them aspire to be `` a phenomenology of everything''@xmath11 related to elastic scattering of hadrons in a wide energy range . doing so in the absence of applicable laws and methods of the fundamental theory , they have to use a large number of adjustable parameters . the free parameters have been determined by fitting the model results to the available experimental data . even then , their predictions often fail when a new energy domain becomes available . and `` the verse''@xmath11 does not grow anymore ! ( if not recultivated . ) independent of their success and failure , we are sure that , `` in the long run , the physical picture may be expected to be much more important than most of the detailed computations '' @xcite . in what follows , we mention and discuss many of them . the scattering of charged particles at extremely small angles is completely dominated by the coulomb amplitude . the absolute value of the born amplitude is well known . the phase of the coulomb amplitude varies depending on the model chosen . however , this variation is rather mild in the considered tiny region of extremely small angles . the interference of the coulomb amplitude with the strong - interaction ( nuclear ) amplitude in the transition region where they are almost equal has been used for the experimental determination of the ratio of the real to imaginary parts of the latter . this interference also depends on the chosen form of the nuclear amplitude . theoretically , this ratio can be estimated with the help of dispersion relations . we briefly discuss this problem and show how the obtained results influence our analysis of scattering at somewhat larger angles . the most numerous group of models deals with phenomenological attempts to describe the main bulk of elastic scattering at small angles in the diffraction cone . in general , they are based on some geometrical models of particle substructure , with peripheral regions playing the decisive role . the approach using the reggeon ( pomeron ) exchanges is the most popular among them . the approximately gaussian ( in angles ) shape of the experimentally measured differential cross section in this region has been fitted just in this way . in addition to it , the simplest classical expressions for diffractive processes and results on the electromagnetic form factors are also used . however , the bold extension of the obtained results to larger angles is usually not very successful , even though some new parameters are introduced . particles scattered at larger angles give insight into the deeper internal regions of particle structure . the multiple iteration ( rescattering ) of diffractive processes may explain the region of angles that are somewhat larger than the diffractive ones . without any additional model building , it can be described as a consequence of the unitarity condition . the only necessary input is the experimentally known energy behavior of the diffraction cone slope and the total cross section . it predicts the observed exponential fall - off with angles and damped oscillations imposed on it , which , depending on their amplitudes , lead to shoulders or dips of the differential cross sections . at somewhat larger angles , the elastic processes may be considered to be dominated by the innermost constituents of the colliding particles . the perturbative qcd approach to hard parton scattering convoluted with some results on the parton structure of colliding particles is then used to describe experimental data . this approach predicts the power - like angular dependence of the differential cross sections . it has been seen in experiment . the dimensional ( or quark ) counting of the number of participating partons has been successful . the convolution with the internal structure of particles implies some coherence in the behavior of its constituents : all of them should coherently turn at the same angle . a particle should not be destroyed during the collision , and its internal wave function must be left intact . therefore we can call such processes coherent large - angle scattering . at angles close to @xmath2 , the effects of symmetrization of the corresponding amplitudes may become important and lead to some flattening of the differential distribution . there are no strict definitions of the lower and upper bounds of these regions . the diffraction peak shrinks with energy , such that the exponential fall - off with squared transferred momenta @xmath8 terminates at ever smaller values . correspondingly , the dip after it shifts to smaller values of @xmath7 as does the @xmath12-exponential . at low energies , this regime approximately occupies the interval between 0.8 and 2 gev@xmath13 , while in the lhc , it has moved to 0.4 - 1.5 gev@xmath13 . according to the qcd prejudice , the scale for parton scattering should be set above 1 gev@xmath13 . this is actually observed with a power - like decrease starting somewhere around @xmath141.5 - 2 gev@xmath13 at the lhc . hence , we can speak , at least , about five subregions of elastic scattering . we mainly discuss three of them : the diffraction cone , the orear regime and coherent hard parton scattering . the diffraction cone is well known to us from semiclassical effects . the regions beyond it became noticeable only at energies of colliding particles above several gev , where processes of scattering at sufficiently large angles or transferred momenta are observable . they persist up to the present lhc energy of 7 tev . who ordered them and whether they will they survive at ever higher energies are also the questions to be discussed in this review . its structure of this paper is as follows . the main relations between different characteristics of elastic scattering are presented in section 2 . then , in section 3 , their global dependences on energy and transferred momenta are discussed , together with our attempts to understand their implications within the simplest approaches . a more detailed analysis of experimental data in the framework of different theoretical ideas and approximations is the content of section 4 . finally , the general picture is briefly discussed in section 5 . we do not consider the scattering of polarized particles , and the spin structure of the amplitude is ignored . |
problems related to the scaling behavior of the differential cross section are considered . the power - law regime at highest momentum transfer is briefly described . * * 4.1.1 the geometry of the internal hadron structure . * * 4.1.2 the modified fraunhofer diffraction . * * 4.1.3 electromagnetic analogies . * 4.2.4 the overlap function and the eikonal . * * 4.4.2 coherent scattering . * * 5 discussion and conclusions . | r | 1206.5474 | colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced . we consider the latter case here . although inelastic processes dominate at high energies , elastic scattering contributes considerably ( 18 - 25@xmath0 ) to the total cross section . its share first decreases and then increases at higher energies . small - angle scattering prevails at all energies . some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms . the steep gaussian peak at small angles is followed by the exponential ( orear ) regime with some shoulders and dips , and then by a power - law drop . results from various theoretical approaches are compared with experimental data . phenomenological models claiming to describe this process are reviewed . the unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power - law , hard parton scattering regime under high momentum transfer . data on the interference of the coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude . the real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude ( the so - called overlap function ) at nonforward transferred momenta are also discussed . problems related to the scaling behavior of the differential cross section are considered . the power - law regime at highest momentum transfer is briefly described . * elastic scattering of hadrons * if only you knew what trash gives rise + to verses that are nt ashamed uprise + a. akhmatova + @xmath1 * 1 introduction . * * 2 the main relations . * * 3 where do we stand now ? * * 4 experimental data and phenomenological models . * * 4.1 the diffraction cone and geometrical approach . * * 4.1.1 the geometry of the internal hadron structure . * * 4.1.2 the modified fraunhofer diffraction . * * 4.1.3 electromagnetic analogies . * * 4.1.4 reggeon exchanges . * * 4.1.5 the qcd - inspired models . * * 4.2 the intermediate angles : the dip and the orear regime . * * 4.2.1 the gaussian fits . * * 4.2.2 the phenomenological models . * * 4.2.3 the unitarity condition . * * 4.2.4 the overlap function and the eikonal . * * 4.2.5 the real part of the elastic scattering amplitude at nonzero transferred momenta . * * 4.3 scaling laws . * * 4.4 the hard scattering at large angles . * * 4.4.1 the dimensional counting . * * 4.4.2 coherent scattering . * * 5 discussion and conclusions . * * references . * pacs numbers : 13.85.dz elastic scattering ; 13.75.cs nucleon - nucleon interactions key words : cross section , amplitude , slope , diffraction , orear regime , partons | as always , our knowledge about particular physical processes is limited by the practical possibility of measuring their characteristics . as mentioned above , numerous experimental data on the elastic scattering of hadrons at various angles and at different energies have been obtained . unfortunately , in some of them the available region of angles is strongly limited by the experimental setup . therefore , a comparison with theoretical proposals is possible only in the corresponding range of angles and energies . the data and their fits at various energies and in different intervals of transferred momenta for different participating particles are so numerous that it is impossible to show all of them in a single review paper . therefore , from the very beginning , we use the latest results of the totem collaboration at the highest lhc energy , 7 tev , as a reference point @xcite . the discussion of theoretical models is also concentrated near these data . the total and elastic cross sections at 7 tev are respectively estimated as 98.3 mb and 24.8 mb .. the figures from published papers @xcite demonstrating the behavior of the differential cross section as function of the transferred momentum are displayed below . they clearly confirm the existence of the three regions discussed above . the cross section shape in the region of the diffraction cone @xcite is shown in fig . the @xmath164-exponential behavior with @xmath16520.1 gev@xmath145 is clearly seen at @xmath166 gev@xmath13 . the peak steepens at the end of the diffraction cone , and its slope becomes approximately equal to 23.6 gev@xmath145 in the @xmath7 interval of ( 0.36 0.47 ) gev@xmath13 . the results at somewhat larger angles @xcite in the orear region are presented in fig . the dip at @xmath167 gev@xmath13 with a subsequent maximum at @xmath168 gev@xmath13 and the @xmath12-exponential behavior are demonstrated . some curves , corresponding to different model predictions , are also drawn here . the same data as in fig . 2 are shown in fig . 3 , but with more details , including the steepend slope , the dip position , and the region of @xmath169-behavior . the last one is ascribed to the hard parton scattering processes . we congratulate all members of the totem collaboration with this fantastic achievement ! their efforts are truly appreciated when estimating the values of angles at which the measurements had to be done . they were even smaller than 10@xmath170 ! detectors had to be installed at very long distances from the collision point to obtain results at low transferred momenta . these data revived interest to elastic scattering . theoretical models usually describe the diffraction cone and values of total and elastic cross sections related to it more or less precisely ( therefore , their fits , that are almost indistinguishable in that region , are not drawn in fig . however , all of them fail to quantitatively predict the behavior of the differential cross section outside the diffraction cone as can be seen in fig . the predictions of five models @xcite are drawn here . they are very widely spread around the experimental line . we can conclude that just this region becomes the occam razor for all models . in what follows , we consider these models , as well as some others , in more detail . 1 . the differential cross section of elastic proton - proton scattering at @xmath10=7 tev measured by the totem collaboration ( fig . 4 in @xcite ) . + the region of the diffraction cone with the @xmath7-exponential decrease is shown . the differential cross section of elastic proton - proton scattering at @xmath10=7 tev measured by the totem collaboration ( fig . 4 in @xcite ) . + the region beyond the diffraction peak is shown . the predictions of five models are demonstrated . 3 . the differential cross section of elastic proton - proton scattering at @xmath10=7 tev measured by the totem collaboration ( fig . 3 in @xcite ) . + the same regions as in fig . 2 are shown with the values of the steepened slope at the outskirts of the diffraction peak , the position of the dip and the power - like behavior at the largest transferred momenta . the three intervals of @xmath7 ( the diffraction cone , the orear regime , and the region of hard parton scattering ) are characterized by different dynamical content , as we understand it now . they require separate approaches to their descriptions . it seems reasonable that these regions are regulated by different but interrelated physical mechanisms . in particular , different spatial regions of overlapping colliding objects are responsible for corresponding effects . three subsections 4.1 , 4.2 and 4.3 are devoted to theoretical approaches to their explanation . the internal structure of colliding , strongly interacting particles plays a crucial role in the outcome of their collisions . in high - energy hadron - hadron scattering , each hadron behaves as an extended object . they can be described by their size and the density of their constituents . the simplest models are demonstrated in table 1 . since long ago , it has been believed that hadrons contain some denser core surrounded by a meson ( pion ) cloud at their periphery . this idea was a cornerstone of the one - pion exchange model , which was first proposed in ref . @xcite to describe particle production in peripheral interactions . it evolved into the well - known multiperipheral and ( multi)reggeon exchange models ( see , e.g. , @xcite for early review papers ) . they are rather successful in describing many features of multiparticle production processes . the multiperipheral approach developed , for instance , in the framework of the bethe - salpeter equation ( see ref . @xcite ) can be considered an attempt to account for the @xmath8-channel unitarity . nowadays , it is commonly believed that , at very high energies , the total cross section is dominated by peripheral events . in modern parlance , this is related to the long - range nature of the field of `` perturbatively massless '' gluons . the exchanged boson mass may mimic a nonperturbative mass gap in qcd with the `` effective '' gluon mass of the order of 1 gev and a gluon - gluon correlation length about 0.3 fm . the pion mass scale is rather small , and more general `` boson '' exchange is preferred . the weight factors of different mass scales take the impact parameter distribution of the particle opacity into account . the role of inelastic channels in describing elastic scattering can be revealed by understanding the origin and prescribing a definite shape to the overlap function @xmath171 in the @xmath30-channel unitarity condition ( [ unit ] ) or , equivalently , to its fourier transform in the impact parameter picture . the scattering is mainly diffractive , i.e. , it is due to the absorption of incoming waves in many open inelastic channels . its quantitative field - theory treatment presents a serious unsolved problem . the overlap function contains the sum of products of a matrix element of the inelastic process with a particular final state and the complex conjugate matrix element with the same final particles content . however , their kinematical difference must be taken into account , due to the fact that the two final protons are scattered at an angle @xmath22 relative to the initial ones . correspondingly , the overlap of the momentum distributions of the intermediate inelastic @xmath172-particle states is nontrivial kinematically and , what is especially important , the phases of these matrix elements become crucial . the phases are related to the position in space where particles are produced . it has been pointed out in many papers @xcite that only the phase cancellation effect , which is closely related to particle correlations in inelastic processes , can lead to a realistic shape of the diffraction cone . the problem of properly accounting for them has not yet been solved . at the same time , elastic scattering should be less peripheral because of a larger number of exchanged objects if regarded as an @xmath30-channel iteration of the overlap function . the great difficulty in transferring large momenta reveals itself already in the sharp shape of the forward diffraction peak . there have been numerous attempts to understand it in terms of the peripheral approach ( see , e.g. , @xcite ) . unfortunately , no framework for commonly accounting both the @xmath30- and @xmath8-channel unitarity conditions has been developed . in general , there have been many ideas proposed for describing elastic scattering processes , but no cogent theoretical arguments to justify the particular forms relying mainly on `` intuition '' have been offered . the fact that they are very simple is usually the only advantage . any strict interpretation is an idealization and as such it should not be expected to be exactly true . the key elements of the geometric approach are : the use 1 ) of the impact parameter picture with fourier - bessel transformation ( [ eik ] ) , ( [ hsb ] ) from the transferred momenta amplitude to the spatial description , 2 ) of eikonal approximation ( [ eik ] ) , and 3 ) of unitarity condition ( [ unib ] ) . the @xmath53-matrix in the impact parameter picture is chosen in the exponential form @xmath173 and the convolution approximation for the real opacity @xmath174 for elastic @xmath175 scattering is used : @xmath176 here , @xmath177 denotes the convolution of hadronic matter density distributions @xmath178 for @xmath15 and @xmath28 . @xmath179 is an energy - dependent factor . the assumptions about the validity of the eikonal approximation , the nearly imaginary character of the scattering amplitudes at low transferred momenta , the proportionality between the hadronic matter distribution and the electric charge distribution , the exponentiation of the @xmath53-matrix in @xmath62-space , and the validity of unitarity condition ( [ unib ] ) are widely used . the droplet model @xcite for elastic collisions was the first to fully exploit all the above elements . particles were pictured as very much similar to nuclei . correspondingly , the notion of the density distribution @xmath178 inside a particle was introduced such that @xmath180 in potential models it corresponds to the wkb approximation . for the gaussian shape of @xmath71 , it is possible to solve for @xmath178 from ( [ dens ] ) , obtaining the function familiar in the theory of bose - einstein condensation of free particles @xcite . in the droplet model , the properties of the disk are independent of the energy at sufficiently high energies . many diffractive minima in the differential cross section have been predicted . the dipole form factors in the @xmath8-representation led to @xmath181 with a shape of the modified bessel functions , which allowed fitting differential cross sections at isr energies @xcite . the intuitive picture of high - energy hadron collisions as two extended objects breaking in fragments ( and thus defining the overlap function ! ) has promoted the hypothesis of limiting fragmentation @xcite inspired by the droplet model . models based on consideration of tower diagrams @xcite predict that the disk becomes larger and more absorptive as energy increases . both the black core and gray fringe expand with energy and become more absorptive . the first estimates of the radii of protons , pions , and kaons from their form factors @xcite showed that protons are larger than pions and kaons . this is not surprising in view of the smaller cross sections of @xmath5 and @xmath182 interactions than those of @xmath3 . the typical size is somewhat smaller than 1 fm . the proton hadronic matter distribution was fitted by a dipole form similar to the electric form factor but with the energy - dependent radius . other early attempts to consider elastic scattering of hadrons also stemmed from the analogous simple geometrical treatment of their internal structure @xcite . later , more complicated models were used . the main focus is , surely , on processes at small angles within the diffraction cone . they define the bulk contribution to the elastic scattering cross section due to the steep fall - off of the distribution with increasing angles . different models happen to fit experimental data in the cone quite well in a wide energy range . but they fail outside the diffraction peak , as mentioned above . large - angle scattering requires more central collisions with a lower impact parameter to probe the internal content of particles . therefore , these regions of transferred momenta are discussed separately below . some ideas stemmed from regularities in inelastic processes . the multiplicity distributions of created particle are closely related to the purely geometric notion of the centrality of collisions . when the scaling of multiplicity distributions @xcite was supported by experimental data , the proposal of the geometric scaling @xcite for the elastic amplitude was promoted . the difficulties in accelerating the various parts of a nucleon without breaking it up had to be accounted for . the basic idea of the geometric scaling is that , at sufficiently high energies , the amplitude @xmath63 depends on a single variable , the scaling parameter @xmath183 : @xmath184 this idea has led to several predictions at asymptotically high energies and is still actively being debated now . such scaling was proved @xcite for cross sections increasing as @xmath185 and for an infinitesimally small ratio of the real to imaginary part of the amplitude @xmath186 at @xmath102 . the latest results on @xmath88 discussed in subsection 4.2.5 do not support this assumption . the purely geometrical standpoint is adopted in refs @xcite . the three regions in the behavior of the differential cross section are clearly reflected in the three spatial scales of the internal hadronic structure considered in @xcite . the authors of this three - scale model claim that the nucleon has an outer cloud of the quark - antiquark condensate , an inner shell of the baryonic charge density , and a still smaller internal core of massless color - singlet valence `` quarks '' surrounded by low-@xmath163 gluon clouds about 0.3 fm in size . this picture is shown in fig . 4 . fig . the nucleon structure according to the model @xcite . + the three regions of the internal structure are supposed to be directly responsible for the three regimes in the behavior of the differential cross section . the diffraction cone is described as a result of cloud - cloud interaction , represented by a class of potentials containing the sum of the modified bessel functions . the least massive exchanged quanta are the most important ones . at larger momentum transfers , the baryonic charge at intermediate distances is probed by the @xmath187-exchange . the internal region filled in by the valence quarks starts playing its role in the presence of even larger transferred momenta . the diffraction profile function , which defines the range of different densities and , correspondingly , different forces , is taken to be @xmath188 . \label{gisl}\ ] ] the parameters @xmath189 and @xmath135 are energy dependent , @xmath190 and @xmath191 is a coupling strength ; @xmath95=1 gev@xmath13 . these functions render the shape of the differential cross section , similar to the fraunhofer diffraction ( see subsection 4.1.2 ) , with the form factor proportional to @xmath192 ( @xmath193 is an adjustable parameter ) proposed a long time ago @xcite . this form factor also extends somewhat to transferred momenta outside the diffraction cone . unfortunately , the contemporary phenomenological analysis of experimental data is not able to determine the impact parameter profiles unambigously . the scattering due to @xmath187-exchange is parameterized by the product of the @xmath187-propagator and two form factors @xmath194 directly in the @xmath195-representation : @xmath196 the amplitude due to quark - quark scattering has two `` structure factors '' @xmath197 of valence quarks ( different from the above form factors ! ) , the propagator with the black disc radius @xmath198 of @xmath199 asymptotic scattering and @xmath30-dependent factors with the hard pomeron intercept equal to @xmath200 : @xmath201 in total , there are seventeen adjustable parameters in the model . as mentioned in @xcite , the fits according to this model predict too low value of the slope @xmath28 at @xmath7=0.4 gev@xmath13 and strongly disagree with experiment at 7 tev outside the diffraction peak ( see fig . 2 ) . formulas ( [ omisl ] ) , ( [ qqisl ] ) are aimed to improve the fit just in this region , but they do not help . in general , an internal region of the nucleon where the gluons cluster around the original valence quarks resembles the valon model @xcite . similar pictures arise in the qcd - inspired models discussed below . surely , some care should be taken for any such model to be accepted and the geometric picture to be considered seriously , especially in view of its success or failure to describe experimental data in the whole range of transferred momenta at various energies . for a long time ( see , e.g. , ref . @xcite ) , the formulas of classical diffraction of light on a ( black or grey ) disk with the traditional bessel functions have been used for hadronic reactions . recently , an analogous expression for the elastic amplitude was considered in ref . @xcite : @xmath202 . \label{ugal}\ ] ] the free parameters in arbitrarily chosen analytic expression ( [ ugal ] ) are @xmath203 . the first term resembles the expression for the black disk ( [ bdis ] ) . the suppression at large transferred momenta is assumed to be approximated by the form factor in front of the bessel functions . in the impact parameter representation this shape corresponds to the ordinary fermi profile used , e.g. , in refs @xcite and shown in eq . ( [ gisl ] ) : @xmath204 the second term in ( [ ugal ] ) in brackets takes the contribution due to the real part of the amplitude into account . it should smooth the behavior of the differential cross section near zeros of the first term . this seems to be the only difference from the first component of the previously discussed model @xcite . and , again , comparison with experimental data shows that the results of fits are satisfactory in the diffraction cone , but not outside it . the form factor in front of common bessel functions does not fit the large @xmath7 trends of experimental distributions . throughout these developments , modifications of early guesses have been found necessary , but the general spirit of the geometrical description remains immutable and viable . the strongly interacting content of hadrons is often considered to be similar to their electromagnetic substructure @xcite . similarly to the droplet model , the assumption of the proportionality between the hadronic matter distribution and the electric charge distribution is used in many models . however , in most of them , the electromagnetic form factors are used in combination with reggeon exchanges because , considered alone , they do not reproduce the energy dependence of the main characteristics . however , the assumption about the full congruence of these distributions is not necessarily valid , since gluons do not carry an electric charge even though they play an important ( if not decisive ) role in high - energy strong interactions . that is why the charge and matter distributions in some models are parameterized separately or some corrections are added . using the experience from calculation of tower diagrams in electrodynamics and the impact - parameter representation , it was proposed @xcite that the possibility of choosing the opacity @xmath205 in a factorized form be considered : @xmath206 where @xmath207 is chosen to be crossing symmetric under @xmath208 and to reproduce the energy dependence of the pomeron , considered as a fixed regge cut , @xmath209 while @xmath210 is taken as the bessel transform of @xmath211 here , @xmath212 stands for the proton `` nuclear form factor '' , parameterized like the electromagnetic form factor with two poles : @xmath213 other factors with the parameter @xmath135 are introduced `` by hand '' . they can be treated just as a correction due to the different shapes of distributions of charge and matter . there are six adjustable parameters in total used at high energies if the regge background is neglected . the noticeable @xmath8-dependence of the slope @xmath214 in the diffraction cone is predicted . however , its values at 7 tev are lower than experimental ones ( about 18 gev@xmath145 instead of 20.1 gev@xmath145 ) at @xmath215 gev@xmath13 , slightly exceed them in the tiny interval near 0.35 gev@xmath13 and do not reach the value 23.6 gev@xmath145 mentioned above . this model is close to the totem data @xcite for the dip position and the exponential at very large @xmath7 , but predicts values of the differential cross section in the orear range , @xmath216 0.36 gev@xmath13 , about twice as large ( see fig . in addition to the dip , some `` oscillations''@xmath11 at the transferred momenta of several gev@xmath13 are predicted ( up to the energy 6000 tev ) but not yet observed . in general , such structures appear as a byproduct of the eikonal approach and unitarization procedure ( see , e.g. , ref . their energy dependence is strongly determined by the parameters used in formula ( [ ss ] ) to account for the crossing symmetry property of the amplitude . the same parameters are crucial for the behavior of the real part of the amplitude . it is interesting that the model predicts the dominance of the imaginary part of the amplitude even at large transferred momenta . the real part becomes important only at zeros of the imaginary part . the dip and oscillations are noticeable precisely there . near the cone , the model predicts two zeros of the real part of the full ( coulomb + nuclear ) amplitude at @xmath2170.0064 gev@xmath13 and the nuclear amplitude alone at @xmath216 0.18 gev@xmath13 , as well as one zero of the nuclear imaginary part at @xmath2170.5 gev@xmath13 . in the differential cross section , the last zero is partly filled in by the real part . we note the difference between the power - like expression for @xmath218 and its exponential behavior in the traditional regge models . the exponentiation of this form of @xmath218 leads to additional oscillations . the similar but more complicated combination of the form factors has been used in refs @xcite . the authors consider the @xmath8-dependent mellin transforms of parton distributions and claim that the first moment defines the form factor of the standard pomeron @xmath197 , while the second moment @xmath219 corresponds to interaction attributed to three nonperturbative gluons . thus , the behavior of the differential cross section at small @xmath8 is determined by the elactromagnetic form factors and by matter distribution at large @xmath8 . the born term of the elastic scattering amplitude is written as @xmath220 where @xmath221 @xmath222 @xmath223 gev@xmath13 , @xmath224 gev@xmath13 , @xmath225 gev@xmath13 , @xmath226 gev@xmath145 . we note that the slope of the second term is chosen as one fourth of the first term . the final form of the amplitude is obtained after eikonalization of the born contribution using the opacity @xmath227 the total cross section at 7 tev was predicted to be equal to 95 mb . authors demonstrate good fits of @xmath3 and @xmath4 differential cross sections , as well as of @xmath38 , in a wide energy range , including the totem data . only five ( three for high energies and two for low energies ) adjustable parameters are claimed to be used if all above values are regarded as fixed . in fact , there are 10 such additional `` hidden '' parameters in total if the hard pomeron is also considered . surely , the contribution from secondary reggeons at lhc energies is negligible , i.e. , smaller than the experimental errors . the real part of the hadron amplitude is completely determined by the complex expression for @xmath228 . its @xmath8-dependence appears just as a byproduct of the eikonalization procedure . as a function of @xmath8 , it tends to zero at @xmath2290.16 gev@xmath13 at the energy of 7 tev . the interesting predictions of the @xmath8-behavior of @xmath88 at nonforward transferred momenta for different energies are presented . they are discussed in more details in subsection 4.2.4 . the regge - pole model is beyond dispute one of the most explored . it has already been noticed that the notion of regge trajectories has been used in the preceding subsections as well . the only reason to discuss these models there separately was their stronger inclination to the use of nonexponential electromagnetic form factors and geometric pictures in the @xmath30-channel approach . at the same time , reggeon models appeal mostly to the @xmath8-channel approach . the amplidutes with reggeon exchanges in the @xmath8-channel are the natural candidates for explaining the exponential decrease of the differential cross section ( [ diff ] ) with the squared transferred momentum @xmath230 inside the diffraction cone . just this shape is typical for them , because it follows from the linearity of regge trajectories . moreover , they predict the logarithmical increase of the hadronic radii as the energy increases , i.e. , the logarithmical increase in the cone slope @xmath28 or the corresponding shrinkage of the width of the diffraction cone . this prediction is also supported by experiment . in the common regge - pole models , the disk becomes larger and slightly more transparent as energy increases . the standard regge - type models @xcite use the combination of contributions due to the exchange by the ( multicomponent ) pomeron , odderon , and secondary reggeon trajectories corresponding to @xmath231 and @xmath187 mesons with or without the form factors chosen in a simple exponential form or as power - like expressions resembling the electromagnetic structure of colliding partners discussed in the preceding subsection . the price to be paid is the increased number of adjustable parameters at each step of sophistication . to be more or less realistic , one has to use the knowledge about some of them from other ( independent ? ) experimental results . but even under this condition , the ambiguity of their choice and sensitivity to fitted parameters leave some freedom in the conclusions . the amplitudes of @xmath3 and @xmath4 scattering are approximated by the sum of terms corresponding to the leading ( pomeron and odderon ) and nonleading ( @xmath231 and @xmath187 meson ) regge trajectories : @xmath232 , \label{appbar}\ ] ] where the labels @xmath233 stand for the relevant contributions . the sign in the @xmath3 and @xmath4 amplitudes differs for @xmath234-even and @xmath234-odd terms . the contributions of the nonleading regge poles are written as @xmath235 with @xmath236 . while the secondary trajectories are usually chosen in a standard linear way , the pomeron and odderon contributions can be regarded , for example , as dipoles with nonlinear trajectories @xcite @xmath237 , \label{apom}\ ] ] where @xmath238 the unknown odderon contribution is assumed to be of the same form as that of the pomeron . the parameters of the trajectories and of the absorption @xmath239 need to be adjusted . their nonlinearity may be connected with the two - pion threshold following from the @xmath8-channel unitarity @xcite . however , there could be double counting of the graphs with pomerons attached on both sides to the pion loop . this is well known from old peripheral models of inelastic processes , where the self - consistent bethe - salpeter equation had to be used for the proper account of the pion - nucleon vertices . different forms of nonlinear trajectories are in use . for instance , the pomeron trajectory is chosen in @xcite with four free parameters as @xmath240 the more complicated nonlinearity was used in @xcite . however , the use of the pion mass as a scale there is questionable in view of the above discussion . the origin of the pomeron and the parameterization of its trajectory are still being debated . there is no strict rule for choosing its shape . the dipole and even tripole forms of unitarized pomeron have been attempted . they mimic cut contributions @xcite . moreover , there are arguments in favor of two pomerons with different intercepts . even the fits with three pomerons are sometimes used @xcite . the soft pomeron contributes a term with the energy dependence @xmath241 to hadron - hadron total cross sections , and the hard pomeron makes a small ( at present energies ) contribution with a stronger energy dependence @xmath242 . these values of the intercepts stem from the discussions of hera data ( see , e.g. , @xcite ) . although the hard - pomeron exchange was unnecessary for describing hadron - hadron total cross sections up to energies @xmath10 below 1 tev , it may reveal itself at lhc energies , as argued in @xcite . the model in @xcite uses only two terms in the expansion for opacity : @xmath243 where @xmath244 stands for the contribution from single exchanges of reggeons ( two pomerons , @xmath231 , and @xmath187 ) with the adjustable parameter @xmath245 as well as for the triple - gluon exchange of the form @xmath246 needed at larger values of @xmath247 and matched at some @xmath248 to exponential shapes of the diffraction peak and to the dip region . certainly , adding such a term allows fitting the total cross section value at 7 tev , but there is a suspicion that the sharp increase of the hard - pomeron contribution will overpredict the cross sections at higher energies . the unitarization will become mandatory once again . the quality of the fit of the differential cross section beyond the diffraction peak is no better than of those fits shown in fig . several variant forms of born amplitudes and different kinds of eikonalization have been attempted . there is no consensus on their choice . the form of the eikonal similar to ( [ dola ] ) is chosen in @xcite with the exponential suppression @xmath249 \label{golo}\ ] ] for central interactions . the peripheral part of the pomeron interaction with the meson cloud is parameterized @xcite by a small term increasing with the energy and resulting in a @xmath250 exponential fall - off of the differential cross section . the geometric picture corresponds to a black disk with a grey fringe , similarly to the above - described model @xcite . in general , it is not easy to estimate the total number of the adjustable parameters in different models . there are parameters related either to @xmath8- ( @xmath62- ) or @xmath30-dependence . in some papers , it is often assumed that part of them are known from fits of other characteristics of hadron or electromagnetic interactions at various energies and can therefore be considered known beforehand . for example , it is claimed that the model in @xcite contains about 15 parameters . in this case , it is quite difficult to find the proper minima for the matrix of @xmath251 values . it is well known how unstable the final results can be : one has to choose the step - by - step procedure for doing this and use some special computer codes . there are 25 adjustable parameters shown in table 1 in papers @xcite . however , they include some values assumed to be apriori fixed in @xcite . at the same time , additional form factors were inserted in the formulas , albeit with preliminary `` fixed '' parameters . they were used to fit 982 @xmath3 and @xmath4 data points in a wide energy range . besides the elastic differential cross sections , the total cross sections and the ratios @xmath34 were considered . the fit in the interference region of coulomb and hadronic amplitudes with the same parameters helped in choosing among the different coulomb phases proposed previously . a similar situation is seen in the fits in ref . @xcite , where it is claimed that the number of parameters is much less ( 5 only ! ) . however , there are many others ( in particular , concerning the energy behavior and form factors ) that are hidden parameters . they are held fixed from the very beginning , as was discussed in subsection 4.1.3 . as mentioned before , the simple exponential form of the differential cross section in the diffraction cone is quite well described . this becomes possible mainly due to the @xmath8-shape of the pomeron trajectory ( [ apom ] ) and other reggeons contributions in ( [ areg ] ) . the fits in this region at the different energies shown , e.g. , in @xcite , are quite impressive . the evolution of the diffraction cone slope with energy is reproduced ( as described by @xmath252 in ( [ apom ] ) ) . unfortunately , the variety of forms of pomeron trajectories with different intercepts , slopes , and shapes of residues unitarized in different ways and/or substituted by regge - cuts is so large that it is impossible to show all of them in this review due to the limited space . the cuts with nonlinear trajectories mimic hard scattering @xcite . a common problem appears in predicting them at larger angles . the fit according to the model in @xcite seems to be most successful in predicting the position of the dip and the shape at large @xmath7 but exceeds the absolute value approximately twofold . the model in @xcite strongly underestimates it , with the wrong position of the dip and much slower decrease at @xmath253 gev@xmath13 . this is well demonstrated in fig . 2 and is also discussed below . we mention that all these papers follow the general approach proposed much earlier @xcite . they just deal with more detailed fits of newly available experimental data . each incident particle consists of a superposition of fock states with @xmath172 partons @xcite , which are scattered instantaneously and simultaneously by the other particle . some qcd - inspired models using this statement have been developed . the role of partons is played by quarks and gluons . the two competing mechanisms of hadron interactions , the increase in the density ( @xmath125 in table 1 ) and in the radius @xmath106 , determine their specific features . in qcd , they can be respectively ascribed to the leading order solution of the bfkl equation @xcite and to the long range ( weizscker - williams ) nature of the field of massless gluons . the density increase due to the bfkl - evolution leads to a power - like increase of the total cross section , which is nonunitary and violates froissart bound ( [ asymp ] ) . therefore , at the critical density of the order @xmath254 , the density saturation must be taken into account @xcite . the qcd evolution in all orders in the gluon density but in the leading logarithmic approximations is treated by the jimwlk equations @xcite . with account of multiple scattering effects , they can be simplified in the large @xmath255 limit to a single nonlinear bk equation for the gluon density @xcite when the induced field density is small . the density growth effects are preasymptotic . according to @xcite , they are described by a hard pomeron , while the growth of the size of the black saturated regions ( the radius ) is attributed to a soft pomeron . the hard pomeron manifests itself in small systems or in small subregions inside hadrons . the soft pomeron appears in hadronic systems of the typical size and is related to an increased size in the impact parameter space . only the increase due to the perturbative expansion in the transverse plane remains effective . there is no common consensus about this scenario proposed in ref . the soft pomeron is often used @xcite in attempts to explain the preasymptotic power growth of cross sections by an additional nonperturbative mechanism superimposed on the bfkl scenario of hard pomeron . it is ascribed mainly to the density growth of gluon clouds around quarks and not to the spatial scale of the interaction . even though the size of gluon clouds increases , it is still limited by a short separation from their source . the proton looks like three valence quarks surrounded by gluon clouds or spots with mean sizes about 0.3 fm , smaller than the proton radius , of the order of 1 fm . radiation of any additional gluon from the cloud adds the factor @xmath256 to the interaction cross section , and hence their sum gives a power - like term of the form @xmath257 with a large constant term @xmath258 and small @xmath259 . using the standard dipole form factors of protons and quasieikonal unitarization in the impact parameter space , the authors of this two - scale model @xcite fit many distributions with 10 parameters for @xmath8-dependence ( subject to 2 additional constraints ) and some parameters for the @xmath30-dependence . such fits are , of course , aimed at high energies of colliding protons where the effects of secondary regge - trajectories die out . they are mainly successful in the diffraction cone and , consequently , in describing the energy dependence of the total and elastic cross sections . such a form of the total cross section with an energy - independent term @xmath258 was proposed a long time ago @xcite and actively developed later @xcite in the framework of the parton model and semihard qcd , with the gluon - gluon interaction playing the main role . the main role of gluons is also incorporated in @xcite . the profile is chosen in a form containing the @xmath260-terms : @xmath261 where the impact parameter distribution functions are @xmath262 and the gluon - gluon interaction cross section is @xmath263 with @xmath264 . the froissart bound for the total cross section is reproduced with @xmath265 the parameter @xmath266 describes the area occupied by gluons in the colliding protons ( the size effect ) , and @xmath267 is defined via their gluonic structure functions and , therefore , controls their soft gluon content ( the density effect ) . again , being successful in the diffraction peak with its shape and normalization , the model in @xcite fails to predict the correct behavior of the differential spectrum outside it @xcite . its prediction is more than three times larger than the experimental value at the dip and subsequent maximum , while falling too steeply at ever higher @xmath230 above 1.5 gev@xmath13 ( see fig . 2 ) . attempts to consider the semihard scattering of quarks and gluons can be found in refs @xcite . the traditional partonic description of the process is considered in a series of papers @xcite . the partonic approach with a hard bfkl pomeron can be merged into the domain regulated by the soft pomeron . the transition from hard to soft is induced by absorptive multi - pomeron effects in a limited energy range . the evolution produces parton cascades , not strongly ordered in transverse momenta , with hot spots of a relatively small size in @xmath62-space . the saturation is driven by the enhanced multi - pomeron graphs , also regulating the high - mass dissociation . the calculations are done with a 3-channel quasi - eikonal unitarization using the opacity formalism . they reproduce the shapes of the differential cross sections from isr to lhc within the diffraction cone . another picture was considered in the framework of the functional integral approach in refs @xcite using the model of the stochastic vacuum and making the assumption that the proton has a quark - diquark structure of the color dipole i.e. two quarks out of three are close together in the transverse directions . a matrix cumulant expansion is used for vacuum expectation values of wegner - wilson loops @xcite related to hadronic amplitudes . the qcd vacuum parameters ( the gluon condensate or the string tension , the vacuum correlation length , and the parameter due to the non - abelian tensor structure ) , as well as the hadron size , have been used . the imaginary part of the amplitude in the @xmath62-representation was calculated . its contribution to experimentally measured quantities was shown to describe the isr and tevatron data in the diffraction peak reasonably well . a more phenomenological approach to the quark - diquark model was attempted in refs @xcite . as above , the correlated quark and diquark constituents are considered . according to the detailed analysis performed in @xcite from isr to lhc energies in the region @xmath268 gev@xmath13 , the model is able to describe the data quite well , even outside the diffraction peak , except the narrow strip around the dip . but it shows a much stronger dip ( by several orders of magnitude ) there than the experimentally observed one . moreover , similarly to the abovementioned calculations , the model ignores the contributions to the real part of the elastic scattering amplitude . as we saw previously , such contributions can smooth this dip . if so , their shape should drastically differ from that of the imaginary part , at least in this strip , as happened , for example , in the models with electromagnetic form factors @xcite . as long ago as the 1960s , experiments on elastic @xmath3- and @xmath5-scattering at comparatively low energies between 6.8 and 19.2 gev in the laboratory system @xcite showed that the steep exponential fall - off of the differential cross section as a function of the squared transferred momentum @xmath7 is replaced by a slower dependence at larger @xmath7 . they showed that just after the diffraction cone a shoulder was observed and , even more surprising , a behavior exponentially decreasing with the angle or with @xmath12 , which was called the orear regime after its investigator @xcite . the special session was devoted to these findings at the 1968 rochester conference in vienna . the shoulder evolved later into the minimum or dip at higher isr energies . it has also been observed at the lhc , as seen in figs 2 and 3 . it is interesting that at fnal - isr energies , @xmath10=6 - 60 gev , the exponential fall - off with an increase of @xmath269 was observed up to quite large values of @xmath229 10 gev@xmath13 @xcite , with the exponent in the range from 6.2 to 7 gev@xmath270 ( see table 7 in ref . it is even larger at the lhc ( about 8 - 9 gev@xmath270 ) . the region becomes more narrow and shifts to lower values of @xmath7 from 0.5 to 1.5 gev@xmath13 . the power - like regime already shows up at about @xmath2292 - 2.5 gev@xmath13 ( see fig . 3 ) . from the very beginning , it was noticed @xcite that it is possible to fit the differential cross sections at intermediate values of the momentum transfer by the dependence exponential in @xmath12 ( or @xmath22 ) except the relatively small shoulder region . to take that into account as well , it was primarely proposed @xcite to use fits with gaussian functions with alternating signs of the coefficients directly in the expression for the amplitude . the similar approach was later advocated in @xcite . in this way , both the diffraction peak and larger @xmath7-behavior could be described . no reference to any phenomenological model is given . from the geometrical point of view , one can imagine an internal structure with envelopes of alternating density . such an empirical approach has been recently used @xcite for fits of experimental data at isr energies . the following parameterization of the amplitude is proposed in ref . @xcite : @xmath271 , \label{fms11}\ ] ] where @xmath272 . the fits at different energies give information about the ratio of the real to imaginary part of the amplitude @xmath273 , besides the values of adjustable parameters @xmath274 . two different methods were used . in total , there are 14 to 16 free parameters . the results of nonlinear fits are rather unstable , and the conclusions are somewhat controversial . in particular , the numbers of zeros in @xmath275 and @xmath276 differ in these methods . the dominance of the real part of the amplitude at intermediate values of the momentum transfer in one of the methods is not confirmed when the other method is used . a similar fit was recently attempted and applied to totem data in refs @xcite . the earlier proposal in ref . @xcite with phenomenologically chosen two @xmath8-exponentials and the relative interference phase responsible for the dip was applied to totem data . using five parameters , it is possible to describe these data in the whole interval of transferred momenta . we note that , similarly to the model in @xcite , the slope of the second exponential term is chosen several times smaller than that of the main term . moreover , when the electromagnetic form factors were tried in place of simple exponentials , the fit became worse . two exponentials without the interference term inside the diffraction peak and a tsallis - type distribution outside it were used in @xcite . it was possible , with the help of nine free parameters , to fit the data at energies from 19.4 gev to 7 tev . in some way , this fit business with no reference to any theoretical model looks more like art than science , especially if no conclusions about the hadron structure are obtained . such an approach will hardly be conclusive in the future . theoretical indications of the possibility of a new regime with an increase in transferred momenta were obtained even earlier @xcite . it was treated as a consequence of the simple iteration of processes approximated by a gaussian within the diffraction cone . the term @xmath277 in unitarity condition with gaussians inserted into the integrand gives rise to a gaussian with a width , that is twice as big , i.e. to a shape twice as wide as the diffraction cone . further iterations lead to further widening . therefore , multiple exchanges were considered . however , the results did not fit new experimental findings . this failure was explained as resulting from the improper treatment of the unitarity requirements and incorrect choice of the overlap function . the droplet model relations between form factors and the elastic amplitude for hadronic scattering at infinite energy ( see eqs ( 1 ) and ( 2 ) in ref . @xcite ) predict a series of kinks ( or zeros ) in the differential cross section , which could be related to dips . dip position movement to lower @xmath7 with a growth of the total cross section was predicted in ref . there is also an indication of several dips ( or shoulders ) at larger @xmath7 in the models @xcite using the electromagnetic form factors with subsequent eikonalization ( cf . figs 2 and 11 ) . in accordance with the experimental data shown in fig . 2 , only one dip is predicted by others . for example , it was described in ref . @xcite on the basis of a modified optical model @xcite . in the framework of the geometric scaling approach @xcite the numerical integration of the relation @xmath278/(1+\rho _ 0 ^ 2 ) , \label{dk78}\ ] ] where @xmath279 was performed with @xmath183 defined by eq . ( [ ddd ] ) . it was predicted that the dip should even disappear at energies higher than @xmath280 gev but , probably , can reappear again at ever higher energies . as we know now , it is clearly seen at 7 tev . the imaginary part has been chosen in such a way that it has a zero at the dip . the absence of additional dips is explained as the deviation of the eikonal from a simple gaussian with some flattening at small impact parameters ( see subsection 4.2.3 ) . that shows strong sensitivity to the choice of tiny details of the phenomenological eikonal and also agrees with the properties of the overlap function to be discussed in more detail below . these results were confirmed and extended to @xmath4 collisions in ref . @xcite . processes described by diagrams with multiple exchange by pomerons are claimed to be responsible for the orear regime at intermediate angles according to ref . the differential cross section is predicted to have the form @xmath281\cdot [ 1+\lambda \cos(2\sqrt { 2\pi \alpha ' ( 0 ) \vert t\vert \xi \tan(\phi /2)}+\varphi _ 0 ) ] , \nonumber \label{adya}\ ] ] where @xmath282 , and @xmath283 are adjustable parameters . there are oscillations directly imposed on the exponential fall - off with the same exponent . they should be well pronounced . so far , no such oscillations have been observed . a less strong statement about some saturation of the diffraction cone due to multiple pomeron exchanges is made in refs @xcite . a theoretical explanation based on the consequences of the unitarity condition in the @xmath30-channel has been proposed in refs @xcite . the careful fit to experimental data showed good quantitative agreement with experiment @xcite . nowadays , the same approach helps explain the totem findings @xcite ( see fig . 5 below ) . we consider the left - hand side and the integral term @xmath277 in unitarity condition ( [ unit ] ) at the angles @xmath22 outside the diffraction peak . because of the sharp fall - off of the amplitude with the angle , the leading contribution to the integral arises from a narrow region around the line @xmath284 . therefore , one of the amplitudes should be inserted at small angles within the cone as a gaussian , while the other is kept at angles outside it . integrating over one of the angles yields the linear integral equation : @xmath285 where @xmath286 . it can be solved analytically ( see @xcite for more details ) with two assumptions : that the role of the overlap function @xmath57 is negligible outside the diffraction cone and the function @xmath287 can be approximated by a constant , i.e. , @xmath288=const . both assumptions are discussed in the next subsections . it is esay to check that the eigensolution of this equation is @xmath289 with @xmath290 this expression contains the term exponentially decreasing with @xmath22 ( or @xmath250 ) ( orear regime ! ) with oscillations strongly damped by their own exponential factors imposed on it . these oscillating terms are responsible for the dip . just this formula was used in refs @xcite for fits of experimental data in a wide energy range . the ratio @xmath91 was approximated by its average values in and outside the diffraction cone , with @xmath291 , where @xmath292 is treated as the average value of @xmath91 in the orear region . the fits at comparatively low energies @xcite are consistent with @xmath293 , i.e. , with small values of @xmath292 close to zero . the great surprise of the fit in @xcite of totem data shown in fig . 5 was the necessity of using the negative value of @xmath294 large in modulus . being model - independent , this solution suffers from some limitations that are inherent for the unitarity relation , in general , and for the unitarity equation ( [ linear ] ) , in particular . first , it predicts the dependence on transferred momenta @xmath295 but not the dependence on the collision energy . second , it is applicable in a restricted ( and not rigorously defined ) range of angles in the orear region . the elastic scattering differential cross section outside the diffraction cone ( in the orear regime region ) is @xmath296 it has been used for the fit in fig . only the very first oscillating term in ( [ solut ] ) is taken into account in this expression , because other terms are more strongly damped with @xmath7 . it is important that the experimentally measured values of the diffraction cone slope @xmath28 and the total cross section @xmath25 of the same experiment mostly determine the shape of the elastic differential cross section in the orear region of transition from the diffraction peak to large - angle parton scattering . the value @xmath121 is so close to 1 at 7 tev that the fit is extremely sensitive to @xmath287 because @xmath297 in the first term determines the slope in this region . therefore , it becomes possible for the first time to estimate the ratio @xmath292 outside the diffraction cone directly from fits of experimental data . the fit of the differential cross section of elastic proton - proton scattering at @xmath10=7 tev in the region beyond the diffraction peak according to the predictions of the unitarity condition @xcite . dots - experimental data , line - theoretical approximation . moreover , in footnote 2 in ref . @xcite it was mentioned that eq . ( [ linear ] ) is in fact an equation for @xmath298 . the factor @xmath299 was omitted in this review and all previous papers because it was assumed that `` retaining it would exceed the accuracy of the derivation '' of the equation . however , it will be worthwhile to take it into account in the future as well , multiplying the right - hand side of ( [ fit ] ) by @xmath300 . this would slightly improve the fit in fig . we note that this shape of differential cross section ( [ fit ] ) differs from formula ( [ adya ] ) , first of all , because of the suppression of oscillations by the exponential factors in front of them , which decrease much more strongly than the leading exponent . in ( [ adya ] ) , the exponent is common for main and oscillating terms , while in ( [ fit ] ) , the oscillations are strongly damped . they may give rise to the dip adjusted to the diffraction cone if their amplitude is sufficiently large . the small secondary damped oscillations at larger values of @xmath7 have been seen at comparatively low energies ( see ref . @xcite ) but have not yet been noticed at the lhc . we stress that the fit ( [ fit ] ) contains only three adjustable parameters : the overall normalization @xmath301 , the amplitude of oscillations @xmath302 , which determines the depth of the dip , and @xmath287 , which helps find the ratio @xmath292 outside the diffraction peak from the slope of the differential cross section there . both the overlap function and the eikonal are subject to the unitarization procedure , albeit in somewhat different approaches . therefore , it is instructive to compare their different forms . we discuss what shapes of the overlap function can be considered as suitable for further use . one of the assumptions used in solving the unitarity equation was the smallness of @xmath57 in the orear region . the results in @xcite give strong support to the validity of this assumption . the overlap function was calculated there directly from experimental data , by subtracting the elastic contribution @xmath277 from the left - hand side of the unitarity equation without appeal to any model . it is described by the formula : @xmath303^{1/2}k^{-1/2}(z , z_1,z_2 ) . % \nonumber \label{overl}\end{aligned}\ ] ] here , @xmath304 ; @xmath305^{1/2}$ ] . the result at 7 tev is shown in fig . the overlap function at @xmath10=7 tev obtained from the unitarity condition with substitution of experimental data about the differential cross section @xcite . + it is large in the diffraction cone and negligibly small outside it . the line nearest to the abscissa axis takes into account the real part of the amplitude . the farthest one is computed with @xmath306 . certainly , the shadow of inelastic processes represented by the overlap function dominates within the diffraction peak . but it is extremely small outside . it is even smaller at the lhc energies @xcite than at lower ones @xcite , where a similar behavior of the overlap function at large @xmath7 was observed previously . hence , this assumption is well founded . moreover , it is quite understandable that @xmath73 is very small at large @xmath7 in fig . this shows that its fit by the solution of the unitarity relation has been done by the proper eigenfunction ( [ solut ] ) with the correct eigenvalues of the integral equation . it is tempting to solve the nonlinear inhomogeneous unitarity equation ( [ unit ] ) by iterations . that has been attempted several times @xcite . the main problem is the choice of the overlap function . the simplest ansatz is the gaussian form at all transferred momenta . the argument in favor of it is just that it plays the decisive role in the diffraction cone , where the elastic amplitude has a gaussian shape . bbut the results fail to describe the orear regime . this may be ascribed to the role of phases of inelastic processes , that determine the genuine shape of the overlap function , or / and to the improper approximation of @xmath91 by a constant outside the diffraction cone . again , similarly to the situation in the @xmath62-representation , the tiny details of the shape prevent from the proper outcome . no approximations for the overlap function demonstrated in fig . 6 have yet been proposed . it is instructive to confront the shape of the overlap function @xmath73 with results obtained in the impact parameter interpretation of proton - proton scattering . they were presented in refs @xcite for isr data and are demonstrated in figs 7 , 8 . the @xmath62-transformed amplitude @xmath71 , the overlap function @xmath72 and the eikonal @xmath181 are shown in fig . 7 at the energy @xmath307 gev @xcite . the transformed amplitude is almost gaussian from the center to 2 fm with little flattening near the center . there is a tail beyond 2 fm with a much flatter slope . the flattening of the overlap function at the center is much stronger , while the eikonal is steeper there . hence , one should not identify these three curves at small @xmath62 , even though they almost coincide beyond 2 fm . the shapes of the amplitude , overlap function and eikonal extracted from experimental data at @xmath307 gev as functions of impact parameter squared ( borrowed from @xcite ) . in the notations of this review , the amplitude @xmath308 , the overlap function @xmath309 , the eikonal @xmath310 . the corresponding space scales are shown in the abscissa axis . the overlap functions at isr energies as functions of the impact parameter look similar ( borrowed from @xcite ) . the solid line at @xmath307 gev is explained in the text . similar features are seen in fig . 8 , taken from @xcite , where @xmath72 at the same energy is displayed . the solid line on the logarithmic scale is a gaussian adjusted to fit at @xmath311 and @xmath312 fm . a gaussian adjusted between 0.6 and 1.6 fm would be higher at @xmath311 and would require additional flattening . this flattening at small @xmath62 corresponds directly to negative values of @xmath73 at large @xmath7 seen in fig . 5 . in the same way , slight variations of eikonal @xmath181 at small @xmath62 may lead to drastic disagreement of model fits with experimental data . therefore , their success or failure at large @xmath7 depends on the accuracy of the chosen form of the eikonal at low @xmath62 . a long tail above the solid line for large impact parameters is clearly seen in fig . these figures demonstrate how accurate model formulas must be to correctly reproduce either the overlap function or the eikonal if the final goal is to describe the differential cross sections outside the diffraction peak . a small `` edge '' correction to the gaussian shape of the eikonal has been claimed to be necessary for fits of experimental data at isr energies on increasing total cross sections and structures of the differential cross sections in refs @xcite . for example , the correction factor @xmath313 with some specific dependence on the impact parameter was introduced @xcite into the overlap function @xmath72 . it changes the shape at small @xmath62 and makes it similar to that shown in fig . 7 : @xmath314 ) . \label{fsbk}\ ] ] it turns out that , in the @xmath8-representation , the corresponding overlap function @xmath73 has two zeros at @xmath7=0.645 and 3.83 gev@xmath13 and becomes practically indistinguishable from zero already at @xmath143.5 gev@xmath13 . the last statement is in full agreement with the conclusions in refs @xcite . although the overlap functions in fig . 8 look quite similar to each other , there is a slight difference , which was analyzed in @xcite . this difference reveals itself in a small increase at the level of 4@xmath31 of the overlap function , with an energy increase at the impact parameters ( radii ) about 1 fm , which implies the peripheral origin of this phenomenon . that was also discussed earlier @xcite . moreover , in ref . @xcite which deals with the direct analysis of experimental data at isr , a shoulder of the overlap function at 2.3 fm was noticed . its origin is unknown . the increase in the peripheral region about 16@xmath31 for @xmath315 data is reported in the latest review @xcite . our recent results ( to be published ) indicate that it is twice larger at lhc . the overlap function in the @xmath62-representation is used in ref . @xcite to distinguish between the mechanisms of absorption and reflection with the help of the unitarity equation . in the latter case , the differential cross section at large momentum transfers is predicted to be 4 times larger . the impact parameter picture used in almost all phenomenological models is very helpful for a qualitative description of the process . however , the forms of the eikonal in the @xmath62-representation turned out to be very approximate . in our opinion , their wide use in most papers dealing with extension to larger angles suffers from this deficiency . there are some arguments @xcite that the eikonal approximation is only valid for sums of leading terms of the tower diagrams , but it is not correct in general . it is applicable to almost collinear processes only and does not properly take the separation due to transverse momenta into account . that is why the quasi - eikonal models were developed where the intermediate states take inelastic diffraction processes into account , in addition to elastic ones . as a result , formulas like ( [ gpps ] ) , ( [ gpps1 ] ) were proposed . the eikonal does not properly reproduce the @xmath30-channel cuts of the scattering amplitude due to multiple scattering @xcite . by itself , it does not guarantee precise unitarization . moreover , the procedure of unitarity corrections is not well defined , because it can be implemented differently . the accuracy of unitarity relation ( [ unib ] ) in the @xmath62-representation is also not absolutely clear , as discussed above , while its use is mandatory for interpretation of experimental data . that is why the model predictions shown in fig . 2 fail to explain the data . there is a drastic difference between the use of the gaussian shape for the amplitude in the @xmath30-channel unitarity condition and the same shape for the overlap function , as well as its use directly in the @xmath62-representation . the exponential decrease ( see eq . ( [ diff ] ) ) of the differential cross section in the diffraction cone as a function of @xmath7 ( or gaussian for angles ) is an experimental observation . it can be used anywhere within the its applicability range , as it was done , for example , in solving eq . ( [ unit ] ) . hence , this solution is quite successful in fits of experimental data in the orear region . the same shape can not be used for the @xmath8-dependence of the overlap function , although it plays an important role in the formation of cone behavior . it is often argued that the fourier transform of the gaussian is a gaussian and therefore this shape can also be used in the @xmath62-representation . while the first part of the statement is correct , the second is wrong . the tails of the differential cross sections are very sensitive to small @xmath62 . slight variations of this shape at small impact parameters lead to crucial changes in the behavior of the amplitude at large transferred momenta . therefore , the predictions shown in fig . 2 , which use the impact parameter profiles close to gaussian ones even in the vicinity of @xmath62=0 , are still successful inside the diffraction cone but completely fail outside it , where central collisions play an important role . it is very difficult in a particular model to guess the proper decline from the gaussian shape at small impact parameters , which drastically influences the differential cross section at large transferred momenta . therefore , attempts to use the non - gaussian electromagnetic form factors were of some help in improving the situation , because they are closer in shape to the eikonal demonstrated in figs 7 and 8 . further progress in this direction is necessary in order to understand the geometric content of the interaction region in ordinary space and time . nevertheless , it is hardly justified to blame the phenomenological model builders for their failure to predict the behavior of the differential cross sections at large transferred momenta , where it is many orders of magnitude lower than in the diffraction peak . the great and important task of fits of the energy behavior of total and elastic cross sections , ( @xmath316)-dependence of the differential cross section , and the ratio @xmath91 in a wide interval of energies and transferred momenta can not be accomplished without free parameters and the physical intuition of model builders . the switch to higher energies allows eliminating corrections due to secondary reggeons and improving the fits . there is hope of gaining clearer insight into the geometrical picture of hadron interactions . there are no reasonable arguments to neglect the @xmath8-dependence of the ratio @xmath88 in ( [ rho ] ) or of the phase @xmath42 in ( [ zeta ] ) . this dependence seems to be important , even inside the diffraction cone , albeit the values of @xmath91 are small there . using formula ( [ rhodit ] ) and assuming that @xmath275 determines mainly the shape of the differential cross section in this region , we find that the real part must vanish at @xmath317 with the @xmath92-dependence of @xmath25 ( [ cst ] ) and @xmath147 ( [ wid ] ) and using relation ( [ sas ] ) , we have @xmath318 and hence @xmath319 at @xmath320 . the estimates at lhc energies are @xmath321 gev@xmath13 . notably , they agree with the results obtained in the models in @xcite . there were several attempts to consider the behavior of @xmath88 at larger transferred momenta in refs . the main efforts were spent on preventing differential cross sections from vanishing at those values of @xmath8 where the imaginary part of the amplitude is zero in a particular model . the ratio @xmath273 should be infinite , e.g. , as in the models in refs @xcite . the number of zeros of the imaginary part is sometimes greater than one . this is typical in the fraunhofer diffraction or in models with electromagnetic form factors . therefore , the singularities of @xmath273 appear at different @xmath8 in different models . the real part of the amplitude fills in these kinks leaving some traces like shoulders or dips in the differential cross sections . for example , it is predicted in ref @xcite that for @xmath3-scattering at 8 tev such traces appear at @xmath322 gev@xmath13 and at 1.5 gev@xmath13 . in refs @xcite , the dispersion relation between the phase and the modulus of the elastic amplitude considered in refs @xcite was used with some input for the modulus fitted to the experimental data at laboratory energies above 100 gev . the conclusion was that the real part exhibits a zero in the @xmath8-distribution above 200 gev , which moves away from the forward direction as the energy increases . in ref . @xcite , the eikonal approximation was used following the proposal in ref . information about the interference region with a coulomb amplitude similar to that in eq . ( [ inter ] ) was inserted into the total amplitude , with the result @xmath323 . \label{klk}\end{aligned}\ ] ] the @xmath8-dependence of the phase was parameterized with the help of 5 parameters as @xmath324 the results showed that the phase ( related to @xmath91 by ( [ rzet ] ) ) increases from values close to zero at @xmath8=0 to about 0.5 in the interval @xmath325 gev@xmath13 . this conclusion disagrees with results in refs @xcite , as well as with the arguments presented below . a more general approach using the @xmath30-channel unitarity condition was developed in ref @xcite . as explained above , the integral equation for the elastic amplitude is valid in the orear region . its analytic solution ( [ solut ] ) was first obtained in the approximation where the values of @xmath91 in @xmath287 were replaced by their average values in the diffraction cone and in the orear region . no zeros of the imaginary part of the amplitude were obtained . the dips at 7 tev and lower energies were explained as resulting from damped oscillations . the necessity to introduce large negative values of @xmath91 into the orear region is the main outcome and surprise of the fit in ref . @xcite . in principle , this could happen if there were zeros of the imaginary part of the amplitude in this region , which would require very large values of @xmath326 near them . but there seem to be no such zeros there . we discuss this problem in more detail . we first recall asymptotic predictions . it was shown in @xcite that the ratio of the real and imaginary parts of the amplitude can be calculated asymptotically at nonzero transferred momenta @xmath8 as @xmath327 . \label{rhotau}\ ] ] we consider the leading term of solution ( [ solut ] ) . with the imaginary part of the amplitude in the orear region represented as @xmath328 it is possible to calculate @xmath91 . the very first approximation was to use the first term of the solution ( [ solut ] ) with average values of @xmath91 both in the diffraction peak ( @xmath329 ) and in the orear region ( @xmath292 ) @xcite . then the following behavior of @xmath91 was obtained @xmath330 \label{rhot}\ ] ] where @xmath331 we note that @xmath91 passes through zero and changes sign at @xmath332 gev@xmath13 . this agrees with the general theorem on the change of sign of the real part of the high - energy scattering amplitude , which was first proved in ref . a similar effect is discussed in ref . but it is difficult to obtain @xmath333 as an average of ( [ rhot ] ) over the orear region . moreover , this behavior of an unlimited decrease in @xmath91 with @xmath7 does not look satisfactory . it can in fact be damped if instead of replacing @xmath91 by @xmath292 in the solution , we differentiate @xmath231 according to ( [ rhotau ] ) , inserting there eq . ( [ ore ] ) , i.e. , the first term in ( [ solut ] ) . the following differential equation is then obtained @xmath334 here , @xmath335 . the dependence of @xmath336 can be obtained from fig . however , one should read @xmath337 on the ordinate axis in place of @xmath273 . i am sorry for this omission . unfortunately , the conclusions at the lhc energies become very indefinite , because @xmath127 is very close to zero there . the only conclusion is that @xmath273 has a single zero at @xmath338 gev@xmath13 , and it steeply changes in the orear region of @xmath339 gev@xmath13 . the result shown in fig . 9 is another extreme approximation compared to eq.([rhot ] ) . 9 . the ratio of the real to imaginary part of the amplitude obtained from the solution of eq . ( [ dvdx ] ) that follows from the unitarity condition @xcite . the ordinate should be read as @xmath337 in place of @xmath273 . i am sorry for this omission . the bold use of this procedure for derivation of eq . ( [ dvdx ] ) with @xmath273 inserted directly in the solution is , nevertheless , not satisfactory , either . the two possibilities above should be considered as two extremes for the shapes of @xmath273 . strictly speaking , the behavior of @xmath273 should be taken into account primarely in the integrand . then , inserting expression ( [ rhotau ] ) in place of @xmath292 in eq . ( [ linear ] ) and integrating by parts , we derive the linear integral equation @xmath340{\rm im}a(y ) \label{nonsymm}\ ] ] with @xmath341 and new variables @xmath342 . the kernel of this equation is not symmetric . its solution has not yet been obtained , even numerically . however , some preliminary asymptotic estimates can be obtained from it @xcite . in the preasymptotic energy region , we obtained @xcite the orear regime @xmath343 with the exponential fall - off of the amplitude as a function of angles . we , therefore , seek a solution of eq . ( [ nonsymm ] ) in the form @xmath344 . the gaussian exponential shifts to @xmath345 . replacing it with the @xmath346-function of this argument , we obtain the equation in finite differences : @xmath347 \phi ( x-\frac { a}{\sqrt { 2b } } ) . \label{findif}\ ] ] again , we can not solve it directly , but reach an important conclusion about the zeros of the imaginary part of the amplitude . the expression in the square brackets is equal to zero at @xmath348\approx \frac { 2}{a\rho _ 0 ^ 2}. \label{pt0}\ ] ] with the present - day values of @xmath349 , this zero would appear at extremely large @xmath350 gev . however , zeros of the imaginary part of the amplitude in the orear region just above the diffraction cone might appear as zeros of @xmath351 itself . this result does not contradict the above statement about the absence of zeros in the case of small oscillatory terms in the solution of a homogeneous linear integral equation . moreover , the equation tells us that @xmath351 and , consequently , the imaginary part of the amplitude can have zeros at @xmath352 . on the @xmath23-axis , these zeros would be placed at rather short distances from one another . in the black disk limit @xmath127 tends to 0.5 . if @xmath91 loses in the competition with @xmath127 within @xmath297 and the argument of the logarithm becomes extremely close to 1 or even less , that would mean the drastic change of the regime in the orear region @xcite . what the outcome of the competition between decreasing @xmath127 and negative values of @xmath91 will be , poses an interesting problem . experimental data at higher energies will be able to give the answer . as we see , the real part of the amplitude can dominate at large transferred momenta according to the unitarity condition . compared to the imaginary part , it can be large and negative there . this conclusion contradicts , for example , the results of the models in @xcite with electromagnetic form factors , where the dominance of the imaginary part , on the contrary , is claimed everywhere except the tiny regions near its zeros placed in the orear region , in particular . this disagrees with the above results . we must remember , however , that @xmath91 is infinite at these zeros ( see fig . . an analogous behavior of @xmath91 in the case of a single zero has been predicted in ref . @xcite at isr energies , as shown in fig . a similar shape of @xmath91 is obtained in ref . @xcite at @xmath2291.5 gev@xmath13 , but for the energy @xmath10=8 tev . the real part decreases with @xmath7 . therefore , the conclusions in different papers about the behavior of the real and imaginary parts of the elastic scattering amplitude are contradictory and require further theoretical studies and new experimental data . the dependence of the ratio of the real part to imaginary part of the amplitude ( depicted here as @xmath353 ) on transferred momenta obtained in a definite phenomenological fit @xcite of experimental data at @xmath307 gev . the singularity points out the position where the imaginary part is equal to zero . we have written two formulae ( [ rhodit ] ) and ( [ rhotau ] ) for the same function @xmath88 . therefore , these two expressions must be identical . equating them , we obtain @xcite the partial differential equation @xmath354 where @xmath355 . as usual , the variables @xmath30 and @xmath7 should be regarded as scaled by the corresponding constant factors @xmath356 and @xmath357 . ( [ partial ] ) can be rewritten as @xmath358 the general solution of eq . ( [ part1 ] ) reveals the scaling law @xmath359 in the asymptotic black - disk limit @xmath360 , we obtain @xmath361 and the solution is @xmath362 this yields the scaling law for @xmath363 which implies a universal scaling dependence on a single variable @xmath364 . we temporarily neglect the contribution of the real part of the amplitude to the differential cross section . then the asymptotic scaling law for the differential cross section times @xmath365 should be @xmath366 we note that the additional @xmath365-factor can be replaced by an @xmath30-dependence if absorbed in the argument of the scaling function @xmath367 . then this formula coincides with that obtained in the geometric scaling approach @xcite . thus we have proved that the solution of partial differential equation ( [ partial ] ) with properly chosen @xmath368 leads to the results known previously about the geometric scaling . at the same time , eq . ( [ partial ] ) is more general and can be used for different assumptions about @xmath368 . in particular , the behavior of the total cross section at present energies is often approximated by formula ( [ kppp ] ) as a sum of a large constant term and another term that increases as some power of energy ( see @xcite for a recent reference ) . in this case , @xmath369 , and the equation is @xmath370 its solution is @xmath371 from here , we obtain another universal scaling dependence of the differential cross section on a single variable @xmath372 @xmath373 which could be valid at preasymptotic energies . it follows from the expressions described above that the energy dependence of the scaling variable is determined by the behavior of the total cross section . @xmath374 if only the first term in eq . ( [ rhodi ] ) is used . were this scaling valid , one would be able to predict the shape of the differential cross section at a higher energy once the total cross section is known there . the preliminary results of work with experimental data at energies from isr to lhc have shown that just this dependence best reproduces the similarity of the shapes of the corresponding lines , even though their normalization differs somewhat . further studies are necessary . the above scaling laws must be satisfied for the imaginary part of the amplitude times the factor @xmath375 ( see ( [ scal ] ) ) . it follows from eq . ( [ rhodit ] ) that the real part satisfies an analogous scaling law albeit with another factor , which differs in the two cases considered above . this would lead to the scaling violating terms when the contribution of the real part of the amplitude to the differential cross section is taken into account . the above scaling dependences of the differential cross section are modified as @xmath376 and @xmath377 the violation of scaling laws is different in these cases . the first law acquires a term with the coefficient depending only on the transferred momentum , while the second law aquires a term with the coefficient that depends both on energy and on the transferred momentum . this violation of scaling laws must be negligible in the diffraction cone because the squared ratio of the real part to imaginary part which is crucial for the differential cross section is extremely small there . it would be interesting to learn about the effect of these terms outside the cone , especially in the orear region of transferred momenta . we note that at small values of their arguments @xmath378 , the scaling functions @xmath379 must be respectively proportional to @xmath380 and to @xmath381 , for the differential cross section to be equal to a constant at @xmath36 . recent fits of totem data have shown @xcite that the geometric @xmath382-scaling is violated even within the diffraction cone and must be replaced at present energies by approximate @xmath383-scaling . the energy dependence of high - energy scattering processes at a fixed center - of - mass angle is of special interest . dimensional scaling laws have been developed as an approach to understanding it . the large angle scattering is determined by contributions due to central interactions of internal domains inside the colliding particles . the estimates according to the perturbative qcd become justified due to its asymptotic freedom property . they depend on the number of constituent fields of the hadrons @xcite . at large @xmath30 and @xmath8 and a fixed ratio @xmath384 , we have @xmath385 where @xmath172 is the total number of fields in @xmath386 that carry a finite fraction of the momentum . assuming the existence of quark constituents , the @xmath102 , fixed-@xmath387 prediction for @xmath3-scattering @xcite is @xmath388 . for the elastic amplitude , it is @xmath389 this form can become more complicated for multiple scatterings . for example , the lowest order graphs for @xmath99 rescatterings @xcite behave as @xmath390 and could become the leading ones . however , due to higher - order corrections , the resulting behavior could change not so drastically , and the result would be close to the initial estimate ( [ mabr ] ) as shown in ref . @xcite . further progress beyond the simple quark counting rules was slowed down by complications in calculating the enormous number of feynman diagrams . in parallel , there were attempts to explain the @xmath169-regime in @xmath3 scattering by dynamical mechanisms with the help of simple feynman graphs . for protons ( or their subregions ) consisting of three valence quarks , we can assume coherent exchange by gluons @xcite or by the color - neutral pairs of gluons @xcite between them . the propagators of three gluons and their couplings produce an @xmath391-dependence , and two powers in the denominator are added by kinematical factors . the general problem of these approaches is the necessity to introduce additional factors in order to preserve both protons in their initial states in large - angle scattering . the corresponding powers of the qcd coupling constant should be included , of course , which leads to possible ( strong ? ) modifications of the simple power law . also , the exchange by three pomerons instead of the three pairs of gluons is possible . because three colliding quarks share the total energy of the proton equally ( ? ) , their shares are smaller , and the whole process is farther from the asymptotic regime if treated at the parton level . none of these questions have been quantitatively resolved yet . we note that the large-@xmath7 behavior of reggeons composed of two reggeized partons ( quarks , gluons ) can be calculated from the bfkl equation @xcite . the multi - pomeron exchange for hadrons in a state with a minimum number of partons was considered in @xcite . it was concluded that the differential cross section factores as a product of two @xmath392 representing the probability of finding the initial and final particles in a `` bare '' state and the @xmath393 describing the hard exchange interaction : @xmath394 the first factor describes the contribution of large transverse distances , and the second factor represents the contribution of small ones . the hard exchange is determined by the pomeron vertices , which are known semiclassically : @xmath395 with @xmath396 , \label{kanc10}\ ] ] where @xmath397 are the numbers of valence quarks in colliding hadrons . this leads to a @xmath169-behavior for @xmath3 and @xmath398 for @xmath5 . the quantitative comparison with experimental data is more difficult because of much smaller values of the differential cross sections in this region and , correspondingly , larger error bars . |
data on the interference of the coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude . the real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude ( the so - called overlap function ) at nonforward transferred momenta are also discussed . * * 4.2.5 the real part of the elastic scattering amplitude at nonzero transferred momenta . * * 4.3 scaling laws . * | c | 1206.5474 | colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced . we consider the latter case here . although inelastic processes dominate at high energies , elastic scattering contributes considerably ( 18 - 25@xmath0 ) to the total cross section . its share first decreases and then increases at higher energies . small - angle scattering prevails at all energies . some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms . the steep gaussian peak at small angles is followed by the exponential ( orear ) regime with some shoulders and dips , and then by a power - law drop . results from various theoretical approaches are compared with experimental data . phenomenological models claiming to describe this process are reviewed . the unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power - law , hard parton scattering regime under high momentum transfer . data on the interference of the coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude . the real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude ( the so - called overlap function ) at nonforward transferred momenta are also discussed . problems related to the scaling behavior of the differential cross section are considered . the power - law regime at highest momentum transfer is briefly described . * elastic scattering of hadrons * if only you knew what trash gives rise + to verses that are nt ashamed uprise + a. akhmatova + @xmath1 * 1 introduction . * * 2 the main relations . * * 3 where do we stand now ? * * 4 experimental data and phenomenological models . * * 4.1 the diffraction cone and geometrical approach . * * 4.1.1 the geometry of the internal hadron structure . * * 4.1.2 the modified fraunhofer diffraction . * * 4.1.3 electromagnetic analogies . * * 4.1.4 reggeon exchanges . * * 4.1.5 the qcd - inspired models . * * 4.2 the intermediate angles : the dip and the orear regime . * * 4.2.1 the gaussian fits . * * 4.2.2 the phenomenological models . * * 4.2.3 the unitarity condition . * * 4.2.4 the overlap function and the eikonal . * * 4.2.5 the real part of the elastic scattering amplitude at nonzero transferred momenta . * * 4.3 scaling laws . * * 4.4 the hard scattering at large angles . * * 4.4.1 the dimensional counting . * * 4.4.2 coherent scattering . * * 5 discussion and conclusions . * * references . * pacs numbers : 13.85.dz elastic scattering ; 13.75.cs nucleon - nucleon interactions key words : cross section , amplitude , slope , diffraction , orear regime , partons | the new experimental data of the totem collaboration at the lhc about elastic scattering of protons at an energy of 7 tev have revived interest to these processes . the picture of very short - wavelength hadron collisions has become available , adding to our insight into the spatial structure of colliding particles and providing new intrinsic information pertaining to very short - distance interactions . the total and elastic cross sections show a stable increase with energy . the share of elastic processes increases . the differential cross section has very intriguing properties . the exponential @xmath7-decrease persists at small transferred momenta , analogously to lower - energy data . but the diffraction cone slope is larger compared with low energies ; it is stable up to transferred momenta @xmath338 gev@xmath13 , then this peak steepens and a dip appears at @xmath167 gev@xmath13 , with a subsequent maximum at @xmath168 gev@xmath13 . at somewhat larger angles , the exponential in @xmath12-regime prevails . it is replaced by the @xmath169-behavior at ever larger transferred momenta @xmath399 gev@xmath13 . at the same time , we are waiting for measurements at extremely small angles in the interference region of coulomb and nuclear amplitudes to gain some knowledge about the real part of the forward scattering amplitude . it would be extremely interesting to learn its energy behavior and check our predictions from the dispersion relations . the steeper slopes of the diffraction peak and of the orear region at higher energies , and , correspondingly , their smaller extensions clearly demonstrate that it becomes more and more difficult for a high - energy particle to preserve its identity when scattering at larger transverse momenta . this increase in the total cross section and , especially , in the share of the elastic cross section , as well as the peculiar change of regimes in the @xmath7-behavior of the differential cross section , require a theoretical interpretation . short of a complete theory of hadron dynamics , we have to turn our attention to phenomenological models and some rare rigorous theoretical relations . the region of large transferred momenta became an occam razor for them , as explained above . the geometric picture of the internal structure of protons and their collisions requires larger disk radii increasing with energy . their blackness increases as well . some separate subregions of different sizes and opacity are considered . the impact parameter approach is decisive in deciphering this structure . at isr energies , the increase of the total cross section was attributed to some peripheral regions of nucleons . it is important to juxtapose these findings with the lhc data . the approach to the black - disk asymptotic limit has become very interesting . the proposal of geometrical scaling reducing the number of independent variables is under investigation . at the same time , the scaling law may happen to be different from the geometrical scaling . there are many phenomenological models , at our disposal , but it is still difficult to choose any particular one among them . most of them are quite successful , albeit with many adjustable parameters , in describing the energy behavior of the cross sections and the main bulk of the elastic processes in the diffraction cone , but fail in their predictions outside it . the dynamical origin of many assumptions is still missing . the small details of the suspected break at small @xmath8 , of the steepened slope and of possible weak oscillations over a smooth exponential behavior of the diffraction peak are under investigation . there are predictions of several dips and/or visible oscillatory behavior imposed on the trend of a generally decreasing dependence on @xmath7 , which appear at larger transferred momenta . as an example , in fig . 11 borrowed from @xcite the results of some model predictions for the differential cross section of proton - proton scattering at @xmath400 tev are shown up to quite high values of @xmath401 gev@xmath13 . they differ significantly , and further accurate experimental data expected to be obtained in 2015 2016 will surely be decisive in the choice of a model ( if any ! ) . the experience with unsuccessful predictions at 7 tev in the region outside the diffraction cone is not very encouraging . the problem of the behavior of the real part of the elastic scattering amplitude at nonforward 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constrained clustering has been well - studied for algorithms such as @xmath0-means and hierarchical clustering . however , how to satisfy many constraints in these algorithmic settings has been shown to be intractable . one alternative to encode many constraints is to use spectral clustering , which remains a developing area . in this paper in contrast to some previous efforts that implicitly encode must - link and cannot - link constraints by modifying the graph laplacian or constraining the underlying eigenspace , we present a more natural and principled formulation , which explicitly encodes the constraints as part of a constrained optimization problem . our method offers several practical advantages : it can encode the degree of belief in must - link and cannot - link constraints ; it guarantees to lower - bound how well the given constraints are satisfied using a user - specified threshold ; it can be solved deterministically in polynomial time through generalized eigendecomposition . furthermore , by inheriting the objective function from spectral clustering and encoding the constraints explicitly , much of the existing analysis of unconstrained spectral clustering techniques remains valid for our formulation . we validate the effectiveness of our approach by empirical results on both artificial and real datasets . | i | 1201.5338 | constrained clustering has been well - studied for algorithms such as @xmath0-means and hierarchical clustering . however , how to satisfy many constraints in these algorithmic settings has been shown to be intractable . one alternative to encode many constraints is to use spectral clustering , which remains a developing area . in this paper , we propose a flexible framework for constrained spectral clustering . in contrast to some previous efforts that implicitly encode must - link and cannot - link constraints by modifying the graph laplacian or constraining the underlying eigenspace , we present a more natural and principled formulation , which explicitly encodes the constraints as part of a constrained optimization problem . our method offers several practical advantages : it can encode the degree of belief in must - link and cannot - link constraints ; it guarantees to lower - bound how well the given constraints are satisfied using a user - specified threshold ; it can be solved deterministically in polynomial time through generalized eigendecomposition . furthermore , by inheriting the objective function from spectral clustering and encoding the constraints explicitly , much of the existing analysis of unconstrained spectral clustering techniques remains valid for our formulation . we validate the effectiveness of our approach by empirical results on both artificial and real datasets . we also demonstrate an innovative use of encoding large number of constraints : transfer learning via constraints . | spectral clustering is an important clustering technique that has been extensively studied in the image processing , data mining , and machine learning communities ( @xcite ) . it is considered superior to traditional clustering algorithms like @xmath0-means in terms of having deterministic polynomial - time solution , the ability to model arbitrary shaped clusters , and its equivalence to certain graph cut problems . for example , spectral clustering is able to capture the underlying moon - shaped clusters as shown in fig . [ fig : two_moon](b ) , whereas @xmath0-means would fail ( fig . [ fig : two_moon](a ) ) . the advantage of spectral clustering has also been validated by many real - world applications , such as image segmentation ( @xcite ) and mining social networks ( @xcite ) . + spectral clustering was originally proposed to address an unsupervised learning problem : the data instances are unlabeled , and all available information is encoded in the graph laplacian . however , there are cases where unsupervised spectral clustering becomes insufficient . using the same toy data , as shown in ( fig . [ fig : two_moon](c ) ) , when the two moons are under - sampled , the clusters become so sparse that the separation of them becomes difficult . to help spectral clustering recover from an undesirable partition , we can introduce side information in various forms , in either small or large amounts . for example : 1 . * pairwise constraints * : domain experts may explicitly assign constraints that state a pair of instances must be in the same cluster ( must - link , ml for short ) or that a pair of instances can not be in the same cluster ( cannot - link , cl for short ) . for instance , as shown in fig . [ fig : two_moon](d ) , we assigned several ml ( solid lines ) and cl ( dashed lines ) constraints , then applied our constrained spectral clustering algorithm , which we will describe later . as a result , the two moons were successfully recovered . * partial labeling * : there can be labels on some of the instances , which are neither complete nor exhaustive . we demonstrate in fig . [ fig : uci_ari ] that even small amounts of labeled information can greatly improve clustering results when compared against the ground truth partition , as inferred by the labels . * alternative weak distance metrics * : in some situations there may be more than one distance metrics available . for example , in table [ table : reuters ] and accompanying paragraphs we describe clustering documents using distance functions based on different languages ( features ) . * transfer of knowledge * : in the context of transfer learning ( @xcite ) , if we treat the graph laplacian as the target domain , we could transfer knowledge from a different but related graph , which can be viewed as the source domain . we discuss this direction in section [ sec : algorithm : transfer ] and [ sec : exp : transfer ] . all the aforementioned side information can be transformed into pairwise ml and cl constraints , which could either be hard ( binary ) or soft ( degree of belief ) . for example , if the side information comes from a source graph , we can construct pairwise constraints by assuming that the more similar two instance are in the source graph , the more likely they belong to the same cluster in the target graph . consequently the constraints should naturally be represented by a degree of belief , rather than a binary assertion . how to make use of these side information to improve clustering falls into the area of constrained clustering ( @xcite ) . in general , constrained clustering is a category of techniques that try to incorporate ml and cl constraints into existing clustering schemes . it has been well studied on algorithms such as @xmath0-means clustering , mixture model , hierarchical clustering , and density - based clustering . previous studies showed that satisfying all constraints at once ( @xcite ) , incrementally ( @xcite ) , or even pruning constraints ( @xcite ) is intractable . furthermore , it was shown that algorithms that build set partitions incrementally ( such as @xmath0-means and em ) are prone to being over - constrained ( @xcite ) . in contrast , incorporating constraints into spectral clustering is a promising direction since , unlike existing algorithms , all data instances are assigned simultaneously to clusters , even if the given constraints are inconsistent . constrained spectral clustering is still a developing area . previous work on this topic can be divided into two categories , based on how they enforce the constraints . the first category ( @xcite ) directly manipulate the graph laplacian ( or equivalently , the affinity matrix ) according to the given constraints ; then unconstrained spectral clustering is applied on the modified graph laplacian . the second category use constraints to restrict the feasible solution space ( @xcite ) . existing methods in both categories share several limitations : * they are designed to handle only binary constraints . however , as we have stated above , in many real - world applications , constraints are made available in the form of real - valued degree of belief , rather than a yes or no assertion . * they aim to satisfy as many constraints as possible , which could lead to inflexibility in practice . for example , the given set of constraints could be noisy , and satisfying some of the constraints could actually hurt the overall performance . also , it is reasonable to ignore a small portion of constraints in exchange for a clustering with much lower cost . * they do not offer any natural interpretation of either the way that constraints are encoded or the implication of enforcing them . in this paper , we study how to incorporate * large * amounts of pairwise constraints into spectral clustering , in a flexible manner that addresses the limitations of previous work . then we show the practical benefits of our approach , including new applications previously not possible . we extend beyond binary ml / cl constraints and propose a more flexible framework to accommodate general - type side information . we allow the binary constraints to be relaxed to real - valued degree of belief that two data instances belong to the same cluster or two different clusters . moreover , instead of trying to satisfy each and every constraint that has been given , we use a user - specified threshold to lower bound how well the given constraints must be satisfied . therefore , * our method provides maximum flexibility in terms of both representing constraints and satisfying them*. this , in addition to handling large amounts of constraints , allows the encoding of new styles of information such as entire graphs and alternative distance metrics in their raw form without considering issues such as constraint inconsistencies and over - constraining . our contributions are : * we propose a principled framework for constrained spectral clustering that can incorporate large amounts of both hard and soft constraints . * we show how to enforce constraints in a flexible way : a user - specified threshold is introduced so that a limited amount of constraints can be ignored in exchange for lower clustering cost . this allows incorporating side information in its raw form without considering issues such as inconsistency and over - constraining . * we extend the objective function of unconstrained spectral clustering by encoding constraints explicitly and creating a novel constrained optimization problem . thus our formulation naturally covers unconstrained spectral clustering as a special case . * we show that our objective function can be turned into a generalized eigenvalue problem , which can be solved deterministically in polynomial time . this is a major advantage over constrained @xmath0-means clustering , which produces non - deterministic solutions while being intractable even for @xmath1 ( @xcite ) . * we interpret our formulation from both the graph cut perspective and the laplacian embedding perspective . * we validate the effectiveness of our approach and its advantage over existing methods using standard benchmarks and new innovative applications such as transfer learning . this paper is an extension of our previous work ( @xcite ) with the following additions : 1 ) we extend our algorithm from 2-way partition to @xmath0-way partition ( section [ sec : algorithm : k - way ] ) ; 2 ) we add a new geometric interpretation to our algorithm ( section [ sec : interpret : geo ] ) ; 3 ) we show how to apply our algorithm to a novel application ( section [ sec : algorithm : transfer ] ) , namely transfer learning , and test it with a real - world fmri dataset ( section [ sec : exp : transfer ] ) ; 4 ) we present a much more comprehensive experiment section with more tasks conducted on more datasets ( section [ sec : exp:2moon ] and [ sec : exp : reuters ] ) . the rest of the paper is organized as follows : in section [ sec : related ] we briefly survey previous work on constrained spectral clustering ; section [ sec : background ] provides preliminaries for spectral clustering ; in section [ sec : model ] we formally introduce our formulation for constrained spectral clustering and show how to solve it efficiently ; in section [ sec : interpret ] we interpret our objective from two different perspectives ; in section [ sec : algorithm ] we discuss the implementation of our algorithm and possible extensions ; we empirically evaluate our approach in section [ sec : exp ] ; section [ sec : conclusion ] concludes the paper . |
continuing our investigation into the numerical properties of the _ hierarchical reference theory _ , we study the square well fluid of range @xmath0 from slightly above unity up to 3.6 . after briefly touching upon the core condition and the related decoupling assumption necessary for numerical calculations , we shed some light on the way an inappropriate choice of the boundary condition imposed at high density may adversely affect the numerical results ; we also discuss the problem of the partial differential equation becoming stiff for close - to - critical and sub - critical temperatures . while agreement of the theory s predictions with simulational and purely theoretical studies of the square well system is generally satisfactory for @xmath1 , the combination of stiffness and the closure chosen is found to render the critical point numerically inaccessible in the current formulation of the theory for most of the systems with narrower wells . | i | cond-mat0208471 | continuing our investigation into the numerical properties of the _ hierarchical reference theory _ , we study the square well fluid of range @xmath0 from slightly above unity up to 3.6 . after briefly touching upon the core condition and the related decoupling assumption necessary for numerical calculations , we shed some light on the way an inappropriate choice of the boundary condition imposed at high density may adversely affect the numerical results ; we also discuss the problem of the partial differential equation becoming stiff for close - to - critical and sub - critical temperatures . while agreement of the theory s predictions with simulational and purely theoretical studies of the square well system is generally satisfactory for @xmath1 , the combination of stiffness and the closure chosen is found to render the critical point numerically inaccessible in the current formulation of the theory for most of the systems with narrower wells . the mechanism responsible for some deficiencies is illuminated at least partially and allows us to conclude that the specific difficulties encountered for square wells are not likely to resurface for continuous potentials . # 1^(#1 ) c_2 | in a large part of the density - temperature plane , integral equation theories are a reliable tool for studying thermodynamic and structural properties of , among others , simple one - component fluids @xcite ; unfortunately , in the vicinity of a liquid - vapor critical point , integral equations are haunted by a host of difficulties , leading to a variety of shortcomings such as incorrect and non - matching branches of the binodal , classical values at best for the critical exponents , or other deviations from the correct behavior at the critical singularity @xcite . asymptotically close to the critical point , on the other hand , renormalization group ( ) theory is the instrument of choice for describing the fluid ; in general , however , approaches do not allow one to derive non - universal quantities from microscopic information only , _ i. e. _ from knowledge of the forces acting between the fluid s particles alone . one of the theories devised to bridge the conceptual gap between these complementary approaches is the _ hierarchical reference theory _ ( ) first put forward by parola and reatto @xcite : in this theory the introduction of a cut - off wavenumber @xmath2 inspired by momentum space theory and , for every value of @xmath2 , of a renormalized potential @xmath3 means that only non - critical systems have to be considered at any stage of the calculation ; consequently , integral equations may successfully be applied to every system with @xmath4 , and critical behavior characterized by non - classical critical exponents is recovered only in the limit @xmath5 . while applicability of to a number of interesting systems , ranging from a lattice gas or ising model @xcite to various one - component fluids @xcite even including three - body interactions @xcite , internal degrees of freedom @xcite , or non - hard - core reference systems @xcite , was demonstrated early on , the main focus of research on has since shifted to the richer phase behavior of binary systems @xcite . nevertheless , in the light of s high promise and low penetration into the liquid physics community , further study and critical assessment of this theory seem worthwhile , even and foremost in the case of simple one - component fluids : indeed , it is in this comparatively simple setting that we may gain important insights into the numerical side of the theory , and barring special mechanisms relevant to some specific model system only , any problems uncovered here must be expected to haunt more advanced applications of , too . in our work we have found it convenient to restrict ourselves even further , implementing in its usual formulation @xcite for purely pairwise additive interactions _ via _ a potential @xmath6 obtained from the superposition of an infinitely repulsive hard sphere serving as reference system , @xmath7 , and a predominantly attractive tail @xmath8 , @xmath9 . here we have made use of the notation introduced previously @xcite : superscripts always denote the system a quantitiy refers to ( here , `` ref '' and `` hs '' for the reference system and hard spheres , respectively ; similarly , `` @xmath10 '' for the system with cut - off @xmath2 ) , and a tilde indicates fourier transformation . in the present contribution we apply our recent re - implementation of the theory @xcite to one of the simplest potentials exhibiting phase separation , _ viz . _ the square well potential @xmath11}$ ] ( cf . sub - section iii b of ref . ): @xmath12}(r ) = v^{{\rm hs}[\sigma]}(r)+w^{{\rm sw}[-\epsilon,\lambda,\sigma]}(r ) \\ v^{{\rm hs}[\sigma]}(r ) = \left\{\begin{array}{ccc } + \infty & : & r<\sigma \\ 0 & : & r>\sigma \end{array}\right . \\ w^{{\rm sw}[-\epsilon,\lambda,\sigma]}(r ) = \left\{\begin{array}{ccc } -\epsilon & : & r<\lambda\,\sigma \\ 0 & : & r>\lambda\,\sigma\ , . \end{array}\right . \end{array}\ ] ] considering density - independent potentials only and chosing the hard core diameter @xmath13 and the well s depth @xmath14 as units of length and energy , respectively , the attractive well s range @xmath0 is the sole remaining parameter ; in this report we will study values of @xmath0 from slightly above unity up to 3.6 . with just one parameter , _ viz . _ @xmath0 , to vary , square wells obviously make for a convenient test case of and , indeed , of liquid state theories in general ; consequently , a great many simulational and theoretical efforts have been directed at this system , and studies of its phase behavior abound @xcite . but square wells are also of interest in their own right , serving as albeit somewhat crude models of a wide variety of physical systems including , _ e. g. _ , @xmath15 , @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 , @xmath21 , @xmath22-pentane and @xmath22-butane @xcite while current interest in this potential derives mainly from the finding that square wells capture the essential features of the interactions found in colloidal systems @xcite . yet another motivation for this first application of to square wells comes from a recent , very accurate simulation study @xcite confirming and quantifying the presence in the system with @xmath23 of the yang - yang ( yy ) anomaly expected and experimentally found for asymmetric fluids @xcite . due to the extensive amount of data available in the literature the more recent of which will shortly be presented later on , and in view of some of the limitations of in its current formulation we can not expect to gain new insight into the system at hand with a level of precision comparable to that of the more sophisticated simulation schemes . instead , in the present contribution our focus of interest lies on some aspects of s numerical side , specifically on those that are sensitive to the potential s range : indeed , as stated already in ref . , for a potential as pronouncedly short - ranged as square wells some of the numerical problems should show up much more prominently than in other systems like , _ e. g. _ , the hard - core yukawa fluid previously considered @xcite where they are , of course , in principle still present but do not manifest themselves as clearly . in accordance with the preceding remarks , another reason why application of to square wells might be worthwhile lies in the closure underlying seemingly all applications so far of to simple one - component fluids with hard sphere reference part : as the usual formulation of in these cases relies on an _ ansatz _ for the two - particle direct correlation function @xmath24 very much in the spirit of stell s _ lowest - order @xmath25-ordered approximation _ @xcite ( ) or the equivalent _ optimized random - phase approximation _ @xcite ( ) by andersen and chandler , the direct correlation function can never extend to larger @xmath26 values than the potential @xmath6 itself . in particular , for the square well potential @xmath11}(r)$ ] we necessarily have @xmath27 for @xmath28 so that all moments of @xmath24 , _ i. e. _ @xmath29 , @xmath30 , exist , which is obviously at variance with the correct behavior near the critical point @xcite ; furthermore , at intermediate @xmath2 the direct correlation function can hardly be considered satisfactory , especially @xcite close to @xmath31 . while some earlier publications @xcite already blamed unsatisfactory aspects of results on this inadequacy of the closure , square wells should bring out related problems of with the usual /-style closure much more clearly , and the numerical procedure s response should provide us with a signature to be looked out for in other systems , too ; also , even within the /-style approximation the implementation of the core condition _ via_approximate ordinary differential equations ( s ) for the relevant expansion coefficients easily shown to be inadequate for very short - ranged potentials @xcite casts some doubt on the range of @xmath0 values amenable to an treatment in the current formulation of the theory . determination of the admissible @xmath0-range , on the other hand , is particularly interesting in the light of refs . and as well as in view of the global renormalization scheme @xcite originally developed by white and co - workers as an extension of wilson s phase - space cell method @xcite to the liquid state ; it is only by combining tests internal to the theory and comparison with data available by other means that we are able to answer this question . in this contribution , after a sketchy presentation of the underlying theory itself ( section [ sec : theory ] ) and the implementation used ( section [ sec : program ] ) , in section [ sec : application ] we turn to the results of applying to square well systems of variable range . after a short summary of the critical point s location as obtained from simulation - based and other purely theoretical studies of square wells for various values of @xmath0 ( sub - section [ sec : non - hrt ] ) we first look into the core condition s implementation , which provides us with a first hint regarding the range of @xmath0 values accessible to in its current formulation and once more highlights the decoupling assumption s _ rle _ ( sub - section [ sec : cc ] ) . the latter is also implicated in the correct choice of the boundary condition imposed at high density as discussed , alongside the boundary condition s location s effect , in sub - section [ sec : boundary ] . a particularly grave aspect of s numerical side is the stiffness of the partial differential equation ( ) for close - to - critical and sub - critical temperatures ( sub - section [ sec : stiff ] ) , the vestiges of which are evident in the results obtained for quasi - continually varying @xmath0 as presented in sub - section [ sec : interference ] . a short summary of our findings and conclusions ends our contribution ( section [ sec : bye ] ) . |
core - collapse supernovae are dramatic explosions marking the catastrophic end of massive stars . the multidimensionality of the supernova engine , which breaks the sphericity of the central core such as convection , rotation , magnetic fields , and hydrodynamic instabilities of the supernova shock , is attracting great attention as the most important ingredient to understand the long - veiled explosion mechanism . based on our recent work , we summarize properties of gravitational waves , neutrinos , and explosive nucleosynthesis obtained in a series of our multidimensional hydrodynamic simulations and discuss how the mystery of the central engines can be unraveled by deciphering these multimessengers produced under the thick veils of massive stars . | i | 1204.2330 | core - collapse supernovae are dramatic explosions marking the catastrophic end of massive stars . the only means to get direct information about the supernova engine is from observations of neutrinos emitted by the forming neutron star , and through gravitational waves which are produced when the hydrodynamic flow or the neutrino flux is not perfectly spherically symmetric . the multidimensionality of the supernova engine , which breaks the sphericity of the central core such as convection , rotation , magnetic fields , and hydrodynamic instabilities of the supernova shock , is attracting great attention as the most important ingredient to understand the long - veiled explosion mechanism . based on our recent work , we summarize properties of gravitational waves , neutrinos , and explosive nucleosynthesis obtained in a series of our multidimensional hydrodynamic simulations and discuss how the mystery of the central engines can be unraveled by deciphering these multimessengers produced under the thick veils of massive stars . | the majority of stars more massive than @xmath08 @xmath1 end their lives as core - collapse supernovae . they have long attracted the attention of astrophysicists because they have many facets playing important roles in astrophysics . they are the mother of neutron stars as well as black holes ; they play an important role for acceleration of cosmic rays ; they influence galactic dynamics triggering further star formation ; they are gigantic emitters of neutrinos and gravitational waves . they are also a major site for nucleosynthesis , so , naturally , any attempt to address human origins may need to begin with an understanding of core - collapse supernovae ( ccsne ) . current estimates of ccsn rates in our galaxy predict one event every @xmath2 year @xcite . when a ccsn event occurs in our galactic center , copious numbers of neutrinos are produced , some of which may be detected on the earth . such `` supernova neutrinos '' will carry valuable information from deep inside the core . in fact , the detection of neutrinos from sn1987a ( albeit in the large magellanic cloud ) opened up the _ neutrino astronomy _ , which is an alternative to conventional astronomy by electromagnetic waves @xcite . even though there were just two dozen neutrino events from sn1987a , these events have been studied extensively ( yielding @xmath0 500 papers ) and have allowed us to have a confidence that our basic picture of the supernova physics is correct ( e.g. , @xcite , see @xcite for a recent review ) . recently significant progress has been made in the large water cherenkov detectors such as super - kamiokande @xcite and icecube @xcite , and also in the liquid scintillator detector as kamland @xcite . if a supernova occurs in our galactic center ( @xmath3 kpc ) , about @xmath4 @xmath5 events are estimated to be detectable by icecube ( e.g. , @xcite and references therein ) . those successful neutrino detections are important not only to study the supernova physics but also to unveil the nature of neutrinos itself such as the neutrino oscillation parameters and the mass hierarchy ( e.g. , @xcite for a recent review ) . ccsne are now about to start even another astronomy , _ gravitational - wave astronomy_. currently long - baseline laser interferometers such as ligo ( usa , e.g. , @xcite ) , virgo ( italy ) , geo600 ( germany ) , and tama300 ( japan , e.g. , @xcite ) are currently operational and preparing for the first observation ( see , e.g. , @xcite for a recent review ) , by which the prediction by einstein s theory of general relativity ( gr ) can be confirmed . these instruments are being updated to their _ advanced _ status , and may start taking data , possibly detecting gws for the first time , as soon as 2015 ( see @xcite for a recent review ) . in fact , _ advanced _ ligo / virgo , which is an upgrade of the initial ligo and vigro , are expected to be completed by 2015 and will increase the observable detection volume by a factor of @xmath6 @xcite . the large - scale cryogenic gravitational - wave telescope ( lcgt , @xcite ) in japan was funded in late 2010 , which is being built under the kamioka mine and is expected to take its first data in 2016 . at such a high level of precision , those gw detectors are sensitive to many different sources , including chirp , ring - down , and merger phases of black - hole and neutron star binaries ( e.g. , @xcite ) , neutron star normal mode oscillations ( e.g. , @xcite ) , rotating neutron star mountains ( e.g. , @xcite ) , and ccsn explosions ( e.g. , @xcite for recent reviews ) , on the final of which we focus in this article . according to the einstein s theory of gr ( e.g. , @xcite ) , no gws can be emitted if gravitational collapse of the supernova core proceeds perfectly spherically symmetric . to produce gws , the gravitational collapse should proceed aspherically and dynamically . observational evidence gathered over the last few decades has pointed towards ccsne indeed being generally aspherical ( see @xcite for a recent review ) . the most unequivocal example is sn1987a . to explain the light - curve , a large amount of mixing of ni outward to the h - he interface and of h inward into the he - core was required ( e.g. , @xcite , and @xcite for a review ) . such mixing processes coming from the rayleigh - taylor instability at the interface with different compositions after shock passage have been examined extensively so far by 2d ( e.g. , @xcite ) and 3d simulations @xcite . the asymmetry of iron and nickel lines in sn1987a was proposed to be explained , if the explosion occurs in a jet - like @xcite or in a unipolar manner @xcite . more directly , the hst images of sn1987a are showing that the expanding envelope is elliptical with the long axis aligned with the rotation axis inferred from the ring ( @xcite , see however @xcite for a recent counter argument ) . the aspect ratio and position angle of the symmetry axis are consistent with those predicted earlier from the observations of speckle and linear polarization . what is more , the linear polarization became greater as time passed ( e.g. , @xcite ) , a fact which has been used to argue that the central engine of the explosion is responsible for the non - sphericity ( e.g. , @xcite ) . by performing a series of time - dependent , non - lte(local thermodynamic equilibrium ) , radiation - transport simulations ( e.g. , @xcite ) , @xcite recently pointed out that asymmetry in the ejecta can explain the increase in the continuum polarization observed at the nebular phases @xcite . dense knots , indications of ejecta clumpiness , and filaments seen in supernova remnants by hst in the visual @xcite and by rosat , chandra , and xmm - newton @xcite in x - rays also provide evidence that small- and large - scale inhomogeneities ( and perhaps even fragmentation ) are a common feature in supernova explosions . advancing ability of the hst has enabled the direct observation of the progenitors of nearby ccsne from pre - explosion images ( see @xcite for a review ) . although observational measurements of the progenitor masses are currently not many and still highly uncertain ( see @xcite for collective references therein ) , evidence has accumulated that sn type ii - plateau ( ii - p ) comes predominantly from stars in the range about of 8 - 16 @xmath1 @xcite . a generic explosion energy of the sn ii - p in the mass range is roughly on the order of @xmath7 erg @xcite , however a large diversity of the explosion signatures ( i.e. explosion energy and the synthesized ni mass ) have been so far observed from quite similar progenitors @xcite . for example , the inferred @xmath8 mass and the kinetic energies differ by a factor of five between sne 2005cs and 2003gd , both of them are among the _ golden events _ in which enough information was obtained to give an accurate estimate on a color or spectral type of the progenitor and the initial mass . more massive stars are expected to lose much of their mass and explode as hydrogen - stripped sne ( ib / c and iib ) . among them , the type ic - bl sne , which are associated with long gamma - ray bursts @xcite , all show much broader lines than sne ic . due to the large kinetic energies of @xmath9 erg , they have been referred to as `` hypernovae '' ( e.g. , @xcite for a recent review ) . these events are likely to come from interacting binaries in which the primary exploding star has a mass lower than what is usually associated with evolution to the massive wr phase ( e.g. , @xcite , see however @xcite ) . in addition to the two branches mentioned above , @xcite predicted yet another branch , in which the sne ii - p with higher progenitor mass result in fainter explosions . by connecting to candidate sn explosion mechanisms or to progenitor structures , it is indeed best if one could obtain a unified picture to understand the mentioned wide diversity which is not only dependent on the progenitor masses but also on the evolution scenarios ( a single vs. binary evolution ) . but , this is an area for future study firstly because it is too computationally expensive to perform a long - term simulation that follows multidimensional ( multi - d ) dynamics consistently from the onset of core - collapse , through explosion , up to the nebular phase , secondly because we are still inaccessible to multi - d stellar evolution models , in which multi - d modeling has been a major undertaking ( see @xcite for recent developments ) . from a theoretical point of view , clarifying what makes the dynamics of the supernova engine deviate from spherical symmetry is essential in understanding the gw emission mechanism . here it is worth mentioning that gws are primary observables , which imprint a live information of the central engine , because they carry the information directly to us without being affected in propagating from the stellar center to the earth . on the other hand , sn neutrinos are exposed to a number of ( external ) environmental effects , including self - interaction that induces collective neutrino flavor oscillations predominantly in the vicinity of the neutrino sphere ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * for reviews of the rapidly growing research field and collective references therein ) and the mikheyev - smirnov - wolfenstein ( msw ) effect @xcite both in the stellar envelope and in the earth ( see @xcite for a review ) . although the time profiles of neutrino signals can be potentially used like a tomography to monitor the envelope profile ( e.g. , @xcite for a recent review ) , sn neutrinos generally could provide a rather indirect information about the central engine compared to gws . the breaking of the sphericity in the supernova engine has been considered as the most important ingredient to understand the explosion mechanism , for which supernova theorists have been continuously keeping their efforts for the past @xmath0 40 years . currently multi - d simulations based on refined numerical models have shown several promising scenarios . among the candidates are the neutrino heating mechanism aided by convection and hydrodynamic instabilities of the supernova shock ( e.g. , @xcite for a review ) , the acoustic mechanism @xcite , or the magnetohydrodynamic ( mhd ) mechanism ( e.g. , @xcite see references therein ) . to pin down the true answer among the candidate mechanisms , gw signatures albeit being a primary observable , will not be solely enough and a careful analysis including neutrinos and photons should be indispensable . the current neutrino detectors is ready to broadcast the alert to astronomers to let them know the arrival of neutrinos ( e.g. , supernova early warning systems ( snews ) @xcite ) . in addition to optical observations using largest 8 - 10 m telescopes such as vlt and subaru telescope ( e.g. , @xcite ) , the planned thirty - meter - telescope ( tmt ) with a refined spectropolarimetric technique is expected to detect more than 20 events of the sn polarization per year . this should provide valuable information to understand the sn asymmetry with increasing statistics . not only for understanding the origin of non - spherical ejecta morphology but more importantly for understanding the origin of heavy elements , it is of crucial importance to accurately determine nucleosynthesis in the sn ejecta , which naturally requires a multi - d numerical modeling ( see , @xcite for recent reviews ) . putting things together , the multidimensionality determines the explosion mechanism , in turn we may extract the information that traces the multidimensionality by the sn multimessengers , which would be only possible by a careful analysis on gws , neutrinos , and photons . in this review article , we hope to bring together various of our published and unpublished findings from our recent multi - d supernova simulations and the obtained predictions of the sn multimessengers so far ( for other high - energy astrophysical sources such as magnetars , gamma - ray bursts , and coalescing binaries , see @xcite for recent reviews ) . before we go into details from the next sections , we first have to draw a caution that the current generation of simulation results that we report in this article should depend on the next generation calculations by which more sophistication can be made not only in determining the efficiency of neutrino - matter coupling ( the so - called neutrino transport calculation ) , but also in the treatment of general relativity . therefore we provide here only a snapshot of the moving ( long - run ) documentary film whose headline we ( boldly ) chose to entitle as `` multimessengers from ccsne to bridge theory and observation '' . among the mentioned candidate mechanisms , we focus on the neutrino - heating mechanism in section [ sec2 ] and the mhd mechanism in section [ sec3 ] , respectively . in each section , we first briefly summarize the properties of the explosion dynamics and then move on to discuss possible properties of the sn multimessengers paying particular attention to their detectability . it may be best if we can cover these sn messengers once for all in this article , but unfortunately not . what we have studied so far is limited to gws and explosive nucleosynthesis in the neutrino - heating mechanism , and to gws and neutrino signals in the mhd mechanism . to compensate the uncovered fields , the related references will be given . although a number of excellent reviews already exist on various topics in this article , this one might go beyond such reviews by its new perspectives on the multimessenger astronomy . |
data - driven understanding of cybersecurity posture is an important problem that has not been adequately explored . in this paper , we analyze some real data collected by caida s network telescope during the month of march 2013 . we propose to formalize the concept of cybersecurity posture from the perspectives of three kinds of time series : the number of victims ( i.e. , telescope ip addresses that are attacked ) , the number of attackers that are observed by the telescope , and the number of attacks that are observed by the telescope . we report that the number of attackers ( and attacks ) from a certain country dominates the total number of attackers ( and attacks ) that are observed by the telescope . we also show that substantially smaller network telescopes might not be as useful as a large telescope . | i | 1603.07438 | data - driven understanding of cybersecurity posture is an important problem that has not been adequately explored . in this paper , we analyze some real data collected by caida s network telescope during the month of march 2013 . we propose to formalize the concept of cybersecurity posture from the perspectives of three kinds of time series : the number of victims ( i.e. , telescope ip addresses that are attacked ) , the number of attackers that are observed by the telescope , and the number of attacks that are observed by the telescope . characterizing cybersecurity posture therefore becomes investigating the phenomena and statistical properties exhibited by these time series , and explaining their cybersecurity meanings . for example , we propose the concept of _ sweep - time _ , and show that sweep - time should be modeled by stochastic process , rather than random variable . we report that the number of attackers ( and attacks ) from a certain country dominates the total number of attackers ( and attacks ) that are observed by the telescope . we also show that substantially smaller network telescopes might not be as useful as a large telescope . * keywords : * cybersecurity data analytics , cybersecurity posture , network telescope , network blackhole , darknet , cyber attack sweep - time , time series data | network telescope @xcite ( aka blackhole @xcite , darknet @xcite , or network sink @xcite , possibly with some variations ) is a useful instrument for monitoring unused , routeable ip address space . since there are no legitimate services associated to these unused ip addresses , traffic targeting them is often caused by attacks . this allows researchers to use telescope - collected data ( together with other kinds of data ) to study , for example , worm propagation @xcite , denial - of - service ( dos ) attacks @xcite , and stealth botnet scan @xcite . despite that telescope data can contain unsolicited but not necessarily malicious traffic that can be caused by misconfigurations or by internet background radiation @xcite , analyzing telescope data can lead to better understanding of _ cybersecurity posture _ , an important problem that has yet to be investigated . * our contributions . * in this paper , we empirically characterize cybersecurity posture based on a dataset collected by caida s /8 network telescope ( i.e. , @xmath0 ip addresses ) during the month of march 2013 . we make the following contributions . * first * , we propose to characterize cybersecurity posture by considering three time series : the number of victims , the number of attackers , and the number of attacks . to the best of our knowledge , this is the first formal definition of cybersecurity posture . * second * , we define the notion of _ sweep - time _ , namely the time it takes for most telescope ip addresses to be attacked at least once . we find that sweep - time can not be described by a probabilistic distribution , despite that a proper subset of the large sweep - times follows the power - law distribution . we show that an appropriate stochastic process can instead describe the sweep - time . this means that when incorporating sweep - time in theoretical cybersecurity models , it can not always be treated as a random variable and may need to be treated as a stochastic process . * third * , we find that the total number of attackers that are observed by the network telescope is dominated by the number of attackers from a certain country @xmath1 . moreover , we observe that both the number of attackers from country @xmath1 and the total number of attackers exhibit a strong periodicity . although we can not precisely pin down the root cause of this _ dominance and periodicity _ phenomenon , it does suggest that thoroughly examining the traffic between country @xmath1 and the rest of the internet may significantly improve cybersecurity . * fourth * , we investigate whether or not substantially smaller network telescopes would give approximately the same statistics that would be offered by a single , large network telescope . this question is interesting on its own and , if answered affirmatively , could lead to more cost - effective operation of network telescopes . unfortunately , our analysis shows that substantially smaller telescopes might not be as useful a single , large telescope ( of @xmath0 ip addresses ) . * related work . * one approach to understanding cybersecurity posture is to analyze network telescope data . studies based on telescope data can be classified into two categories . the first category analyzes telescope data _ alone _ , and the present study falls into this category . these studies include the characterization of internet background radiation @xcite , the characterization of scan activities @xcite , and the characterization of backscatter for estimating global dos activities @xcite . however , we analyze cybersecurity posture , especially with regard to attacks that are likely caused by malicious worm , virus and bot activities . this explains why we exclude the backscatter data ( which is filtered as noise in the present paper ) . the second category of studies analyzes telescope data together with other kinds of relevant data . these studies include the use of telescope data and network - based intrusion detection and firewall logs to analyze internet intrusion activities @xcite , the use of out - of - band information to help analyze worm propagation @xcite , and the use of active interactions with remote ip addresses to filter misconfiguration - caused traffic @xcite . there are also studies that are somewhat related to ours , including the identification of one - way traffic from data where two - way traffic is well understood @xcite . the other approach to understanding cybersecurity posture is to analyze data collected by honeynet - like systems ( e.g. , @xcite ) . unlike network telescopes , these systems can interact with remote computers and therefore allow for richer analysis , including the automated generation of attack signatures @xcite . to the best of our knowledge , we are the first to formally define _ cybersecurity posture _ via three time series : the number of victims , the number of attackers , and the number of attacks . the rest of the paper is organized as follows . section [ sec : data - representation ] describes the data and defines cybersecurity posture . section [ sec : statistical - preliminaries ] briefly reviews some statistical preliminaries . section [ sec : victim - situation ] defines and analyzes the sweep - time . section [ sec : attacker - situation ] investigates the dominance and periodicity phenomenon exhibited by the number of attackers . section [ sec : inference ] investigates whether substantially smaller network telescopes would be sufficient or not . section [ sec : limitations ] discusses the limitations of the present study . section [ sec : conclusion ] concludes the paper . |
but decoherence can also be thought of in a purely classical context , as the loss of phase coherence in the classical phase space . , we report on the methods available to define pure dephasing in these systems , while demonstrating the intrinsic almost - ideal properties of silicon - nitride beams . | i | 1511.02120 | decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours , while imposing technological bounds for quantum devices . little is known about quantum coherence of mechanical systems , as opposed to electromagnetic degrees of freedom . but decoherence can also be thought of in a purely classical context , as the loss of phase coherence in the classical phase space . indeed the bridge between quantum and classical physics is under intense investigation , using in particular classical nanomechanical analogues of quantum phenomena . in the present work , by separating pure dephasing from dissipation , we quantitatively model the classical decoherence of a mechanical resonator : through the experimental control of frequency fluctuations , we engineer artificial dephasing . building on the fruitful analogy introduced between spins / quantum bits and nanomechanical modes , we report on the methods available to define pure dephasing in these systems , while demonstrating the intrinsic almost - ideal properties of silicon - nitride beams . these experimental and theoretical results , at the boundary between classical nanomechanics and quantum information fields , are prerequisite in the understanding of decoherence processes in mechanical devices , both classical and quantum . | [ intro ] decoherence can be viewed either in its quantum picture , where it stands for the loss of phase coherence of a superposition state @xcite , or as its classical equivalent , where the phase of an oscillating signal is smeared due to frequency fluctuations @xcite . until recently , dissipation , which accounts for an energy loss over time @xcite , was not distinguished from decoherence in nanomechanical resonators . the first reason for this oversight lies in the acquisition method : spectral acquisition , in which the driving frequency is swept through the mechanical resonance , does not separate the two processes , since both lead to broadened resonance lines . the response linewidth then leads to the definition of a decoherence time @xmath0 , in analogy with nuclear magnetic resonance ( nmr ) @xcite or quantum information experiments @xcite . one way to unravel a dephasing mechanism is to perform a complementary time - domain ringdown measurement . here , the free decay of the response amplitude yields an energy relaxation time , since the decay rate only depends on dissipation , not frequency fluctuations . this procedure is analogous to a @xmath1 measurement for spins or qubits . having @xmath2 then leads to the definition of a pure dephasing rate @xmath3 @xcite . while the reported @xmath1 and @xmath0 for a particular qubit are often significantly different @xcite , such a difference in a nanomechanical resonator is still rare in the literature : usually mechanical systems seem to experience frequency fluctuations small compared to dissipation mechanisms , and do not exhibit visible spectral broadening due to dephasing @xcite . nonetheless , pure dephasing has been observed in refs . @xcite . but direct comparisons between time - domain ( @xmath1 ) and frequency - domain ( @xmath0 ) are still rare : thus , the second and main reason for the scarcity of experimental studies on mechanical decoherence is a lack of data _ combining _ these techniques . to our knowledge , only one recent work reports , for a suspended carbon nanotube , a signature of a pure ( yet nonlinear ) dephasing mechanism demonstrating @xmath2 @xcite , while another study which _ did not _ contain @xmath1 measurements presents similar features interpreted as nonlinear damping @xcite . indeed , the effects of frequency noise ( and its origin ) in nanomechanical devices is a subject intensely investigated today , both for its fundamental aspects and the technical limitations it poses to actual devices @xcite . besides , with the advances of quantum nanomechanics , the decoherence of quantum mechanical states also becomes a challenging issue @xcite . in this article we report on a model experiment using a high quality nanoelectromechanical system ( nems ) , top - down fabricated from high - stress silicon - nitride ( sin ) @xcite . using a gate electrode @xcite , we capacitively control the oscillator s frequency fluctuations by applying voltage noise , leading to a completely quantitative description of mechanical decoherence . first we perform time and frequency domain measurements without noise applied on the gate , in order to ensure that no pure dephasing is observed over our whole dynamic range , from linear to highly nonlinear regimes : we thus establish our device as ideal for our study . in a second part , a low - frequency noise gate voltage is injected , leading to resonance frequency fluctuations increasing with the noise level : indeed , a significant spectral broadening is observed , while ringdown measurements leave @xmath1 unchanged , demonstrating pure dephasing with @xmath2 . we present the complete formalism applying to low - frequency fluctuations of the resonance frequency . building on the new methods presented , we furthermore discuss the possibility to extract information about the fluctuations statistics from the shape of the spectral response in actual devices suffering from dephasing . |
decoherence is the main obstacle to the realization of quantum computers . until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem . here we present an alternative that is based on a combination of a decoherence - free subspace encoding and the application of strong and fast pulses : `` encoded recoupling and decoupling '' ( erd ) . | i | quant-ph0302198 | decoherence is the main obstacle to the realization of quantum computers . until recently it was thought that quantum error correcting codes are the only complete solution to the decoherence problem . here we present an alternative that is based on a combination of a decoherence - free subspace encoding and the application of strong and fast pulses : `` encoded recoupling and decoupling '' ( erd ) . this alternative has the advantage of lower encoding overhead ( as few as two physical qubits per logical qubit suffice ) , and direct application to a number of promising proposals for the experimental realization of quantum computers . | in the quest to construct large - scale quantum information processors , in particular quantum computers , decoherence is still the main obstacle to realization . decoherence is the degradation of quantum information due to inevitable interactions with the environment . early skepticism @xcite concerning the viability of quantum computation ( qc ) in the presence of decoherence was overcome by the discovery of quantum error correcting codes ( qeccs),@xcite that flourished into a comprehensive theory that incorporates all elements of quantum computation.@xcite a qecc relies on an encoding of quantum information into the state of several quantum bits ( qubits ) , and a closed - loop , active error diagnosis and correction procedure.@xcite in principle , it is possible to correct arbitrary errors using sufficiently large qeccs.@xcite in practice , however , this may require a very large overhead , especially in terms of qubit resources.@xcite this is troubling in light of the substantial difficulties associated with generating and controlling systems with very large numbers of qubits . in addition , the theory of qeccs is rather abstract , in that it presumes that one can execute certain logical operations , but does not refer to the underlying hamiltonians governing specific physical systems . hence it is of interest to explore alternatives to qeccs , that are more economical in qubit resources , and that are direcly tailored to specific quantum computer proposals . here we review our recent progress in developing such an alternative , `` encoded recoupling and decoupling '' ( erd),@xcite and report on some new results . erd is based on a combination of encoding quantum information into a decoherence - free subspace ( dfs ) @xcite ( for a review see ref . ) , and the application of fast and strong dynamical - decoupling ( or `` bang - bang '' , bb ) pulses.@xcite the dfs encoding provides a first layer of protection against decoherence , while the bb pulses are used to efficiently reduce the remaining decoherence . the encoded `` recoupling '' part of erd refers to the application of control operations that enact universal quantum logic , in a manner that is fully compatible with the dfs encoding and the bb pulses , and takes into account the experimentally available control resources , such as the underlying system hamiltonian @xcite . the utility of erd as a general method for quantum simulation , universal qc , and decoherence suppression has also been stressed and explored by viola.@xcite our work builds in part on earlier efforts to combine universal qc with dfs encoding ( without bb pulses).@xcite the structure of the paper is as follows . we begin in section [ decoherence ] with a brief formal summary of decoherence . we then give in section [ dfs ] a simple example of a dfs encoding , protecting against collective dephasing . section [ logic ] shows how to perform universal qc on this encoding . we then briefly and formally review the dynamical decoupling method , in section [ decoupling ] . the methods are then combined in sections [ createdfs],[leakage - elim ] , where we show how bb pulses can eliminate decoherence sources beyond collective dephasing . in section [ offres ] we present a new and somewhat surprising result : the elimination of off - resonant transitions , that will typically be induced by bb pulses , via bb pulses . section [ all ] shows how to combine all the pieces together , by including logic gates with the bb pulses . concluding remarks are presented in section [ conclusions ] . |
we present a numerical method to identify trajectories with atypical chaoticity , pathways that are either more regular or more chaotic than average . the method is based on the definition of an ensemble of trajectories weighted according to their chaoticity , the lyapunov weighted path ensemble . we demonstrate our approach by applying it to several systems with numbers of degrees of freedom ranging from one to several hundred and in all cases the algorithm found rare pathways with atypical chaoticity . for a double - well dimer embedded in a solvent , which can be viewed as simple model for an isomerizing molecule | c | 1004.2654 | depending on initial conditions , individual finite time trajectories of dynamical systems can have very different chaotic properties . here we present a numerical method to identify trajectories with atypical chaoticity , pathways that are either more regular or more chaotic than average . the method is based on the definition of an ensemble of trajectories weighted according to their chaoticity , the lyapunov weighted path ensemble . this ensemble of trajectories is sampled using algorithms borrowed from transition path sampling , a method originally developed to study rare transitions between long - lived states . we demonstrate our approach by applying it to several systems with numbers of degrees of freedom ranging from one to several hundred and in all cases the algorithm found rare pathways with atypical chaoticity . for a double - well dimer embedded in a solvent , which can be viewed as simple model for an isomerizing molecule , rare reactive pathways were found for parameters strongly favoring chaotic dynamics . | in this paper , we have presented a flexible numerical method to find particularly chaotic or regular trajectories in dynamical systems . the basic idea of the method , inspired by the work of tailleur and kurchan @xcite and called lyapunov weighted path sampling , is to first define an ensemble of trajectories weighted by a measure of their chaoticity , for instance their finite time lyapunov exponent . in this trajectory ensemble a parameter , which can be viewed as conjugate to the lyapunov exponent , can be tuned to favor either very chaotic or very regular trajectories . the trajectory ensemble is then sampled with methods adopted from transition path sampling . other chaoticity indicators besides finite time lyapunov exponents can be easily integrated into the algorithm as well . since the calculation of finite time lyapunov exponents can be computationally demanding , we have , for instance , used relative lyapunov indicators ( rli ) to bias trajectories according to their level of chaos . these indicators are particularly sensitive and are capable of distinguishing weakly chaotic trajectories from regular ones . while in this paper we have used lyapunov weighted path sampling to study only systems evolving deterministically , the method can be applied as easily to stochastic dynamics provided an appropriate chaoticity indicator is available . the complexity of the examples studied here ranges from a simple one - dimensional double well system to the fpu - model and a bistable dimer in a solvent with hundreds of degrees of freedom . in all cases , the lyapunov weighted path sampling algorithm successfully identified trajectories with atypical chaoticity properties . while for the fpu - model we used lyapunov weighted path sampling to find weakly chaotic solitonic modes of motion , we concentrated on highly chaotic trajectories for the dimer in solution . the results obtained for this simple model of a chemical reaction indicate that it is possible to use lyapunov weighted path sampling to find rare reactive trajectories that pass through saddle points in the potential energy surface as they connect long - lived stable states with each other . further studies will be necessary to clarify to which degree identifying such trajectories is made difficult by the chaos arising from degrees of freedom not directly coupled to the reaction ( for instance solvent degrees of freedom ) and possibly eclipsing the dynamical instability of the reactive subsystem . it will also be interesting to investigate whether chaoticity indicators such as the maximum lyapunov exponent , the kolmogorov - sinai entropy or the relative lyapunov indicators used in the present study correlate with the measures of mobility used by chandler and collaborators to link the glass transition with a first order phase transition in trajectory space @xcite . in their work , these authors started from the equilibrium distribution of pathways and added to it a bias that favors trajectories with low dynamical activity . chandler an coworkers demonstrated numerically that this transition displays all the features of a first - order transition occurring in trajectory space . it would be interesting to study if an analogous bias based on chaoticity indicators also leads to an equivalent first order transition in path space . in such research it may be fruitful to combine lyapunov weighted path sampling with advanced equilibrium simulation methods such as umbrella sampling @xcite , metadynamics @xcite , or parallel replica sampling @xcite directly acting on chaoticity indicators . |
a _ hubble space telescope _ our accidental observation also provides the first high - quality ultraviolet spectrum of a globular cluster cv . that we have detected such an object in an observation that includes just a few percent of the central area of the cluster | i | astro-ph9909344 | despite indications that classical cataclysmic variable ( cv ) stars are rare in globular clusters in general , and in the cluster ngc6624 in particular , we have serendipitously discovered such a star @xmath0 from the cluster center . a _ hubble space telescope _ spectrum of the @xmath1 object shows strong , broad emission lines typical of numerous field cvs , and the inferred optical and uv luminosity are also similar . our accidental observation also provides the first high - quality ultraviolet spectrum of a globular cluster cv . that we have detected such an object in an observation that includes just a few percent of the central area of the cluster may indicate that cluster cvs are more common than previously thought , at least near the core . -0.6 in 9.6 in 0.210 in accepted for publication in the astronomical journal + to appear in the 1999 december issue , volume 118 + _ received 1999 july 28 ; accepted 1999 august 31 _ | a small number of close binary stars are thought to dominate the dynamic evolution of many globular star clusters ( hut et al . 1992 , bailyn 1995 ) , yet classes of such objects which are relatively easily found in the field have proven frustratingly difficult to discover in clusters . a prime example is cataclysmic variables ( cvs ) , which call attention to themselves via large amplitude light outbursts , and peculiar , ultraviolet - excess colors in quiescence . with quiescent absolute magnitudes @xmath2 , modern ground - based photometric techniques should easily uncover such objects in clusters with typical distances of @xmath3 , even with modest telescopes , unless all such objects are lost to the crowded cores . yet prior to the launch of _ hubble space telescope _ ( _ hst _ ) , we are aware of only two candidate identifications of cvs in globular clusters , m5 v101 ( margon et al . 1981 ) , whose classification and cluster membership seems secure ( naylor et al . 1989 , shara et al . 1990 ) , and m30 v4 ( margon & downes 1983 ) , whose membership is unclear ( shara et al . 1990 , machin et al . 1991 ) . observations from _ hst _ have certainly improved the situation , although perhaps not as much as many would have expected . a few clusters are now known to have a handful of spectroscopically - confirmed cvs ; a recent review is given by grindlay ( 1999 ) . however despite intensive photometric and color - selected searches deep into the cores of a number of clusters , few outbursting objects are found , and most authors believe there is a serious discrepancy with theoretical predictions ( shara & drissen 1995 ; livio 1996 ; shara et al . 1996 , hereafter s96 ) . whether the problem lies with formation / destruction rates , or some unique property of cluster cvs , remains to be clarified , and will surely require a larger sample of objects . here we discuss _ hst _ observations of the cluster ngc6624 using the _ space telescope imaging spectrograph _ ( stis ) . this cluster contains near its center a highly luminous bursting x - ray source with an 11-minute period , the shortest - known binary star ; the system is thought to be a double - degenerate ( stella et al . 1987 , king et al . 1993 , anderson et al . another object in the cluster has also been suggested by s96 as a candidate cv , although we discuss its nature further in 3 . as part of a program to study the central bright x - ray source , we obtained deep stis spectroscopic exposures of this object , and these results will be discussed elsewhere ( deutsch et al . 2000 ) . here we report the completely serendipitous discovery of @xmath1 emission line object , which fell by good fortune in the stis slit , and has the properties of a classical cv . this object deepens the mystery of the cv content of clusters . s96 report a multi - epoch sensitive photometric search of the core of ngc6624 which identifies only one candidate cv , and suggest these objects are very rare , at least in this cluster . yet we have found another such an object completely by accident , in the first long - slit ultraviolet spectral exposure made of the cluster . |
despite the importance of isotopically purified samples in current experiments , there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations . isotopic purification eliminates the well - studied nuclear spin baths which usually dominate decoherence . we model the coherence of electronic spin qubits in silicon near so called clock transitions ( ct ) where experiments have electronic @xmath0 times of seconds . despite the apparent simplicity of the residual decoherence mechanism , this regime is not well understood : the state mixing which underpins cts allows also a proliferation of contributions from usually forbidden channels ( direct flip - flops with non - resonant spins ) ; in addition , the magnitude and effects of the corresponding overhauser fields and other detunings is not well quantified . for purely magnetic detunings , we identify a regime , potentially favourable for quantum computing , where forbidden channels are completely suppressed but spins in resonant states are fully released from overhauser fields and applied magnetic field gradients . | i | 1509.08326 | despite the importance of isotopically purified samples in current experiments , there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations . isotopic purification eliminates the well - studied nuclear spin baths which usually dominate decoherence . we model the coherence of electronic spin qubits in silicon near so called clock transitions ( ct ) where experiments have electronic @xmath0 times of seconds . despite the apparent simplicity of the residual decoherence mechanism , this regime is not well understood : the state mixing which underpins cts allows also a proliferation of contributions from usually forbidden channels ( direct flip - flops with non - resonant spins ) ; in addition , the magnitude and effects of the corresponding overhauser fields and other detunings is not well quantified . for purely magnetic detunings , we identify a regime , potentially favourable for quantum computing , where forbidden channels are completely suppressed but spins in resonant states are fully released from overhauser fields and applied magnetic field gradients . we show by a general argument that the enhancement between this regime and the high field limit is @xmath1 , regardless of density , while enhancements of order 50 are measured experimentally . we propose that this discrepancy is likely to arise from strains of exclusively non - magnetic origin , underlining the potential of cts for isolating and probing different types of inhomogeneities . we also identify a set of fields , dipolar refocusing points " ( drps ) , where the hahn echo fully refocuses the effect of the dipolar interaction . | there is considerable interest in the use of isotopically pure samples , with both diamond and silicon platforms , for implementation of solid state spin qubits for quantum information . dramatic improvements in performance have been measured in silicon @xcite with some of the longest coherence times ever observed . decoherence of the electron qubit is dominated by a bath of @xmath2si nuclear spin impurities in natural silicon , or @xmath3c impurities in natural diamond , which lead to dephasing decoherence ( spectral diffusion ) of the electronic spin . the theory of decoherence by nuclear spin baths is well understood in both cases @xcite . in purified samples , it is instead interactions between electronic donor spins themselves which dominate decoherence in typical esr experiments . for the case of silicon , many studies used ensembles , but there have also been a significant number of studies with single spin systems @xcite . although most implementations in silicon use phosphorus , there is also growing interest in other donor species @xcite such as bismuth , arsenic and antimony where there is strong mixing between the donor electronic and nuclear spins at modest magnetic fields ( @xmath4 t ) , leading to rich and surprising coherence behavior . for these , optimal working points ( owps ) also referred to as cts ( `` clock transitions '' ) @xcite of enhanced electronic coherence have been identified , and there have been several studies investigating these @xcite . however , all the theoretical work on cts / owps has to date been restricted to nuclear spin baths . , but for atomic species with strong electronic coupling to the host nuclear spins ( purple arrows ) the @xmath5 eigenvalues @xmath6 are not good quantum numbers . instead , each spin quantum state @xmath7 corresponds to eigenstates of an effective field , tilted to the @xmath8-axis by an angle @xmath9 , with @xmath10 . microwave pulses resonantly drive transitions @xmath11 between two selected states ; the figure exemplifies two donor atoms , each in one of these resonant spin states . * ( b ) * the dipolar coupling allows two decoherence mechanisms : instantaneous diffusion ( i d ) , a dephasing arising in hahn echo experiments where nearby spins are both rotated by the microwave pulse ; and direct flip - flops ; for esr lines the relative magnitude of the contributions is given in terms of @xmath12.,title="fig:",width=182 ] , but for atomic species with strong electronic coupling to the host nuclear spins ( purple arrows ) the @xmath5 eigenvalues @xmath6 are not good quantum numbers . instead , each spin quantum state @xmath7 corresponds to eigenstates of an effective field , tilted to the @xmath8-axis by an angle @xmath9 , with @xmath10 . microwave pulses resonantly drive transitions @xmath11 between two selected states ; the figure exemplifies two donor atoms , each in one of these resonant spin states . * ( b ) * the dipolar coupling allows two decoherence mechanisms : instantaneous diffusion ( i d ) , a dephasing arising in hahn echo experiments where nearby spins are both rotated by the microwave pulse ; and direct flip - flops ; for esr lines the relative magnitude of the contributions is given in terms of @xmath12.,title="fig:",width=134 ] we address this gap here by modelling the extremely long , measured @xmath0 times in enriched samples , in particular a detailed experimental study of ct behavior for both isotopically enriched bismuth ( si : bi ) and natural silicon @xcite . for si : p there have been cluster correlation expansion ( cce ) quantum simulations of the donor - donor spectral diffusion @xcite ( indirect flip - flop decoherence mechanism ) which is the dominant mechanism away from cts . near cts , a quantum calculation of spectral diffusion becomes extremely challenging : a many - body calculation ( beyond pair correlation ) is required to even obtain finite decay times @xcite . for the nuclear baths , good agreement with experimental results was obtained recently @xcite for si : bi , in natural silicon . fortunately , for enriched samples , spectral diffusion is suppressed at cts and typically represents a negligible contribution . the dynamics either ( i ) at the ct point @xmath13 or at ( ii ) high fields @xmath14 t is comparatively simple . ( i ) at the cts , since spectral diffusion is strongly suppressed , the dominant process is the mutual decoherence of spins via direct flip - flops ( dff ) . ( ii ) at high fields there is a well - known dominant dephasing mechanism , instantaneous diffusion ( i d ) @xcite ( illustrated in fig.[fig1 ] ) . i d is a dephasing effect , arising because microwave pulses , applied as part of the usual hahn echo sequence used to measure @xmath15 times , produce unwanted rotations of neighbouring resonant spins . further details of the spin mixing leading to cts and of the decoherence dynamics are given in the appendix . ( see eq.[gamma ] ) . the experimentally measured @xmath16 transition of si : bi is investigated . at high magnetic fields @xmath17 t ( solid blue line ) behavior is dominated by instantaneous diffusion leading to a short coherence time @xmath18 . at clock transitions ( ct ) direct flip - flops ( dff ) are dominant ( dashed blue line ; 799 g ct shown ) . for @xmath19 , the clock transition offers very little enhancement over the high field limit , because of non - resonant flip - flops . as @xmath20 increases , non - resonant dff decline ; the decays near a ct tend to a saturation value @xmath21 , where the resonant states are fully released from overhauser fields , but non - resonant channels are fully suppressed . here @xmath22 ^ 2/[\frac{1}{2}(1+p_u(b_\text{ct}))(1-p_d(b_\text{ct}))]\simeq 8 $ ] . however , the observed @xmath15 are considerably longer ; we conclude that the discrepancy between @xmath21 and @xmath15 isolates inhomogeneities of non - magnetic origin , so may usefully probe different components of the detuning fields . * ( a ) * low donor density @xmath23 * ( b ) * higher density @xmath23 . the behaviors , to a good approximation , scale with @xmath23 . at typical overhauser fields of @xmath24s hz for purified samples with 50 ppm of @xmath2si , there is still an appreciable contribution from non - resonant flip - flops . at very large detunings the ct position itself becomes perturbed ( dashed red line ) . , title="fig:",width=259 ] ( see eq.[gamma ] ) . the experimentally measured @xmath16 transition of si : bi is investigated . at high magnetic fields @xmath17 t ( solid blue line ) behavior is dominated by instantaneous diffusion leading to a short coherence time @xmath18 . at clock transitions ( ct ) direct flip - flops ( dff ) are dominant ( dashed blue line ; 799 g ct shown ) . for @xmath19 , the clock transition offers very little enhancement over the high field limit , because of non - resonant flip - flops . as @xmath20 increases , non - resonant dff decline ; the decays near a ct tend to a saturation value @xmath21 , where the resonant states are fully released from overhauser fields , but non - resonant channels are fully suppressed . here @xmath22 ^ 2/[\frac{1}{2}(1+p_u(b_\text{ct}))(1-p_d(b_\text{ct}))]\simeq 8 $ ] . however , the observed @xmath15 are considerably longer ; we conclude that the discrepancy between @xmath21 and @xmath15 isolates inhomogeneities of non - magnetic origin , so may usefully probe different components of the detuning fields . * ( a ) * low donor density @xmath23 * ( b ) * higher density @xmath23 . the behaviors , to a good approximation , scale with @xmath23 . at typical overhauser fields of @xmath24s hz for purified samples with 50 ppm of @xmath2si , there is still an appreciable contribution from non - resonant flip - flops . at very large detunings the ct position itself becomes perturbed ( dashed red line ) . , title="fig:",width=259 ] however , simulating the experimentally measured ct behavior in enriched silicon is still far from straightforward ; there is the richness introduced by the mixing : one must consider the proliferation of usually `` forbidden '' channels allowing for non - resonant direct flip - flops ( dff ) . in systems like si : p , with little state mixing , only flip - flops between resonant states ( in the sense of resonant with the applied microwave pulse ) are considered . most importantly , the nature of the detuning fields , whether effective magnetic fields fields originating from other spins or contributions which are non - magnetic in origin ( in the broad sense that they do not probe the @xmath25 component of the donor , which can be electric fields ) is not well - understood . the effective magnetic fields from both other donor spins as well as from residual @xmath2si are , for convenience , both grouped together and termed the overhauser field ( though commonly overhauser fields refer to the nuclear spins only ) . these can be estimated numerically , given knowledge of the spin densities . but the non - magnetic inhomogeneities are not known . nevertheless , even without precise quantitative knowledge of the detuning fields we can obtain some robust conclusions . we show that we can exploit the properties of the ct to isolate the effects of different types of detunings on dff and propose a favourable operating regime for quantum information , where all forbidden channels are suppressed while resonant spins are fully released from the overhauser field . we show that in future qubit implementations , the fact that i d and dff arise from the dipolar operator means that they can interfere destructively in spin systems with mixing , leading to full refocusing of the dipolar operator by a hahn sequence , at arbitrary pulse spacing . the fields where this occurs are labeled dipolar refocusing points " ( drps ) . |
we show by a general argument that the enhancement between this regime and the high field limit is @xmath1 , regardless of density , while enhancements of order 50 are measured experimentally . we propose that this discrepancy is likely to arise from strains of exclusively non - magnetic origin , underlining the potential of cts for isolating and probing different types of inhomogeneities . we also identify a set of fields , dipolar refocusing points " ( drps ) , where the hahn echo fully refocuses the effect of the dipolar interaction . | c | 1509.08326 | despite the importance of isotopically purified samples in current experiments , there have been few corresponding studies of spin qubit decoherence using full quantum bath calculations . isotopic purification eliminates the well - studied nuclear spin baths which usually dominate decoherence . we model the coherence of electronic spin qubits in silicon near so called clock transitions ( ct ) where experiments have electronic @xmath0 times of seconds . despite the apparent simplicity of the residual decoherence mechanism , this regime is not well understood : the state mixing which underpins cts allows also a proliferation of contributions from usually forbidden channels ( direct flip - flops with non - resonant spins ) ; in addition , the magnitude and effects of the corresponding overhauser fields and other detunings is not well quantified . for purely magnetic detunings , we identify a regime , potentially favourable for quantum computing , where forbidden channels are completely suppressed but spins in resonant states are fully released from overhauser fields and applied magnetic field gradients . we show by a general argument that the enhancement between this regime and the high field limit is @xmath1 , regardless of density , while enhancements of order 50 are measured experimentally . we propose that this discrepancy is likely to arise from strains of exclusively non - magnetic origin , underlining the potential of cts for isolating and probing different types of inhomogeneities . we also identify a set of fields , dipolar refocusing points " ( drps ) , where the hahn echo fully refocuses the effect of the dipolar interaction . | given the modest overhauser fields present in current experiments , we conclude that decoherence at clock transitions includes a very substantial contribution from direct flip - flops with non - resonant spins . we have shown that quantum bath calculations can not account for measured electronic spin coherence @xmath0 times at clock transitions if only detuning fields of magnetic origin are included and so much of the enhancement found over the high field limit is due to non - magnetic detunings of unknown origin . despite these uncertainties , some robust conclusions are still possible . were it not for non - magnetic detunings , the coherence times at cts could be about an order of magnitude shorter and enhancements over the high field limit would be modest . the study identifies a regime where non - resonant flip - flops are fully suppressed but where , because of the ct , resonant spins ( not detuned by non - magnetic fields ) are fully released from the overhauser field . here they may interact and entangle via the dipolar interaction , but may also be selectively detuned , if required , by electric fields . we identify also dipolar refocusing points where in future , if qubit detunings and state preparation is possible , the full dipolar interaction can be eliminated by a simple hahn echo sequence of arbitrary pulse spacing . _ acknowledgements _ : we are grateful for helpful discussions and advice from gary wolfowicz and sougato bose . jel acknowledges an epsrc dta studentship . rg acknowledges funding from epsrc grant ep / j010561/1 . |
electron - electron interactions are responsible for a correction to the conductance of a diffusive metal , the `` altshuler - aronov correction '' @xmath0 . here , the ehrenfest time @xmath1 enters as an additional time scale that determines the magnitude of quantum interference effects . the ehrenfest time effectively poses a short - time threshold for the trajectories contributing to the interaction correction . as a consequence , @xmath0 becomes exponentially suppressed if the ehrenfest time is larger than the dwell time or the inverse temperature . | i | 1211.1843 | electron - electron interactions are responsible for a correction to the conductance of a diffusive metal , the `` altshuler - aronov correction '' @xmath0 . here we study the counterpart of this correction for a ballistic conductor , in which the electron motion is governed by chaotic classical dynamics . in the ballistic conductance , the ehrenfest time @xmath1 enters as an additional time scale that determines the magnitude of quantum interference effects . the ehrenfest time effectively poses a short - time threshold for the trajectories contributing to the interaction correction . as a consequence , @xmath0 becomes exponentially suppressed if the ehrenfest time is larger than the dwell time or the inverse temperature . we discuss the explicit dependence on ehrenfest time in quasi - one and two - dimensional antidot arrays . for strong interactions , the sign of @xmath0 may change as a function of temperature for temperatures in the vicinity of @xmath2 . | electronic transport in weakly disordered metals is successfully described by the boltzmann theory , in which electrons are treated as effectively classical particles moving freely between scattering events . the wave nature of electrons gives rise to a number of corrections to transport properties , such as the weak localization correction,@xcite the altshuler - aronov interaction correction,@xcite or the universal conductance fluctuations.@xcite weak localization results from the constructive interference of electrons propagating along time - reversed paths.@xcite the physical intuition behind the interaction correction is constructive interference of electron trajectories which are scattered on impurities and friedel oscillations of the electron density.@xcite these quantum corrections become increasingly important as the temperature is lowered , the effective dimensionality of the sample is reduced , or as the disorder level is increased . they have a distinctive and universal dependence on external parameters , such as temperature or magnetic field , which makes them identifiable in experiments . in particular , the two quantum corrections to the conductivity , weak localization and the altshuler - aronov correction , can be distinguished by application of a magnetic field , since weak localization is suppressed by already a very small magnetic field , whereas the altshuler - aronov correction is not . a `` classical analog '' of a disordered metal is realized in high - mobility semiconductor structures with randomly placed large antidots.@xcite the absence of impurities ensures that electrons move ballistically between reflections off the antidots . the reason why these systems are referred to as classical is that the size of the antidots @xmath3 is much larger than the fermi wavelength @xmath4 . as a result , not only the electron s motion through the two - dimensional electron gas , but also the reflection off an antidot is described by classical mechanics . ( in contrast , in a disordered metal , the size of impurities is comparable to @xmath4 , so that the scattering event is strongly diffractive . ) for an irregular arrangement of antidots , the classical dynamics is chaotic . nearby trajectories separate exponentially in time , the exponential separation being characterized by the lyapunov coefficient @xmath5 . the chaotic dynamics is essential for the existence of quantum corrections in this system , as it magnifies the quantum uncertainty of even a minimal wavepacket up to classical dimensions within the short time @xmath6 thus transforming the classical dynamics into quantum - diffractive dynamics on time scales larger than @xmath1.@xcite the time @xmath1 is known as the `` ehrenfest time '' . since wave effects are not operative for times shorter than @xmath1 electrons essentially move along classical trajectories up to the ehrenfest time , the ehrenfest time serves as a short - time threshold for the duration of the trajectories contributing to the quantum corrections in an antidot array . for weak localization , it was found that the correction to the conductivity is exponentially suppressed if @xmath1 is larger than the dwell time @xmath7 , the typical time to be transmitted through the system , or the dephasing time @xmath8.@xcite in contrast , other quantum corrections , such as the universal conductance fluctuations , remain finite if @xmath9.@xcite the goal of this article is to present a theory of the ehrenfest - time - dependence of the altshuler - aronov correction @xmath0 . our analysis significantly extends a previous calculation by kupferschmidt and one of the authors,@xcite which studied the @xmath1 dependence of the interaction correction to the conductance of a ballistic double quantum dot and found that @xmath0 is strongly suppressed if @xmath1 exceeds the dwell time @xmath7 or the inverse temperature @xmath10 . the double quantum dot studied in ref . is the simplest system with nonzero altshuler - aronov correction to the conductance , and is characterized by a long - range interaction , which is spatially homogeneous within each dot . the theory presented here is valid for both short - range and long - range interactions and can be applied to any geometry in which the classical electron dynamics is chaotic although we will focus our discussion on the case of an antidot array . for the general case considered here we confirm the suppression of @xmath0 for @xmath11 and we calculate the precise functional dependence of @xmath0 on @xmath7 and @xmath12 for finite ehrenfest time . the explicit dependence on temperature is characteristic for the interaction correction , which has its origin in virtual processes with an energy transfer larger than temperature . our calculation makes use of a semiclassical formalism that starts from the saddle - point approximation around classical trajectories for the single - particle green function . in this way , the conductance in the absence of electron - electron interactions is written as a double sum over classical trajectories that connect source and drain reservoirs.@xcite weak localization and other quantum corrections to the conductance then follow from special configurations of trajectories , in which the two trajectories in the summation are piecewise paired , and proceed through `` crossings '' at points where the pairing is changed.@xcite in the language of diagrammatic perturbation theory , segments where the trajectories are paired correspond to diffusons or cooperons , whereas the crossings correspond to hikami boxes . the application to interacting electrons requires a modification of the formalism , which will be described in detail below . our analysis applies to a `` ballistic '' conductor , where the label `` ballistic '' is meant to specify that the electrons move along well - defined classical trajectories . in the literature , `` ballistic '' sometimes refers to a different limit , and several calculations of the interaction correction to the conductance have been reported for such `` ballistic limits '' . whereas the original work of altshuler and aronov@xcite addressed a disordered metal with short - range scatterers in the diffusive regime @xmath13 , the theory was generalized to account for the effects of higher temperatures @xmath14 , a regime referred to as `` ballistic''.@xcite the case of a smooth disorder potential , in which scattering is predominantly forward , was considered in ref . . another type of system , where interaction corrections appear , are networks of capacitively coupled ballistic quantum dots,@xcite where , however , ehrenfest - time - related phenomena can be neglected as long as @xmath1 is much smaller than the dwell time in a single quantum dot . interactions also affect the conductance through their effect on the weak localization correction ( dephasing ) . semiclassical studies of the effect of interaction - induced dephasing on weak localization can be found in refs . , for electronic systems and in ref . for bosonic matter waves . in section [ sec : sctheory ] we present our theory of the ehrenfest - time dependence on the interaction correction for a generic ballistic chaotic conductor . in sec . [ sec : antidot ] we then apply our formalism to an antidot array , where the classical electronic motion is diffusive on length scales much larger than the spacing between antidots , and the coulomb interaction is dynamically screened by the diffusively moving electrons . for the antidot array , we find @xmath15 in the limit that the ehrenfest time is larger than dwell - time and inverse temperature . for small ehrenfest times , we recover the results of a disordered metal with quantum impurities , which show a much weaker temperature dependence ( algebraic or logarithmic , depending on dimensionality ) . we conclude in [ sec : conclusion ] . |
elliptical galaxies and their groups having the largest @xmath0 lie close to the locus @xmath1 expected for closed systems having baryon fractions equal to the cosmic mean value , @xmath2 . gas retention in these groups implies that non - gravitational heating can not exceed about 1 kev per particle , consistent with the heating required to produce the deviation of groups from the @xmath4 correlation for more massive clusters . isolated galaxies / groups with x - ray luminosities significantly lower than baryonically closed groups may have undermassive dark halos , overactive central agns , or higher star formation efficiencies . | c | astro-ph0511152 | elliptical galaxies and their groups having the largest @xmath0 lie close to the locus @xmath1 expected for closed systems having baryon fractions equal to the cosmic mean value , @xmath2 . the estimated baryon fractions for several of these galaxies / groups are also close to @xmath3 when the gas density is extrapolated to the virial radius . evidently they are the least massive baryonically closed systems . gas retention in these groups implies that non - gravitational heating can not exceed about 1 kev per particle , consistent with the heating required to produce the deviation of groups from the @xmath4 correlation for more massive clusters . isolated galaxies / groups with x - ray luminosities significantly lower than baryonically closed groups may have undermassive dark halos , overactive central agns , or higher star formation efficiencies . the virial mass and hot gas temperatures of nearly or completely closed groups correlate with the group x - ray luminosities and the optical luminosities of the group - centered elliptical galaxy , i.e. @xmath5 , an expected consequence of their merging history . the ratio of halo mass to the mass of the central galaxy for x - ray luminous galaxy / groups is @xmath6 . | we propose that galaxy groups lying near the upper envelope of the @xmath10 distribution in figure 1 are nearly or completely baryonically closed boxes similar to more massive clusters . this conclusion is supported by the baryon fraction estimates listed in table 1 and the proximity of the observations in figure 1 to the approximate dotted line locus for the maximum @xmath98 expected from baryonically closed groups observed to @xmath8 . the projected x - ray luminosity of our mass model for ngc 5044 beyond @xmath117 varies as @xmath118 so we expect that @xmath98 for galaxies with filled symbol points in figure 1 will creep upward toward the dotted line when observed with larger apertures and more sensitive detectors . nevertheless , we do not expect to find galaxy / groups in the future that lie significantly above the filled circles and squares in figure 1 . baryonically closed groups provide interesting constraints on the amount of non - gravitational heating acquired by the intragroup gas . to retain most or all of the gas in these groups , the gas heating by the central black hole ( agn ) must be @xmath119 or @xmath120 kev per particle , consistent with typical values @xmath121 kev per particle required to account for deviations from self - similarity in the @xmath4 plot for clusters ( e.g. tornatore et al . 2003 ; voit 2005 ) . we also find that the combined energy of all past supernovae is insufficient to remove significant amounts of intragroup gas unless the imf is flatter than salpeter ( brighenti & mathews 1999 , 2001 ) . another necessary attribute of baryonically closed groups is that they are spatially isolated , i.e. they have not lost mass by ram - stripping during mergers with comparable or larger systems . spatially isolated e galaxies and groups are of particular interest because of the strong limits they impose on non - gravitational heating . it is therefore remarkable that some isolated e galaxies have much lower @xmath98 than ellipticals in baryonically closed groups . for example , in figure 1 we mark with + symbols two isolated e galaxies found recently by reda et al . ( 2004 ) that are near the bottom of the distribution . this large variation of @xmath98 for isolated es of similar @xmath86 in figure 1 may result from normal cosmic variance . it would be interesting to determine if these and other isolated galaxies have unusually undermassive dark halos ( allowing winds ) , if they contain more energetically active ( and massive ) black holes or if their star formation efficiencies are unusually large , since such variations could help explain why these isolated galaxy / groups are not baryonically closed . by this means it will eventually be possible to determine if the non - gravitational heating arises primarily from the central black hole . it would also be worthwhile to assemble @xmath7 , @xmath122 and optical luminosities for all isolated e galaxies and groups throughout the @xmath10 plane . finally , we have shown that baryonically closed groups can inform us about the important relationship between the optical luminosity and mass of the group - centered galaxy and the mass of the surrounding ( group ) dark halo . the preliminary data currently available suggest that the dark halos are about @xmath123 times more massive than the central ( non - cd ) elliptical galaxy . these conclusions can be explored further in the @xmath10 plane by considering all elliptical galaxies for which x - ray observations provide accurate @xmath7 . studies of the evolution of hot gas in elliptical galaxies at uc santa cruz are supported by nasa grants nag 5 - 8409 & atp02 - 0122 - 0079 and nsf grants ast-9802994 & ast-0098351 for which we are very grateful . gastaldello , f. et al . 2005 , _ cluster substructure and its evolution with redshift _ eds . t. e. jeltema , c. r. canizares , m. w. bautz & d. a. buote , 35th cospar scientific assembly , july 25 , 2004 , paris , france p. 3139 lccclcl ngc5044 & 10.76 & 42.80 & 1.2 & 13.60 & @xmath124 & 1rxj1159 & 11.09 & 43.05 & 2.2 & 14.15 & @xmath125 & 2wj943.7 & 10.94 & 43.07 & 1.7 & 13.74 & @xmath126 & 3rxj0419 & 10.64 & 42.75 & 1.4 & @xmath12713.6 & @xmath128 & 4ngc6482 & 10.47 & 42.04 & 0.7 & 12.60 & @xmath129 & 5eso3060170 & 11.30 & 43.82 & 2.7 & 14.25 & na & 6rxj1340 & 11.02 & 43.11 & 2.3 & 14.33 & na & 2,10rxj2114 & 10.96 & 43.01 & 2.1 & 14.27 & na & 2rxj2247 & 11.13 & 43.32 & 2.8 & 14.45 & na & 2ngc1132 & 10.73 & 42.71 & 1.0 & 13.52 & na & 7,8rxj1416 & 11.24 & 44.05 & 1.5 & na & na & 9rxj1119 & 10.36 & 41.94 & na & na & na & 9rxj1256 & 11.16 & 43.49 & na & na & na & 9rxj1331 & 10.68 & 42.48 & na & na & na & 9rxj1552 & 11.12 & 43.51 & na & na & na & 9rxj0116 & 10.76 & 42.94 & na & na & na & 9 |
ergodic homeomorphisms @xmath0 and @xmath1 of polish probability spaces @xmath2 and @xmath3 are _ evenly kakutani equivalent _ if there is an orbit equivalence @xmath4 between full measure subsets of @xmath2 and @xmath3 such that , for some @xmath5 of positive measure , @xmath6 restricts to a measurable isomorphism of the induced systems @xmath7 and @xmath8 . the study of even kakutani equivalence dates back to the seventies , and it is well known that any two zero - entropy loosely bernoulli systems are evenly kakutani equivalent . but even kakutani equivalence is a purely measurable relation , while systems such as the morse minimal system are both measurable and topological . recently del junco , rudolph and weiss studied a new relation called _ nearly continuous kakutani equivalence_. a nearly continuous kakutani equivalence is an even kakutani equivalence where also @xmath9 and @xmath10 are invariant @xmath11 sets , @xmath12 is within measure zero of both open and closed , and @xmath6 is a homeomorphism from @xmath9 to @xmath10 . | i | 1404.0246 | ergodic homeomorphisms @xmath0 and @xmath1 of polish probability spaces @xmath2 and @xmath3 are _ evenly kakutani equivalent _ if there is an orbit equivalence @xmath4 between full measure subsets of @xmath2 and @xmath3 such that , for some @xmath5 of positive measure , @xmath6 restricts to a measurable isomorphism of the induced systems @xmath7 and @xmath8 . the study of even kakutani equivalence dates back to the seventies , and it is well known that any two zero - entropy loosely bernoulli systems are evenly kakutani equivalent . but even kakutani equivalence is a purely measurable relation , while systems such as the morse minimal system are both measurable and topological . recently del junco , rudolph and weiss studied a new relation called _ nearly continuous kakutani equivalence_. a nearly continuous kakutani equivalence is an even kakutani equivalence where also @xmath9 and @xmath10 are invariant @xmath11 sets , @xmath12 is within measure zero of both open and closed , and @xmath6 is a homeomorphism from @xmath9 to @xmath10 . it is known that nearly continuous kakutani equivalence is strictly stronger than even kakutani equivalence , and nearly continuous kakutani equivalence is the natural strengthening of even kakutani equivalence to the _ nearly continuous _ category the category where maps are continuous after sets of measure zero are removed . in this paper we show that the morse minimal substitution system is nearly continuously kakutani equivalent to the binary odometer . | even kakutani equivalence is one of the most natural examples in the theory of restricted orbit equivalence of ergodic and finite measure preserving dynamical systems . in this paper we study even kakutani equivalence in the nearly continuous category . a nearly continuous dynamical system is given by a triple @xmath13 , where @xmath2 is a polish space , @xmath14 is a borel probability measure on @xmath2 , and @xmath15 is an ergodic measure preserving homeomorphism . recall that a measurable orbit equivalence between two such systems @xmath13 and @xmath16 is an invertible , bi - measurable , and measure preserving map @xmath17 that sends orbits to orbits . a measurable orbit equivalence @xmath18 is a _ nearly continuous orbit equivalence _ if there exist invariant and @xmath11 subsets @xmath19 and @xmath20 of full measure so that @xmath21 is a homeomorphism . the first result in this category is the celebrated theorem of keane and smorodinsky @xcite that any two bernoulli shifts of equal entropy are finitarily isomorphic , namely , that the isomorphism between them can be made a homeomorphism almost everywhere . in a later paper , denker and keane @xcite established a general framework for studying measure preserving systems that also preserve a topological structure . we refer the reader to a paper by del junco , rudolph , and weiss @xcite for a more complete history of the area . we only mention here that interest in the orbit equivalence theory for this category was more recently revived by the work of hamachi and keane in @xcite where they proved that the binary and ternary odometers are nearly continuously orbit equivalent . their work inspired similar results for other pairs of examples ( see @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite ) . these examples were later subsumed as special cases of a dye s theorem in this category proved by del junco and ahin @xcite . around the same time as a nearly continuous dye s theorem was established , del junco , rudolph , and weiss proved in @xcite that if one does not impose the condition that the invariant sets of full measure on which the orbit equivalence is a homeomorphism are @xmath11 sets , then any restricted orbit equivalence classification is exactly the same as in the measure theoretic case . in particular , they showed that any orbit equivalence can be regularized to be a homeomorphism on a set of full measure , but could not prove that the set of full measure had any topological structure . the importance of the topological structure in the theory is even more striking for the study of even kakutani equivalence . recall that in the measurable category two ergodic and finite measure preserving systems @xmath13 and @xmath16 are even kakutani equivalent if there exists a measurable orbit equivalence @xmath22 , and measurable sets @xmath23 with @xmath24 with the property that @xmath25 is a measurable isomorphism of the induced transformations @xmath7 and @xmath26 . we call the orbit equivalence @xmath6 an _ even kakutani equivalence _ between @xmath0 and @xmath1 . it follows from @xcite that any even kakutani equivalence can be made to be a homeomorphism on a set of full measure . in the same paper they show that if one imposes the additional condition that the sets @xmath12 and @xmath27 be _ nearly clopen _ , meaning within a set of measure zero of an open set and also of a closed set , then there is a new invariant for even kakutani equivalence of nearly continuous dynamical systems called _ near unique ergodicity_. they use this new invariant to show that nearly continuous even kakutani equivalence is stronger than measure theoretic even kakutani equivalence . the example they construct is , in some sense , not natural , and begs the question whether there are any natural examples of nearly continuous systems that are measurably evenly kakutani equivalent but not nearly continuously so . rudolph began looking for examples in the family of zero entropy loosely bernoulli systems . recall that any two zero entropy loosely bernoulli transformations are measurably even kakutani equivalent . furthermore , many natural examples of nearly continuous systems including rotations , all adding machines , and in fact all finite rank transformations , are loosely bernoulli . in @xcite , roychowdhury and rudolph proved that any two adding machines are nearly continuously even kakutani equivalent . shortly after , dykstra and rudolph showed in @xcite that all irrational rotations are nearly continuously kakutani equivalent to the binary odometer . in @xcite , new machinery , called _ templates _ , was introduced to construct the nearly continuous kakutani equivalence . there , templates were defined using the natural topological tower structure present in adding machines . the construction in @xcite showed that the template machinery can be adapted to the case where the underlying system does not have a canonical symbolic structure . more recently , springer @xcite expanded on their ideas and adapted templates further to prove that all minimal isometries of compact metric spaces are nearly continuously kakutani equivalent to the binary odometer . salvi @xcite adapted templates to the setting of @xmath28 actions and used the machinery to prove rudolph s two - step coding theorem in the nearly continuous category . each result mentioned above has required more sophisticated and technically intricate incarnations of templates . on the other hand each proof has also established the usefulness and flexibility of the machinery . in this paper we adapt the template machinery even further to show our main result : the morse minimal system is nearly continuously even kakutani equivalent to the binary odometer . the version of the template machinery in this paper is designed to address the new complication of the additional tower present in the rank two morse system . we believe the generalization we give here is the appropriate starting place to prove more generally that finite rank nearly continuous systems are all nearly continuously kakutani equivalent to the binary odometer . finally we note that this manuscript is a culmination of work that the first author began in 2009 while he was a post - doctoral fellow working with daniel rudolph at colorado state university . the initial architecture of the constructions and the main ideas were all established collaboratively by dykstra and rudolph . the second author joined the project after the untimely death of rudolph in 2010 , and the manuscript was completed in 2014 . |
estimating vaccination uptake is an integral part of ensuring public health . it was recently shown that vaccination uptake can be estimated automatically from web data , instead of slowly collected clinical records or population surveys @xcite . all prior work in this area assumes that features of vaccination uptake collected from the web are temporally regular . | i | 1702.07326 | estimating vaccination uptake is an integral part of ensuring public health . it was recently shown that vaccination uptake can be estimated automatically from web data , instead of slowly collected clinical records or population surveys @xcite . all prior work in this area assumes that features of vaccination uptake collected from the web are temporally regular . we present the first ever method to remove this assumption from vaccination uptake estimation : our method dynamically adapts to temporal fluctuations in time series web data used to estimate vaccination uptake . we show our method to outperform the state of the art compared to competitive baselines that use not only web data but also curated clinical data . this performance improvement is more pronounced for vaccines whose uptake has been irregular due to negative media attention ( hpv-1 and hpv-2 ) , problems in vaccine supply ( ditekipol ) , and targeted at children of 12 years old ( whose vaccination is more irregular compared to younger children ) . | vaccination programs are an efficient and cost effective method to improve public health . with sufficiently many people vaccinated the population gains herd immunity , meaning the disease can not spread . timely actions to avoid drops in vaccination coverage are therefore of great importance . many countries have no registries of timely vaccination uptake information , but rely for example on yearly surveys . in such countries estimations of near real - time vaccination uptake based solely on web data are valuable . we extend prior work in this area @xcite , which showed that vaccination uptake can be estimated sufficiently accurately from web search data . our extension consists of a new estimation method that adapts dynamically to temporal fluctuations in the signal ( web search queries in our case ) instead of assuming temporal stationarity as in @xcite . this contribution is novel within vaccination uptake estimation . linear models have been used previously to estimate health events , for instance by combining data from multiple sources with an ensemble of decision trees @xcite , or , closer to our work , by using query frequencies for influenza like illness @xcite or vaccination uptake estimation @xcite . these approaches are designed for stationary time - series analysis , i.e. they assume data is generated by a stationary stochastic process . our motivation is that vaccination uptake often does not follow stationary seasonal patterns . external events such as disease outbreaks , suspicion of adverse effects , or temporary vaccine shortages can alter uptake patterns for shorter or longer periods of time . hence , while historical data is a good estimator in stable periods , as shown in @xcite , we reason that adapting the estimation to any unstability can reduce estimation error . we experimentally confirm this on all official children vaccines data used in denmark between 2011 - 2016 . |
we confirm that the increased bulge prominence among quiescent galaxies , as reported previously based on rest - optical observations , remains in place when considering the distributions of stellar mass . , our findings suggest that significant bulge growth precedes a departure from the star - forming main sequence . | r | 1402.0866 | exploiting the deep high - resolution imaging of all 5 candels fields , and accurate redshift information provided by 3d - hst , we investigate the relation between structure and stellar populations for a mass - selected sample of 6764 galaxies above @xmath0 , spanning the redshift range @xmath1 . for the first time , we fit 2-dimensional models comprising a single fit and two - component ( i.e. , bulge + disk ) decompositions not only to the @xmath2-band light distributions , but also to the stellar mass maps reconstructed from resolved stellar population modeling . we confirm that the increased bulge prominence among quiescent galaxies , as reported previously based on rest - optical observations , remains in place when considering the distributions of stellar mass . moreover , we observe an increase of the typical index and bulge - to - total ratio ( with median @xmath3 reaching 40 - 50% ) among star - forming galaxies above @xmath4 . given that quenching for these most massive systems is likely to be imminent , our findings suggest that significant bulge growth precedes a departure from the star - forming main sequence . we demonstrate that the bulge mass ( and ideally knowledge of the bulge and total mass ) is a more reliable predictor of the star - forming versus quiescent state of a galaxy than the total stellar mass . the same trends are predicted by the state - of - the - art semi - analytic model by somerville et al . in the latter , bulges and black holes grow hand in hand through merging and/or disk instabilities , and agn - feedback shuts off star formation . further observations will be required to pin down star formation quenching mechanisms , but our results imply they must be internal to the galaxies and closely associated with bulge growth . | exploiting the bulge - disk decompositions of the stellar mass maps derived for our sample of massive galaxies , we first evaluate the average mass budget of disks and bulges . let us consider picking a random star out of our sample of massive galaxies above @xmath0 . at @xmath70 , the probability that this star belongs to a bulge component is @xmath71 . increasing the mass limit to @xmath72 or 11 yields a higher probability for the star to be associated to the bulge , of @xmath73 and @xmath74 , respectively . perhaps somewhat surprisingly , the fraction of stars residing in a bulge component rises only slightly to @xmath75 , to @xmath76 , @xmath77 , and @xmath78 for galaxies more massive than @xmath79 , 10.5 , and 11 respectively . the formal uncertainties to the above stated probabilities including sample variance and typical measurement errors on @xmath3 are limited to a few percent . the total error budget is likely dominated by systematics , for example related to the assumptions made in stellar population modeling ( see section 3.1 ) . we note , however , that only @xmath39 uncertainties with a differential impact on bulges and disks will affect the above numbers . even if the @xmath39 ratio of bulges were systematically under- or overestimated by 0.2 ( 0.3 ) dex with respect to those of disks , the change in the above numbers would be limited to @xmath80 . as bulges , unlike stellar disks , can be considered sinks in the continuous assembly of a galaxy s stellar component , the rising mass density of stars in bulges ( by a factor of @xmath81 from the higher to the lower redshift bin ) therefore seems to be compensated largely by the continuing assembly of new disks . splitting our sample in finer redshift bins , we do find the fraction of stellar mass in bulges to increase more significantly , by a factor @xmath82 over the entire 6 gyr timespan sampled by our study . overall , the bulge mass fractions are higher than what would be inferred from fits to the @xmath2-band surface brightness profiles , as the median mass - to - light ratio of disk components is 0.2 dex lower than of bulge components . the above numbers address the evolving mass budget of disks and bulges for a mass - limited sample including both star - forming and quiescent galaxies . in the remainder of the paper , we will delve into more depth by breaking down our sample by star formation activity . in recent years , several hst - based studies have investigated the structural differences between star - forming and quiescent galaxies at high redshift . in common to all of these analyses , star - forming systems are found to have significantly larger rest - optical sizes than their quiescent counterparts at the same mass and redshift ( e.g. , toft et al . 2009 ; van der wel et al . in addition , their surface brightness profile shapes tend to be shallow ( @xmath83 ) , while quiescent galaxies feature cuspier light profiles ( e.g. , wuyts et al . 2011 ; bell et al . 2012 ; cheung et al . 2012 , although see also bruce et al . 2012 for decomposed light profiles at high stellar masses and redshifts ) . at the same time , the same multi - wavelength high - resolution lookback surveys have also established that substantial mass - to - light ratio variations in the rest - optical can occur , not only between but also within galaxies ( see , e.g. , wuyts et al . 2012 ; guo et al . 2012 ; boada et al . in prep ) . typically , as new stars tend to form from gas settled in a disk configuration , such @xmath39 ratio variations are anticipated to give rise to a composite light profile in which the disk component has a relatively larger weight ( per unit mass ) than the bulge . it is therefore important to address to which degree the above structural distinction between the two classes of galaxies is intrinsic to their distribution of stellar mass , or , conversely , can be attributed to stellar population effects . the answer to this question is of immediate relevance to our understanding of quenching , as in principle the latter scenario could imply that compact quiescent systems can evolve from the star - forming main sequence by simple fading , without invoking an associated morphological transition . kriek et al . ( 2009 ) investigate this scenario for a spectroscopically confirmed sample of massive @xmath36 galaxies , finding that 3 out of 6 massive star - forming systems have dense cores , and thus may passively evolve into compact galaxies due to fading of the outer star - forming regions . szomoru et al . ( 2010 ) , on the other hand , exploit the exquisite depth of the hubble ultra deep field to probe the surface brightness profile of a massive compact quiescent galaxy at @xmath84 , ruling out the existence of a faint extended envelope or disk around the observed galaxy . another argument against fading comes from cheung et al . ( 2012 ) , who derived the stellar masses of bulges for both star - forming and quiescent galaxies at @xmath85 . they found that bulges of sfgs are half as massive as those of similar - mass quiescent galaxies , implying they can not simply fade onto the red sequence without structural evolution . using the stellar mass maps reconstructed for our mass - selected sample of 6764 galaxies at @xmath15 with @xmath86 , we are now able to draw statistically significant conclusions on the structural distinction between high - z galaxies prior to and after quenching . in figure [ struc.fig ] , we compare the shape of the stellar mass distributions ( i.e. , corrected for spatial @xmath39 variations ) of star - forming and quiescent galaxies , and study their dependence on the total galaxy stellar mass . we consider profile parameters based on single - component ( i.e. , ) fits as well as two - component ( bulge + disk ) decompositions , and show the results for two separate redshift intervals : @xmath87 and @xmath88 . in both cases , we identified a galaxy as quiescent if its specific sfr ( ssfr ) satisfied @xmath89 , where @xmath90 is the hubble time at the redshift of the galaxy , and as star - forming otherwise . we tested that a definition of quiescence based on the location of a galaxy in the uvj diagnostic diagram ( wuyts et al . 2007 ; williams et al . 2009 ) yields effectively identical results . figure [ struc.fig ] immediately highlights that the distinct structural appearance of star - forming and quiescent galaxies is intrinsic to its internal distribution of stellar mass , and not just driven by stellar population or obscuration effects . in fact , a comparison to the equivalent plots based on @xmath2-band surface brightness profiles rather than mass maps ( see appendix b ) indicates that stellar population effects ( when measuring at rest - optical wavelengths ) only induce a modest , albeit non - negligible shift . at all masses , quiescent galaxies feature cuspier stellar mass distributions ( i.e. , higher @xmath41 ) than star - forming systems . their typical best - fit index is furthermore an increasing function of galaxy mass . interestingly , also among sfgs the profile shape is not independent of stellar mass . an increase in @xmath41 is apparent above @xmath4 , both at @xmath35 and at @xmath36 . a similar trend of increasing cuspiness at the tip of the ms was noted by wuyts et al . ( 2011 , figure 1 ; see also nelson et al . in prep ) . next , it is worthwhile reflecting on what it is that we measure when fitting profiles . appendix a illustrates that , when considering galaxies as superpositions of bulge and disk components , a given best - fit index does not necessarily correspond one - to - one to a unique @xmath3 value , even though it is often interpreted as such . given a bulge+disk system with associated best - fit @xmath41 , one can increase its @xmath41 either by boosting @xmath3 , or , alternatively , by growing the extent of the disk with respect to that of the bulge without any change to @xmath3 . turning to the right - hand panel of figure [ struc.fig ] , we now explore the @xmath3 ratio as a function of galaxy mass , for sfgs and quiescent galaxies separately . again , we find a clear anti - correlation between star formation activity and bulge prominence . focussing on the star - forming population , the median @xmath3 is limited to below 30% for intermediate mass sfgs ( @xmath91 ) , while typical bulge mass fractions rise to 40 - 50% above @xmath4 . we note that there is a significant scatter in the distribution of individual @xmath3 values around the median for both quiescent and star - forming galaxies . we investigated the variation in median trends when varying the binning intervals , finding negligible changes at lower masses , while the median @xmath3 of the most massive ( @xmath92 ) sfg bin changes by @xmath93 , depending on the applied binning intervals is such that the most massive bin still contains more than 10 galaxies , allowing a robust estimation of the median . ] . we note that measurements on the @xmath2-band yield bulge mass fractions among sfgs that are lower by on average @xmath94 , as can be understood from a disk component composed of a younger , lower @xmath39 stellar population than the bulge . from the two - component fits , we infer a typical @xmath43 size ratio of @xmath95 , albeit with significant scatter ( see figure [ n_bd.fig ] ) . the median size ratio shows little dependence on star formation activity or mass , over the range probed by our sample . given the enhanced @xmath3 values in quiescent galaxies , and the fact that bulges have smaller half - mass radii than disks , one may wonder if the difference in total size between sfgs and quiescent galaxies can be accounted for completely by a redistribution of stellar material from the disk to the bulge , without changing the extent of each of the components individually . our analysis confirms that the change in @xmath3 of sfgs prior or during quenching is to a large extent responsible for the size difference between the quiescent and star - forming population . however , some fraction of the shrinking size is still attributed to the individual components being smaller . in figure [ radii.fig ] , we show the total sizes as well as the sizes of the individual components for star - forming and quiescent galaxies , as measured on the mass maps . while the total sizes of sfgs and qgs are noticeably different ( by a factor @xmath96 at @xmath97 ) , the difference in size of bulge and disk components between sfgs and qgs respectively is smaller , typically by a factor @xmath82 . with the morphological parameters of the mass maps for our entire galaxy sample in hand , we now proceed to relate those with galaxy - integrated star formation properties . the three panels of figure [ fquench_all.fig ] show , from left to right , the fraction @xmath98 of quenched galaxies as a function of total stellar mass , bulge mass , and disk mass , respectively . here , we again define galaxies as quenched / quiescent when @xmath99 , and as star - forming otherwise . the uncertainties in @xmath98 are derived via a bootstrapping method and represent the 68% confidence levels . they include both sample variance and the typical measurement errors on @xmath3 , which are derived as described in section 3.2 . for the bootstrapping , we computed @xmath98 for 1000 samples , which are randomly drawn from the original sample , with replacement . for each bootstrap iteration , we displace the @xmath3 values for each galaxy by the typical measurement error in @xmath3 , given the galaxy s magnitude , size and measured profile shape . the top left panel of figure [ fquench_all.fig ] illustrates that the fraction of quenched galaxies increases with increasing mass , from @xmath100 at around @xmath101 to @xmath102 at @xmath103 . a second conclusion is that the fraction of quenched galaxies is overall higher for the lower redshift bin , by a factor of @xmath104 on average . both of these results are well established in the literature . the rising mass function of quiescent galaxies over cosmic time has most recently been quantified on a firm statistical footing by muzzin et al . ( 2013 ) and ilbert et al . ( 2013 ) , both of which exploit the wide - area ultravista survey . what candels lacks in number statistics compared to ultravista , it adds in depth and high resolution . exploiting these key strengths , we now turn to the dependence of the quenched fraction on galaxy subcomponents : the mass of their bulge ( middle panel ) and disk ( right - hand panel ) . clearly , the dependence of @xmath98 on the bulge mass is much stronger than on the disk mass , which does not show any significant correlation with @xmath98 above @xmath105 . towards lower disk masses , @xmath98 increases rapidly , but we point out that this trend is entirely driven by the ( total ) stellar mass limit of our sample ( @xmath106 ; i.e. , the galaxies occupying the lowest @xmath107 bins are necessarily heavily bulge - dominated systems , that tend to form relatively few stars ) . if lower mass galaxies were to be included , less massive , disk - dominated sfgs would likely outnumber these massive spheroids with small residual disks in the low @xmath107 bins , producing a flat relation of @xmath98 with @xmath107 over the full range probed . above respective masses of @xmath108 , @xmath98 increases more rapidly with bulge mass than with total stellar mass in both redshift ranges ( @xmath109 per dex of @xmath110 compared to @xmath111 per dex @xmath112 , or @xmath100 per dex of @xmath107 ) . with the bulge - to - disk decompositions in hand , we next split the galaxy sample in bins of @xmath3 , and explore second parameter dependencies . considering first the dependence of @xmath98 on the total stellar mass , it is apparent that , at a given total mass , @xmath98 is increasing significantly with increasing @xmath3 ratio . the middle panels of figure [ fquench_all.fig ] illustrate that , when considering the dependence of @xmath98 on bulge mass , the different @xmath3 bins align along a much tighter locus . in contrast , a large spread is seen as a function of disk mass ( right - hand panels of figure [ fquench_all.fig ] ) . in order to quantify these trends , we compute the spearman s rank correlation coefficient ( @xmath113 ) for the relations of @xmath98 with @xmath114 , @xmath115 , and @xmath116 for respective masses @xmath86 . we find that @xmath117 is indeed significantly higher for the relation @xmath98 vs. @xmath116 ( @xmath118 ) than for both @xmath98 vs. @xmath119 ( @xmath120 ) and @xmath98 vs. @xmath115 ( @xmath121 ) , as measured for @xmath35 . consistent results are found for @xmath36 . we investigated the impact of defining quiescence based on a @xmath122 color - color criterion instead of a ssfr cut . when applying a uvj - based selection of quiescent galaxies , we find an overall good agreement with the trends presented in figure [ fquench_all.fig ] . quantitatively , small changes occur , with @xmath98 increasing by @xmath123% for the entire @xmath15 sample integrated over all masses . the good agreement is not surprising , since the precise threshold in ssfr used to select quiescent galaxies ( @xmath99 ) was chosen to yield maximum overlap with the @xmath122 selection criterion . taken together , this demonstrates that the build - up of a bulge seems to play a critical role in the quenching process of galaxies , whereas the disk does not . the amount of stars in the disk component of a galaxy has little to no predictive power regarding its star - forming or quenched state , unless also @xmath3 ( and hence the bulge mass ) is known . we find a qualitatively similar behavior at @xmath36 as at @xmath35 , but note that the cosmic evolution in the quiescent fraction can not solely be attributed to continuing bulge growth over time , as galaxies in the same @xmath112 and @xmath3 bin at @xmath35 are more likely to be quenched than those at @xmath36 . appendix b illustrates how the equivalent diagrams composed from fits to the @xmath2-band surface brightness rather than the stellar mass distribution exhibit a larger spread from low to high @xmath3 bins . this generic behavior can be understood from a physical picture where the disk component has a relatively larger weight in light than in mass . our work is in agreement with , and takes the next step beyond previous reports that the inner stellar mass density is better related to the star formation history than the total stellar mass @xcite , as inferred from rest - optical imaging of smaller samples of high - redshift galaxies ( see kauffmann et al . 2003 and fang et al . 2013 for a local universe reference , and cheung et al . 2012 for intermediate redshifts @xmath124 ) importantly , the same behavior explored here over the redshift range @xmath15 extends in a strikingly similar fashion all the way to the present day , as demonstrated by bluck et al . ( 2014 ) who exploit the large number statistics of sdss . |
we demonstrate that the bulge mass ( and ideally knowledge of the bulge and total mass ) is a more reliable predictor of the star - forming versus quiescent state of a galaxy than the total stellar mass . grow hand in hand through merging and/or disk instabilities , and agn - feedback shuts off star formation . further observations will be required to pin down star formation quenching mechanisms , but our results imply they must be internal to the galaxies and closely associated with bulge growth . | c | 1402.0866 | exploiting the deep high - resolution imaging of all 5 candels fields , and accurate redshift information provided by 3d - hst , we investigate the relation between structure and stellar populations for a mass - selected sample of 6764 galaxies above @xmath0 , spanning the redshift range @xmath1 . for the first time , we fit 2-dimensional models comprising a single fit and two - component ( i.e. , bulge + disk ) decompositions not only to the @xmath2-band light distributions , but also to the stellar mass maps reconstructed from resolved stellar population modeling . we confirm that the increased bulge prominence among quiescent galaxies , as reported previously based on rest - optical observations , remains in place when considering the distributions of stellar mass . moreover , we observe an increase of the typical index and bulge - to - total ratio ( with median @xmath3 reaching 40 - 50% ) among star - forming galaxies above @xmath4 . given that quenching for these most massive systems is likely to be imminent , our findings suggest that significant bulge growth precedes a departure from the star - forming main sequence . we demonstrate that the bulge mass ( and ideally knowledge of the bulge and total mass ) is a more reliable predictor of the star - forming versus quiescent state of a galaxy than the total stellar mass . the same trends are predicted by the state - of - the - art semi - analytic model by somerville et al . in the latter , bulges and black holes grow hand in hand through merging and/or disk instabilities , and agn - feedback shuts off star formation . further observations will be required to pin down star formation quenching mechanisms , but our results imply they must be internal to the galaxies and closely associated with bulge growth . | in order to study the morphological differences between sfgs and quiescent galaxies , and to draw conclusions on the possible structural changes of star - forming galaxies as they move along the ms , we first examined the mass dependence of the profile shape of sfgs and quiescent galaxies as traced by the index and @xmath3 ratio . we have shown that quiescent galaxies are structurally distinct from the star - forming population as seen by overall higher indices and @xmath3 ratios at a given stellar mass . sfgs show rising trends of their median index and @xmath3 ratio with increasing stellar mass , with the latter rising up to @xmath144 above @xmath4 . these findings give insights about the link between the structural evolution of sfgs and the quenching process as they move along the ms . analyzing the schechter functional forms of the sfg and qg mass function as a function of redshift , @xcite conclude that the quenching rate of galaxies climbing the ms rises proportionally to the sfr ( and given the near - linear ms slope therefore also proportionally to the stellar mass , hence their terminology mass quenching ) . this corresponds to a survival probability on the ms that drops exponentially with mass , implying that , while nearly all low - mass sfgs are destined to continue growing along the ms , toward the high - mass end the ms becomes progressively more dominated by near - to - be - dead sfgs . in fact , the sub - unity slope of the ms , and possible flattening at the high - mass end ( whitaker et al . 2012 ) , may well be interpreted in this context : the typical sfg above @xmath4 is already undergoing some level of quenching , thereby deviating from the projected path along a sfr - mass relation of slope unity , that could be expected from cosmological accretion rates in the absence of quenching . tying in our observational results on galaxy structure , the deviation toward high median @xmath41 and @xmath3 at the massive end reflects the typical structure of soon - to - be - dead star - formers that account for the bulk of sfgs above @xmath4 . the fact that they are structurally distinct implies that the morphological transition happens first , to be followed later by the departure from the ms . bulge growth precedes quiescence . such a morphological change prior to quenching is in line with qualitative predictions based on a toy model by dekel & burkert ( 2013 ) . in the latter study , about half of the star - forming disk galaxies at @xmath55 are predicted to evolve into compact star - forming blue nuggets due to violent disk instabilities before they are quenched into compact quiescent galaxies ( red nuggets ) . an observed population of blue nuggets has been proposed by barro et al . ( 2013a , b ) to represent an evolutionary link , originating from extended disk galaxies , and evolving into compact quiescent systems . this does not refute that galaxies also undergo further structural evolution after they are quenched . at least part of the size growth ( cassata et al . 2013 ; van der wel et al . 2014 ) and evolution toward rounder axial ratios ( chang et al . 2013 ) has been attributed to ( minor and/or major ) dry mergers , and it is conceivable that similar processes contribute to the observed trend of increasing @xmath3 toward the massive end for the quiescent population . we have demonstrated that the bulge mass of a system is well correlated with its quenched state and has a stronger predictive power of quiescence than the total stellar mass . the observed trends of @xmath98 with total stellar mass , bulge mass and disk mass as viewed among galaxies in different @xmath3 bins are in good qualitative agreement with predictions from the somerville et al . sam . in the context of this model , the growth of the central supermassive black hole , which is the primary quenching agent for massive galaxies in this sam , is tightly coupled with the growth of bulges through both merging and disk instabilities . if a black hole - bulge scaling relation is in place during the peak of cosmic star formation as it is in the present - day universe ( hring & rix 2004 ) , our observational results together with the model comparison could therefore hint at the bulge not being the causal link to quenching , but rather the most accessible observational proxy for the agn acting as the quenching agent . in detail , however , there are quantitative differences between the sam and our observations , most severely in the highest redshift bin ( @xmath88 ) , where the observed quenched fraction exceeds the value predicted by the sam by a factor of @xmath145 . the latter difference could hint at a need for more frequent , efficient , or lasting quenching , a possible mechanism we speculate about below . we also note that the same behavior is not necessarily a generic feature to all sams ( see appendix c ) . it is tempting to draw connections between the emerging bulges in massive ms galaxies out to @xmath9 revealed by our analysis , and recent observational results based on deep ao - assisted integral field data sets and grism spectroscopy over the same redshift range . frster schreiber et al . ( 2013 ) found a high prevalence of powerful nuclear outflows in @xmath146 galaxies driven by agn , which appear to be absent in galaxies at lower masses . along with star formation driven winds in the outer parts of the galaxies , such outflows could efficiently remove gas out of galaxies and , in this way , contribute to the quenching process . meanwhile , the 3d - hst and candels legacy programs have yielded evidence for nuclear depressions in the h@xmath147 equivalent width in @xmath35 sfgs ( nelson et al . 2012 , 2013 ; wuyts et al . 2013 ) . at the highest stellar surface mass densities , star formation no longer appears to proceed in lockstep with the assembled stellar mass . likewise , genzel et al . ( 2014 ) report on ring - shaped h@xmath147 distributions in @xmath36 sfgs , surrounding a more quiescent center where the dynamically inferred toomre q parameter significantly exceeds unity , owing to the emergence of a stellar bulge . as such , the toomre stability criterion is satisfied in the central galaxy regions , which consequently could prevent the gas reservoir , if present there , from fragmenting and forming stars . while this result suggests that some causal connection between bulge growth and quenching may be at play , it should be noted ( as is done also by genzel et al . 2014 ) that gravitational quenching by itself does not expel the gas present , neither does it stop the accumulation of a larger gas reservoir by continuing cosmological accretion . additional maintenance mode might be required for a long - term shut - down of further gas supply . |
for the first time , we fit 2-dimensional models comprising a single fit and two - component ( i.e. , bulge + disk ) decompositions not only to the @xmath2-band light distributions , but also to the stellar mass maps reconstructed from resolved stellar population modeling . the same trends are predicted by the state - of - the - art semi - analytic model by somerville et al . in the latter , bulges and black holes | c | 1402.0866 | exploiting the deep high - resolution imaging of all 5 candels fields , and accurate redshift information provided by 3d - hst , we investigate the relation between structure and stellar populations for a mass - selected sample of 6764 galaxies above @xmath0 , spanning the redshift range @xmath1 . for the first time , we fit 2-dimensional models comprising a single fit and two - component ( i.e. , bulge + disk ) decompositions not only to the @xmath2-band light distributions , but also to the stellar mass maps reconstructed from resolved stellar population modeling . we confirm that the increased bulge prominence among quiescent galaxies , as reported previously based on rest - optical observations , remains in place when considering the distributions of stellar mass . moreover , we observe an increase of the typical index and bulge - to - total ratio ( with median @xmath3 reaching 40 - 50% ) among star - forming galaxies above @xmath4 . given that quenching for these most massive systems is likely to be imminent , our findings suggest that significant bulge growth precedes a departure from the star - forming main sequence . we demonstrate that the bulge mass ( and ideally knowledge of the bulge and total mass ) is a more reliable predictor of the star - forming versus quiescent state of a galaxy than the total stellar mass . the same trends are predicted by the state - of - the - art semi - analytic model by somerville et al . in the latter , bulges and black holes grow hand in hand through merging and/or disk instabilities , and agn - feedback shuts off star formation . further observations will be required to pin down star formation quenching mechanisms , but our results imply they must be internal to the galaxies and closely associated with bulge growth . | we analyzed the structural properties of a sample of 6764 massive ( @xmath148 ) galaxies in the redshift range @xmath32 , by exploiting the multi - wavelength candels hst imaging data set in all five candels/3d - hst fields . we carried out single - component ( ) fits and two - component ( bulge + disk ) decompositions , on stellar mass maps reconstructed from a resolved panchromatic sed modeling technique ( wuyts et al . 2012 , 2013 ) , as well as on images of the @xmath2-band surface brightness distribution . in addition , we compared our findings to predictions by the state - of - the - art semi - analytic model from somerville et al . ( 2008 , 2012 ; with extensions including disk instabilities presented by porter et al . 2014 ) . our main results are the following : 1 . at fixed stellar mass , quiescent galaxies have overall higher indices and @xmath3 ratios than sfgs as measured on their mass maps , in line with previous findings using monochromatic observations . we find an increase of indices among sfgs with increasing total stellar mass , with the median mass profiles increasing from ( @xmath149 ) at @xmath0 , to @xmath150 above @xmath4 . two - component bulge - disk decompositions confirm that the same rising trend is present when considering the median @xmath3 ratio of sfgs , which is rising up to @xmath144 above @xmath4 . the same characteristic behavior is seen at @xmath35 and @xmath36 . 2 . quantifying the same trends on the h - band light profiles rather than the mass maps , the indices and @xmath3 fractions are overall lower for sfgs , confirming previous non - parametric measurements for a subset of our sample ( wuyts et al . the emergence of bulges above @xmath4 in sfgs appears to be also slightly less prominent when viewed in light , consistent with the steepest color gradients ( blue disks with red central bulges ) being found among massive sfgs . 3 . the likelihood of a galaxy being quenched , as traced by the fraction of quiescent galaxies , is better correlated with the bulge mass than the total stellar mass and further shows no appreciable correlation with the amount of stellar mass in the disk component . the quenched fraction at redshift 1 is on average higher by a factor @xmath151 than at redshift 2 . 4 . at a given total stellar mass , the quenched fraction exhibits a strong positive correlation with @xmath3 , while different @xmath3 bins are confined to a significantly tighter locus in a diagram of @xmath98 versus @xmath110 . these findings imply that the bulge mass of a system is the single observable parameter with the most predictive power regarding its quenched state , although a somewhat tighter constraint on the probability of quiescence can be obtained if in addition also the total stellar mass is known . the same trend is seen over the full redshift range probed , with the distinction that quenched fractions are lower at higher lookback times . we find a good qualitative agreement between the semi - analytic model by somerville et al . sam and our observational findings . since bulge and black hole growth are tightly coupled in the sam , the strong dependence of @xmath98 on bulge mass follows rather naturally in this model . our observational results can _ in the context of this model _ therefore be interpreted as the bulge being the closest observable proxy to the underlying agent of quenching : the black hole . quantitatively , the largest discrepancy between model and observations is found in the highest redshift bin ( @xmath88 ) , where the observed quenched fraction is larger by a factor of @xmath145 than predicted by the sam . we note that the same behavior is not necessarily a generic feature to all sams . [ [ section ] ] the authors acknowledge fruitful discussions with edmond cheung , david c. koo , yu lu , casey j. papovich , mohammadtaher safarzadeh , benjamin j. weiner and steven p. willner . support for program number hst - go-12060 and hst - go-12177 was provided by nasa through a grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , incorporated , under nasa contract nas5 - 26555 . |
few high - redshift , radio - loud quasars are known to date . the extremely luminous , radio - bright quasar , sdss j013127.34@xmath0032100.1 was recently discovered at a redshift of @xmath1 . we observed the source with high resolution very long baseline interferometry ( vlbi ) at 1.7ghz with the european vlbi network ( evn ) and found a single compact radio component . additionaly , when compared to archival radio data , the source showed significant flux density variation . [ firstpage ] techniques : interferometric galaxies : active quasars : individual : sdss j013127.34@xmath0032100.1 galaxies : high - redshift | i | 1503.06593 | few high - redshift , radio - loud quasars are known to date . the extremely luminous , radio - bright quasar , sdss j013127.34@xmath0032100.1 was recently discovered at a redshift of @xmath1 . we observed the source with high resolution very long baseline interferometry ( vlbi ) at 1.7ghz with the european vlbi network ( evn ) and found a single compact radio component . we estimated a lower limit to the brightness temperature of the detected radio component , @xmath2k . additionaly , when compared to archival radio data , the source showed significant flux density variation . these two findings are indicative of the blazar nature of the source . [ firstpage ] techniques : interferometric galaxies : active quasars : individual : sdss j013127.34@xmath0032100.1 galaxies : high - redshift | high - redshift ( @xmath3 ) quasars are of major importance since they can provide information on the growth of the supermassive black holes and the evolution of active galactic nuclei ( agn ) in the early universe . the mere existence of black holes with a few million solar masses ( or more ) at @xmath4 constrains the black hole growth and the accretion process ( e.g. * ? ? ? * and references therein ) . among the high - redshift quasars , the radio - loud ones constitute a very attractive subsample , since their radio jets can be studied with the highest angular resolution , via very long baseline interferometry ( vlbi ) technique . typically , radio - loud agn contain a flat - spectrum core and a steep - spectrum jet . the higher redshift is , the fainter the agn radio jet will appear if observed at a fixed wavelength . thus , if core - jet agn constitute the same population of objects throughout the redshift space , the apparent `` prominence '' of jets at higher redshifts must decrease @xcite : well pronounced jets at high redshifts must appear less frequent than at low redshifts . additionaly , recent vlbi studies suggest that the naive expectation that relativistically beamed sources ( blazars ) should dominate the high - redshift radio - loud quasar population might not be true . there seems to exist a population of steep - spectrum high - redshift ( @xmath3 ) radio - loud quasars @xcite , which may be very young radio quasars , similar to the gigahertz - peaked spectrum ( gps ) sources observed in the local universe @xcite . on the other hand , a few high - redshift , beamed blazars are known as well . three are identified at @xmath5 : sdss j114657.79 + 403708.6 @xcite , sdss j102623.61 + 254259.5 @xcite , and q0906 + 6930 @xcite . recently @xcite reported the discovery of a high - redshift , radio - bright quasar , sdss j013127.34@xmath0032100.1 ( j0131@xmath00321 , hereafter ) . the source was first selected as a candidate high - redshift quasar @xcite using the optical infrared selection criteria based on the sloan digital sky survey ( sdss , * ? ? ? * ) and _ wide - field infrared survey explorer _ ( _ wise _ , * ? ? ? * ) photometry . its optical spectrum was first measured with the yunnan fainter object spectrograph and camera @xcite in 2013 november . later higher resolution optical and near - infrared spectra were obtained by the magellan echelette and folded port infrared echelette ( fire ) spectrographs in 2014 january . according to these measurements , the source has a redshift of @xmath6 @xcite . using the optical spectra and the empirical scaling relation between the mg ii line width and the black hole mass @xcite , @xcite estimated the total bolometric luminosity and the black hole mass of j0131@xmath00321 to be @xmath7w and @xmath8 , respectively . using the latest relation of @xcite , the black hole mass can be even higher , @xmath9 . according to the faint images of the radio sky at twenty centimeters ( first , * ? ? ? * ) survey , j0131@xmath00321 is radio - bright with a flux density of 33.7mjy at 1.4ghz . here we report on the results of our high resolution radio interferometric observation of the source with the european vlbi network ( evn ) . throughout this paper , we use flat @xmath10 cold dark matter cosmological model with @xmath11kms@xmath12mpc@xmath12 , @xmath13 , @xmath14 ( the same as used in the discovery paper , * ? ? ? |
flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces . fluid dynamics predicts this circular motion to be clockwise ( cw ) above a rigid surface ( when viewed from inside the fluid ) and counter - clockwise ( ccw ) below a free surface . | i | 1406.4412 | flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces . fluid dynamics predicts this circular motion to be clockwise ( cw ) above a rigid surface ( when viewed from inside the fluid ) and counter - clockwise ( ccw ) below a free surface . recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation , both at solid surfaces absorbing slip - inducing polymers and interfaces covered with surfactants . motivated by these results , we use a far - field hydrodynamic model to predict the kinematics of swimming near three types of interfaces : clean fluid - fluid interface , slipping rigid wall , and a fluid interface covered by incompressible surfactants . representing the helical swimmer by a superposition of hydrodynamic singularities , we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it , both of which are a consequence of the stokes dipole component of the swimmer flow field . we then show that circular motion is induced by a higher - order singularity , namely a rotlet dipole , and that its rotation direction ( cw vs. ccw ) is strongly affected by the boundary conditions at the interface and the bacteria shape . our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria . | swimming microorganisms are ubiquitous in nature , and have long been known to play important roles in marine life ecosystems , animal reproduction , and infectious diseases . in these processes , cell motility is crucial.@xcite at the small scales relevant to swimming cells , inertial forces are negligible , and locomotion is constrained by purcell s `` scallop '' theorem stating that any body deformation reversible in time yields zero net motion.@xcite fluid - based cellular motility relies therefore on non - time reversible deformation , for instance by propagating waves along cilia or flagella.@xcite among the various types of locomotion seen in nature , one commonly observed for bacteria is that of helical propulsion , where a flagellum ( or a bundle of flagella ) rotates as a helix , inducing forward propulsion . a typical example of an organism employing helical propulsion is the bacterium _ escherichia coli _ coli_).@xcite this bacterium alternates `` run '' and `` tumble '' periods : in the former , flagella are synchronized in a coherent bundle and propel the cell forward , whereas in the latter flagella are disorganized , changing the cell orientation and subsequent swimming direction . during run periods , when _ e. coli _ cells are isolated in a bulk flow , they swim in straight ( noisy ) lines . however , cell locomotion is strongly affected by nearby boundaries . swimming microorganisms often evolve in confined environments , be it by solid boundaries , free surfaces , or liquid interfaces . in some cases , confinement results from channel boundaries , for example along the mammalian female reproductive tract.@xcite surfaces can also be a key element in the microorganism function , as in the case of surface associated infection or biofilm formation.@xcite since such problems are dominated by viscous dissipation , long - range hydrodynamic interactions have been argued to play important roles , resulting in a significant alteration of the locomotion of microorganisms.@xcite over the past years , intensive theoretical , numerical and experimental work has helped uncover the kinematics and dynamics modifications of swimming properties by boundaries.@xcite for bacteria employing helical propulsion ( such as _ e. coli _ ) , two different effects induced by boundaries have been discovered and quantified . these organisms swim in the forward direction ( cell body forward ) and are being propelled from the back . they thus push on the surrounding fluid forward and backward , and such swimmers are referred to as `` pushers '' . in the presence of a nearby solid wall , _ e. coli _ tends to aggregate close to walls.@xcite this is in fact observed for any kind of pusher , not necessarily one exploiting helical propulsion.@xcite a second property , observed solely for helical swimmers , is a circular motion of the cells in a plane parallel to the surface . this was accounted for both experimentally and theoretically in the case of a solid wall @xcite and a free surface.@xcite notably , the circular motion occurs in an opposite direction in the presence of a solid wall ( clockwise , cw , when viewed from inside the fluid ) or a free surface ( counterclockwise , ccw , see fig . [ fig:1 ] ) . this change in rotation direction is qualitatively similar to the drag increase or decrease observed for the motion of a colloidal particle near a rigid wall and a free surface.@xcite indeed , a solid wall and a free surface induce opposite effects , no - slip for a rigid boundary vs. free slip in the case of a free interface . , and counter - clockwise motion at a free surface ( right panel ) [ reprinted figure with permission from r. di leonardo , d. dellarciprete , l. angelani , and v. iebba , phys . rev . 106 , 038101 ( 2011 ) . copyright ( 2011 ) by the american physical society ] . ] past experimental results have been explained theoretically considering newtonian fluids and perfect interfaces , meaning either a no - slip wall or a shear - free surface . theoretical models do predict a single circular direction , cw in the presence of a solid wall vs. ccw in the presence of a free surface , and are consistent with the results illustrated in fig . [ fig:1 ] . however , recent experiments on _ e. coli _ swimming near glass plates and free surfaces show that the distinction in the direction of the circular motion is not straightforward , and both cw and ccw rotations are observed under seemingly similar experimental conditions.@xcite in the initial study of lemelle _ et al . _ ( 2010),@xcite only cw motion was observed above a glass plate , but both cw and ccw at a free surface , suggesting that particles and surfactants could alter the free slip boundary condition . this hypothesis was further investigated by changing the concentration of a particular polymer that can aggregate at a free surface.@xcite the authors confirmed this qualitative change of behavior , observing a clear dependence on the polymer concentration of the fraction of cells undergoing ccw motion . a similar change in rotation direction was recently highlighted experimentally at a solid wall , when the solution contains polymers.@xcite using a special surface treatment , the polymer concentration at the solid wall was modified , generating possible slip , and resulting in ccw motion . these recent experiments demonstrate that the presence of polymers or surfactants could have a dramatic effect on motility of nearby cells . in this paper we present a modeling approach to quantify the dynamics of swimming bacteria near complex interfaces . when polymers are present in the solution , their concentration close to surfaces is reduced due to higher shear and confinement.@xcite this wall depletion results in the formation of a thin fluid layer of lower viscosity at the wall , thereby modifying significantly the no - slip condition . on scales larger than this thin layer , the equivalent behavior at the wall is an apparent partial slip , characterized by its slip length @xmath0 ranging from @xmath1 nm to 10 @xmath2m.@xcite similarly , a liquid interface covered with surfactants acts as a thin two - dimensional fluid layer separating the liquid phases . this layer has its own rheological properties , and modifies the stress and velocity jumps between the two fluids.@xcite as a consequence , the presence of surfactants can affect significantly the boundary conditions and resulting flow.@xcite in the present work , we address the role of altered boundary conditions on swimming microorganisms , focusing on interface - induced reorientation , attraction vs. repulsion by the surface , and the impact on circular motion . using an analytical framework based on multipole expansions for describing the hydrodynamic interactions between a swimming microorganism and an interface , we show how complex interfaces affect hydrodynamic interactions , providing possible explanations to past experimental results . whereas interface alignment and attraction are seen to be universal properties , the direction of the circular motion turns out to strongly depends on the properties of the fluid , on the bacterium shape and , in some cases , the distance to the interface . in sec . [ sec : modeling ] we present the modeling approach used throughout the paper . we first introduce the different interfaces considered , and then our solution method quantifying the leading - order effect of hydrodynamic singularities . in sec . [ sec : stokesletclosetoaboundary ] we recall some existing results for the flow generated by a point force near boundaries and derive in particular the solution in the case of a surfactant - covered interface . sec . [ sec : resultstruetrue ] is devoted to the main results of the paper , quantifying the impact of complex boundary conditions on swimming bacteria , first on reorientation and attraction , and then on circular motion . we finally conclude in sec . [ sec : ccl ] while some of the technical details are given in appendices [ sec : appb]-[sec : typicaldifferentialequationsandsolutions ] . |
recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation , both at solid surfaces absorbing slip - inducing polymers and interfaces covered with surfactants . motivated by these results , we use a far - field hydrodynamic model to predict the kinematics of swimming near three types of interfaces : clean fluid - fluid interface , slipping rigid wall , and a fluid interface covered by incompressible surfactants . we then show that circular motion is induced by a higher - order singularity , namely a rotlet dipole , and that its rotation direction ( cw vs. ccw ) is strongly affected by the boundary conditions at the interface and the bacteria shape . our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria . | c | 1406.4412 | flagellated bacteria exploiting helical propulsion are known to swim along circular trajectories near surfaces . fluid dynamics predicts this circular motion to be clockwise ( cw ) above a rigid surface ( when viewed from inside the fluid ) and counter - clockwise ( ccw ) below a free surface . recent experimental investigations showed that complex physicochemical processes at the nearby surface could lead to a change in the direction of rotation , both at solid surfaces absorbing slip - inducing polymers and interfaces covered with surfactants . motivated by these results , we use a far - field hydrodynamic model to predict the kinematics of swimming near three types of interfaces : clean fluid - fluid interface , slipping rigid wall , and a fluid interface covered by incompressible surfactants . representing the helical swimmer by a superposition of hydrodynamic singularities , we first show that in all cases the surfaces reorient the swimmer parallel to the surface and attract it , both of which are a consequence of the stokes dipole component of the swimmer flow field . we then show that circular motion is induced by a higher - order singularity , namely a rotlet dipole , and that its rotation direction ( cw vs. ccw ) is strongly affected by the boundary conditions at the interface and the bacteria shape . our results suggest thus that the hydrodynamics of complex interfaces provide a mechanism to selectively stir bacteria . | in this paper we have used a far - field hydrodynamic approach to model the surface swimming of bacteria employing helical flagella . the motivation for this work was the discrepancy between theoretical predictions and experimental observations . specifically , theory predicts that near a rigid wall the cells should always display cw motion , whereas recent experiments where polymers were used to induce slip at the wall showed that rotation in the opposite direction was possible . similarly , cells should rotate in a ccw motion at a free surface whereas if surfactants are present experiments show that cw motion is also observed . to develop a model we have represented the helical swimmer as a superposition of hydrodynamic singularities and investigated its hydrodynamic interactions with three types of surfaces : a clean fluid - fluid interface , a rigid wall with a finite slip length , and an interface covered by incompressible surfactants . the leading - order singularity in the flow field of the cell is a stokes dipole ( stresslet ) , characterized by a @xmath128 spatial decay . the interactions between that singularity and all three types of surfaces systematically lead to a reorientation of the swimming cells parallel to , and an attraction by , the surface . circular motion of the cells are due to wall effects on a higher - order singularity , namely a rotlet dipole , which decays spatially as @xmath130 . in that case , the specific boundary conditions at the interface , together with the shape of the cell , play a crucial role in determining the direction of rotation of the cell , and transitions between cw and ccw are predicted to take place in similar experimental setups . our results indicate thus that the recent experimental finding on transition in rotation direction can be understood as the consequence of complex boundary conditions on the nature of hydrodynamic interactions between the swimming cells and the surfaces . the main assumption made in our paper is that we have only considered the leading - order hydrodynamics effects for all influences of the interfaces ( attraction and rotation ) . this is , admittedly , a severe assumption which is expected to break down as soon as the cell is within about one body length from the interface . in order to obtain more quantitative predictions , one would then need to either include the effect of higher - order singularities , or resort to a fully computational approach . the advantage of our approach however is that it allows us to identify the fundamental physical process at play in setting the direction of rotation , and that it is expected to remain valid generically for all cells exploiting helical swimming . our findings could potentially be exploited in a numbers of ways , for example surface swimming could be used as a proxy for determining the rheological properties of the nearby interface or to selectively stir or sort individual cells from bacterial populations . we hope that our study will motivate further work along these directions . |
we argue that the doppler effect is insufficient to explain the finding and propose that the lines originate in accretion columns on the verge of optical thickness , where compton scattering of resonantly - trapped line photons broadens the profile . we suggest that the broadening is a valuable diagnostic of conditions in the accretion column . | c | astro-ph9802040 | following a recent report that ao psc has broad iron emission lines we have looked at the spectra of 15 magnetic cataclysmic variables . we find that half of the systems have lines broadened by 200 , while the remainder have narrow lines . we argue that the doppler effect is insufficient to explain the finding and propose that the lines originate in accretion columns on the verge of optical thickness , where compton scattering of resonantly - trapped line photons broadens the profile . we suggest that the broadening is a valuable diagnostic of conditions in the accretion column . # 1@xmath0 # 1@xmath1 # 1@xmath2 accretion , accretion discs novae , cataclysmic variables binaries : close x - rays : stars . | from the above discussion we conclude that the broad iron lines found in roughly half of the mcvs studied are caused by a mixture of doppler broadening due to radial infall , compton down - shifted line emission from a reflected component , and , probably most importantly , compton scattering of the line emission in the accretion column . a significant optical depth to scattering in the column may also be required to explain the line fluxes ( e.g. swank 1984 ; done 1995 ) . we have suggested that the broadening originates in the transition region between optical thickness and optical thinness ; that systems in which this transition occurs at a temperature too low for significant emission have narrow lines ; and that systems with broad lines must have regions of column which are still optically thick at a higher temperature ( 3 ) . we can test this by comparison with other work , taking the well studied stars ex hya , as an example of a system with narrow lines , and ao psc , the system with the clearest line broadening . in ex hya the presence of lines of elements with a lower ionization than iron implies a transition to optical thickness at @xmath101 ( fujimoto & ishida 1997 ) . in ao psc the line ratios imply a higher temperature transition [ fujimoto & ishida ( 1995 ) quote @xmath10 3 , although this estimate is less certain due to the weaker lines ] in agreement with the above reasoning . further , we can detect optical thickness in the accretion column by looking at changes in the x - ray continuum as the white dwarf spins . from spin - resolved spectroscopy of ao psc , hellier ( 1996 ) found that the column contained several phases of absorption . the densest , affecting regions of the column emitting at energies of at least 8 , requires an electron scattering column which changes by 6 cm over the spin cycle , suggesting an actual column of 2 cm , and thus an optical depth of 1 . this column is compatible with an accretion rate of 10 g s and an accretion area covering @xmath13 of the white dwarf surface ( hellier 1996 ) , values which are in line with current estimates for intermediate polars ( e.g. patterson 1994 ; hellier 1997 ) . in contrast , ex hya shows much less absorption , and in data has no spin modulation above 6 ( ishida , mukai & osborne 1994 ; allan , hellier & beardmore 1998 ) , implying that it is optically thin throughout the hard x - ray emitting regions . we can extend this difference into a test of our explanation , and predict that the other systems with clearly narrow lines , such as v1223 sgr , will also be optically thin in the hard x - ray emitting regions . thus spin - resolved spectroscopy with would not show a counterpart of the very dense absorber revealed in ao psc . unfortunately the test is nt clear cut since we need to distinguish between a flux reduction caused by an optically thick accretion column , and a flux reduction caused by emitting regions passing over the limb of the white dwarf . however , at any one pole , occultation effects and absorption effects are likely to occur in anti - phase in mcvs ( e.g. hellier , cropper & mason 1991 ) allowing the test to be performed given -quality spectroscopy and an understanding of the spin pulse in each system . analysis of x - ray spectroscopy of other mcvs is thus needed to confirm these ideas . |
for sequences of random backward nested subspaces as occur , say , in dimension reduction for manifold or stratified space valued data , asymptotic results are derived . in fact , we formulate our results more generally for backward nested families of descriptors ( bnfd ) . under rather general conditions , asymptotic strong consistency holds . under additional , still rather general hypotheses , among them existence of a.s . local twice differentiable charts , asymptotic joint normality of a bnfd can be shown . if charts factor suitably , this leads to individual asymptotic normality for the last element , a principal nested mean or a principal nested geodesic , say . secondary 62h11 , 58c06 , 60d05 . | i | 1609.00814 | for sequences of random backward nested subspaces as occur , say , in dimension reduction for manifold or stratified space valued data , asymptotic results are derived . in fact , we formulate our results more generally for backward nested families of descriptors ( bnfd ) . under rather general conditions , asymptotic strong consistency holds . under additional , still rather general hypotheses , among them existence of a.s . local twice differentiable charts , asymptotic joint normality of a bnfd can be shown . if charts factor suitably , this leads to individual asymptotic normality for the last element , a principal nested mean or a principal nested geodesic , say . it turns out that these results pertain to principal nested spheres ( pns ) and principal nested great subsphere ( pngs ) analysis by @xcite as well as to the intrinsic mean on a first geodesic principal component ( imo1gpc ) for manifolds and kendall s shape spaces . a nested bootstrap two - sample test is derived and illustrated with simulations . in a study on real data , pngs is applied to track early human mesenchymal stem cell differentiation over a coarse time grid and , among others , to locate a change point with direct consequences for the design of further studies . _ keywords : _ frchet means , dimension reduction on manifolds , principal nested spheres , asymptotic consistency and normality , geodesic principal component analysis , kendall s shape spaces , flags of subspaces _ ams subject classifications : _ primary 62g20 , 62g25 . secondary 62h11 , 58c06 , 60d05 . | in this paper , the novel statistical problem of deriving asymptotic results for nested random sequences of statistical descriptors for data in a non - euclidean space is considered . it can be viewed as a generalization of classical pca s asymptotics , e.g. by @xcite , where , as a consequence of pythagoras theorem , nestedness of approximating subspaces is trivially given and thus requires no special attention . for pca analogs for data in non - euclidean spaces , due to curvature , nestedness considerably complicates design of descriptors and , to the best knowledge of the authors , has hindered any asymptotic theory to date . for dimension reduction of non - euclidean data , _ procrustes analysis _ by @xcite and later _ principal geodesic analysis _ by @xcite are approaches to mimic pca on shape spaces and riemannian manifolds , respectively . both build on the concept of a frchet mean , a minimizer of expected squared distance , around which classical pca is conducted for the data mapped to a suitable tangent space . asymptotics for such means have been subsequently provided , among others , by @xcite , allowing for inferential methods such as two - sample tests . asymptotics for these _ tangent space pca _ methods , however , reflecting the _ forward nestedness _ due to random basepoints ( i.e. corresponding means ) of tangent spaces with random pcs therein , remain open to date . moreover , these tangent space pca methods are in no way canonical . not only may statistical outcomes depend on specific choices of tangent space coordinates , more severely , given curvature , no tangent space coordinates can correctly reflect mutual data distances . for this reason , among others , _ geodesic principal component analysis _ ( gpca ) has been introduced by @xcite , _ iterated frame bundle development _ by @xcite and _ barycentric subspaces _ by @xcite . as the following example teaches , nestedness may be lost . [ intro.ex ] consider data on a two - sphere that is confined to its equator and nearly uniformly spread out on it . then the best @xmath0 approximating geodesic is the equator and far away there are two ( due to symmetry ) intrinsic frchet means , each close to one of the poles , see @xcite . let us now detail our ideas , first by elucidating the following . * classical pca from a geometric perspective . * given data on @xmath1 , for every @xmath2 a unique affine subspace @xmath3 of dimension @xmath4 is determined by equivalently minimizing residual sums of squares or , among those containing the classical mean @xmath5 , maximizing the projected variance . also equivalently , these subspaces have representations as @xmath6 , the affine translates of spans from an eigenvector decomposition @xmath7 of the data s covariance matrix with descending eigenvalues . in consequence , one may either start from the zero dimensional mean and subsequently add most descriptive dimensions ( forward ) or start from the full dimensional space and remove least descriptive dimensions ( backward ) to obtain the same forward and backward nested sequence of subspaces @xmath8 for non - euclidean data , due to failure of pythagoras theorem , this canonical decomposition of data variance is no longer possible . for a detailed discussion see @xcite . * nestedness of non - euclidean pca * is highly desirable , when due to curvature and data spread , intrinsic frchet means are away from the data . for instance in example [ intro.ex ] , in order to have a mean on the equator , also in this case , @xcite devised _ principal arc analysis _ with the _ backward nested mean _ confined to the best approximating circle . this method and its generalization _ backward nested sphere analysis _ ( pns ) by @xcite give a tool for descriptive shape analysis that often strikingly outperforms tangent space pca , e.g. @xcite . here , the data space is a unit sphere @xmath9 of dimension @xmath10 , say , and in each of the @xmath3 is a @xmath4-dimensional ( small ) subsphere for pns and for _ principal nested great spheres _ ( pngs ) it is a @xmath4-dimensional great subsphere . in passing we note that pns is _ higher dimensional _ in the sense of having higher dimensional descriptor spaces than classical pca and pngs which are equally high dimensional , cf . @xcite . to date , however , there is no asymptotic theory for pns available , in particular there are no inferential tools for backward nested means , say . asymptotic results for non - data space valued descriptors , geodesics , say , are only available for single descriptors ( cf . @xcite ) that are directly defined as minimizers , not indirectly as a nested sequence of minimizers . * challenges for and results of this paper . * it is the objective of this paper to close this gap by providing asymptotic results for rather general random _ backward nested families of descriptors _ ( bnfds ) on rather general spaces . the challenge here is that random objects that are constrained by other random objects are to be investigated , requiring an elaborate setup . into this setup , we translate strong consistency arguments of @xcite and @xcite , and introducing a _ constrained _ m - estimation technique , we show joint asymptotic normality of an entire bnfd . in the special case of nested subspaces , bnfds may terminate at any dimension and @xmath11 is not required . as we minimize a functional under the constraining conditions that other functionals are minimized as well , our approach can be called _ constrained m - estimation_. in the literature , this term _ constrained m - estimation _ has been independently introduced by @xcite who robustify m - estimators by introducing constraining conditions and by @xcite , who consider m - estimators that are confined to closed subsets of a euclidean space with specifically regular boundaries . it seems that our m - estimation problem , which is constrained to satisfying other m - estimation problems has not been dealt with before . we solve it using a random lagrange multiplier approach . furthermore , in order to obtain asymptotic normality of each single sequence element , in particular for the last , we require the rather technical concept of _ factoring charts_. our very general setup will be illustrated , still with some effort , by example of pns , pngs and the _ intrinsic mean on a first geodesic principal component _ ( imo1gpc ) . in order to exploit nested asymptotic normality for a _ nested two - sample test _ , we utilize bootstrapping techniques . while for frchet means , as they are descriptors assuming values in the data space , one can explicitly model the dependence of the random base points of the tangent spaces as in @xcite , so that suitable statistics can be accordingly directly approximated , this modeling and approximation can be avoided using the bootstrap as in @xcite . for our application at hand , as data space and descriptor space are different , we can not approximate the distribution of random descriptors and we fall back on the bootstrap . * suggestions for live imaging of stem cell differentiation . * after illustrations of our nested two - sample test by simulations for pns and pngs , we apply it to a cutting edge application in adult human stem cell differentiation research . `` rooted in a line of experimentation originating in the 1960s '' ( from @xcite ) , the promise that stem cells taken from a patient s bone marrow may be used to rebuild specific , previously lost , patient s tissue is currently undergoing an abundance of clinical trials . although the underlying mechanisms are , to date , not fully understood , it is common knowledge that early stem cell differentiation is triggered by biomechanical cues , e.g. @xcite , which result in specific ordering of the cellular _ actin - myosin filament skeleton_. in collaboration with the third institute of physics at the university of gttingen we map fluorescence images of cell structures to two - spheres , where each point stands for a specific ordering . with our 2d pngs two - sample test we can track the direction of increased ordering over the first 24 hours . we find , however , a consistent reversal of ordering between hours 16 to 20 which hint toward the effect of cell division . this effect suggests that the commonly used time point of 24 hours for fixated hmscs imaging , e.g. as in @xcite , may not be ideal for cell differentiation detection . in fact , our method can be used to direct more elaborate and refined imaging techniques , such as time resolved in - vivo cell imaging , using @xcite , say , to investigate specifically discriminatory time intervals in detail . * we conclude our introduction * by noting that our setup of bnfds has a canonical form on a riemannian manifold with @xmath3 in ( [ backward - nested - subspaces : eq ] ) being a totally geodesic submanifold , not necessarily of codimension one in @xmath12 , however . for example for kendall s shape spaces @xmath13 which is a complex projective space of real dimension @xmath14 , cf . @xcite , we have a sequence of @xmath15 where the numbers below the inclusions denote the corresponding co - dimensions . more generally , we believe that our setup can be generalized to riemann stratified spaces . for example , ( [ nested - shape - spaces : eq ] ) generalizes at once to @xmath16 ( the shape space of @xmath17-dimensional @xmath18 landmark configurations which has dimension @xmath19 ) with @xmath20 , cf . @xcite , now with @xmath21 indeed , in section [ scn : kendalls - shape - spaces ] we illustrate the generalization to the sequence @xmath22 , giving the imo1gpc for arbitrary @xmath16 . our setup may also generalize to phylogenetic tree spaces as introduced by @xcite , cf . also @xcite , or torus - pca and the more general polysphere - pca , cf . moreover , our setup may be applied to flags of barycentric subspaces as introduced by @xcite . * our paper is organized as follows . * in the following section we introduce the abstract setup of bnfds and show that the essential assumptions are fulfilled for pns , pngs and imo1gpcs for riemannian manifolds and kendall s shape spaces . in the section to follow we will develop a set of assumptions necessary for the main results on asymptotic strong consistency and normality which are stated in section [ main - results : scn ] . also in section [ main - results : scn ] , we give our nested bootstrap two - sample test . the elaborate proof of asymptotic strong consistency is deferred to the appendix . in section [ application : scn ] we show simulations and our applications to stem cell differentiation . |
" concept was utilized for shielding the detection cavity , while a vector signal analyzer was used as a microwave receiver with a very narrow resolution bandwidth in the order of a few micro - hz . this contribution will present the experimental layout and the results to date . | r | 1207.3275 | for the microwave equivalent of `` light shining through the wall '' ( lsw ) experiments , a sensitive microwave detector and very high electromagnetic shielding is required . the screening attenuation between the axion generating cavity and the nearby detection cavity should be greater than 300 db , in order to improve over presently existing exclusion limits . to achieve these goals in practice , a box in a box " concept was utilized for shielding the detection cavity , while a vector signal analyzer was used as a microwave receiver with a very narrow resolution bandwidth in the order of a few micro - hz . this contribution will present the experimental layout and the results to date . | wisps can be probed in the laboratory by `` light shining through the wall '' ( lsw ) experiments . they exploit the very weak coupling to photons , allowing an indirect proof of the otherwise hidden particles without relying on any cosmological assumptions . previous lsw experiments have been carried out with optical laser light at desy ( alps ) , cern ( osqar ) and fermilab ( gammev ) . the concept of an optical lsw experiment can be adapted to microwaves @xcite . a block diagram of the setup is shown in fig . [ fig : ovrblock ] , it consists of two identical low loss microwave cavities with a diameter of 140 mm , a height of 120 mm and a spacing between them of 150 mm . one serves as wisp emitter and is excited by an external microwave source . it develops a strong electromagnetic ( em ) field , which corresponds to a large amount of microwave photons @xmath2 . theory predicts that some of these photons convert to paraphotons @xmath3 by kinetic mixing ( similar to neutrino oscillations ) or if the cavities are placed in a strong static magnetic field to axion - like particles by the primakoff effect @xcite . both particles only interact very weakly with matter ( similar to neutrinos in this respect ) and thereby , in contrast to the photons , can traverse the cavity walls . some wisps propagate towards the detection cavity , which is connected to a very sensitive microwave receiver . the reciprocal conversion process transforms wisps to microwave photons , which can be observed as an excitation of the seemingly empty and well shielded detection cavity . since there is no energy loss associated with the wisp conversion process , the regenerated photons in the detecting cavity have exactly the same energy as the photons in the emitting cavity . thus , the signal which is coupled out from the detection cavity has the same frequency as the one which is generated on the emitting side , making a narrowband receiving concept feasible . this paper will focus on the latest exclusion results for * paraphotons * from the microwave wisp search at cern . in a future upgrade , an additional magnet will allow the search for axions . considering current exclusion limits , it takes @xmath4 photons on the emitting side to generate one photon on the detection side , making this the most challenging aspect of an lsw experiment . the expected output power ( or photon flux ) from the detecting cavity towards the microwave receiver due to paraphotons is given by eq . [ equ : power ] , @xmath5 where @xmath6 and @xmath7 are the loaded q factors of emitting and detection cavity , @xmath8 is the frequency where the experiment is carried out ( and to which the cavities are tuned ) , @xmath9 is planck s constant and @xmath10 is a dimensionless geometric form factor in the order of 1 , describing the position , shape and resonating mode of the cavities @xcite . the rest mass of hidden photons is a priori unknown and given by @xmath11 . the kinetic mixing parameter @xmath12 describes the likeliness of paraphoton - photon oscillations . a previous examination of coloumb s law indicates that @xmath13 in this energy range . if there is no significant signal detected , an exclusion result can be produced by determining @xmath12 from the other known values . this provides a convenient way to compare the achieved sensitivity to other experiments . the parameters of the paraphoton experiment as it has been set up and carried out at cern in march 2012 , are summarized in table [ tbl : param ] . as no paraphotons were observed , the corresponding exclusion limit in comparison to other experiments is shown in fig . [ fig : exclplot ] . .parameters of the paraphoton run in march 2012 [ cols="^ " , ] |
a version of the dirichlet problem is solved . self adjoint laplace operators and the probability semigroups they generate are constructed using reflecting and absorbing conditions on subsets of the graph boundary . boundary value problems on networks , resistance networks , dirichlet forms , markov chain explosions . | i | 1109.3137 | formal laplace operators are analyzed for a large class of resistance networks with vertex weights . the graphs are completed with respect to the minimal resistance path metric . compactness and a novel connectivity hypothesis for the completed graphs play an essential role . a version of the dirichlet problem is solved . self adjoint laplace operators and the probability semigroups they generate are constructed using reflecting and absorbing conditions on subsets of the graph boundary . _ mathematics subject classification . _ primary 34b45 _ keywords . _ boundary value problems on networks , resistance networks , dirichlet forms , markov chain explosions . | this work has its roots in the challenge of extending differential equation models for diffusion or wave propagation from domains in euclidean space to infinite graphs intended to resemble biological transport systems such as the arteries of the human circulatory system . such biological systems can include enormous numbers of branching segments . short time transport across the network is essential , so treelike structures with small numbers of large edges and vast collections of microscopic edges are typical . faced with such complex heterogeneous structures , one hopes that appropriate infinite graph models will suggest useful structural features and robustly posed problems . building on an earlier quantum graph analysis of such problems @xcite , this work uses infinite graph and operator theoretic methods to treat a class of continuous time markov chains . recall that continuous time markov chains use a system of constant coefficient differential equations @xmath0 to describe the evolution of probability densities @xmath1 on a finite or countably infinite set of states . an associated graph may be constructed by connecting states ( vertices ) @xmath2 and @xmath3 with an edge if @xmath4 . in the finite state case the solution of is simply @xmath5 . when the set of states is infinite the formal description of the operator @xmath6 may not be adequate to determine the semigroup @xmath7 , an issue known in probability as the problem of explosions . infinite graph models inspired by biological transport systems will typically face the explosion problem . by imposing restrictions on both the form of the markov chain generator @xmath6 and the structure of the associated graph viewed as a metric space , this work provides a resolution in terms of reflecting and absorbing behavior at a graph boundary . it will be advantageous to use the dirichlet form theory @xcite . to that end , consider a graph @xmath8 whose edges @xmath9 $ ] are equipped with positive weights @xmath10 which are interpreted as edge length . with @xmath11 , a symmetric bilinear form for functions on the vertex set is defined by @xmath12 each vertex is also given a positive weight @xmath13 . formal semigroup generators @xmath14 are defined by @xmath15 @xmath10 is often interpreted as electrical resistance . the electrical network analogy is treated at length in @xcite . the recent work @xcite treats electrical currents in a context similar to this paper , while @xcite treats related topological questions . an analysis of function theory on infinite trees motivated by modeling the human lungs is in @xcite . with the domain of functions with finite support , @xmath14 is a symmetric operator on @xmath16 . in contrast to this paper , other recent work @xcite has stressed cases when this symmetric operator is essentially selfadjoint , and so behavior at the graph boundary is not an issue . the vertex set @xmath17 of an edge weighted locally finite graph @xmath8 can be equipped with a metric @xmath18 obtained by minimizing the sum of the edge lengths of paths from @xmath19 to @xmath20 . by completing this metric space we obtain a metric space @xmath21 in which one can discuss features like the graph boundary and compactness . if @xmath8 is a tree , then distinct points of @xmath21 can be separated by deleting a suitable edge . generalizing this idea , our graphs will be required to have weakly connected completions , with the property that , for any two distinct points , any path joining them must include an edge from a finite set . this generalization identifies a rich class of edge weighted graphs with useful topological and function theoretic properties . the properties of weakly connected graph completions are developed in the second section . in addition to trees , arbitrary graphs with finite volume have weakly connected completions . this class is also preserved if we add suitably constrained edge sequences to a graph . weakly connected completions are totally disconnected metric spaces . when also compact , these spaces are topologically stable with respect to decrease of the metric . the weakly connected class will be characterized using the separation of points property for an algebra of eventually flat functions . the third section treats the bilinear forms , vertex weights , and associated operators . the choice of vertex weights typically used for discrete time markov chains are contrasted with weights making @xmath14 resemble a discretized second derivative . the bilinear form is used to construct several sobolev style hilbert spaces on @xmath8 whose elements extend continuously to @xmath22 . two main problems are treated in the fourth section . the first , a version of the dirichlet problem , asks for conditions under which continuous functions on @xmath23 have a unique harmonic extension to @xmath8 . an example shows that a lack of compactness can lead to a negative result . using assumptions of compactness and weak connectivity , a general positive result is established . the second problem is the resolution of the explosion problem in terms of reflecting and absorbing boundary conditions . the semigroups generated by the operators defined using these boundary conditions are positivity preserving contractions on @xmath24 . despite the connections with probability , this work will not explicitly use probabilistic techniques or interpretations . we simply mention the classic work @xcite , and the recent works @xcite as pointers to the enormous literature related to analysis of infinite state markov chains . |
gamma - ray bursts ( grbs ) are proposed as candidate sources of ultra - high energy cosmic rays ( uhecrs ) . we study the possibility that the pev neutrinos recently observed by icecube are produced by grb cosmic rays interacting with the interstellar gas in the host galaxies . by studying the relation between the x - ray absorption column density @xmath0 and the surface star - formation rate of grb host galaxies , we find that @xmath0 is a good indicator of the surface gas density of the host galaxies . then we are able to calculate the neutrino production efficiency of crs for grbs with known @xmath0 . | i | 1503.04932 | gamma - ray bursts ( grbs ) are proposed as candidate sources of ultra - high energy cosmic rays ( uhecrs ) . we study the possibility that the pev neutrinos recently observed by icecube are produced by grb cosmic rays interacting with the interstellar gas in the host galaxies . by studying the relation between the x - ray absorption column density @xmath0 and the surface star - formation rate of grb host galaxies , we find that @xmath0 is a good indicator of the surface gas density of the host galaxies . then we are able to calculate the neutrino production efficiency of crs for grbs with known @xmath0 . we collect a sample of grbs that have both measurements of @xmath0 and accurate gamma - ray fluence , and attempt to calculate the accumulated neutrino flux based on the current knowledge about grbs and their host galaxies . when the cr intensity produced by grbs is normalized with the observed uhecr flux above @xmath1 , the accumulated neutrino flux at pev energies is estimated to be about @xmath2 ( per flavor ) under the assumption that grb energy production rate follows the cosmic star - formation rate and the favorable assumption about the cr diffusion coefficient . this flux is insufficient to account for the icecube observations , but the estimate suffers from some assumptions in the calculation and thus we can not rule out this scenario at present . | gamma - ray bursts ( grbs ) have been proposed as a potential origin of ultra - high - energy cosmic rays ( uhecrs ) ( e.g. , waxman 1995 ; vietri 1995 ; milgrom and usov 1995 ) . high - energy neutrinos are thought to be a useful messenger to probe cr acceleration in grbs , as they are predicted to be produced in the dissipative fireballs , where cosmic - ray protons interact with fireball gamma - ray photons through photopion process ( e.g. , waxman & bahcall 1997 ; guetta et al . 2004 ; dermer & atoyan 2006 ; murase et al . 2006 ; wang & dai 2009 ) . however , search for high - energy neutrinos in coincident with grbs using icecube has failed to find any associated neutrinos so far ( abbasi et al . 2012 ; aartsen et al . 2015 ) . the non - detection has put stringent constraints on the neutrino production efficiency and fireball properties of grbs ( he et al . 2012 ; zhang & kumar 2013 ; gao et al . 2013 ; yacobi et al . 2014 ) . because the low neutrino flux could be simply due to a low efficiency in converting crs to neutrinos , as expected in some grb models with large dissipation radius , one can not rule out cr acceleration in grbs with the non - detection of neutrinos . crs accelerated by grbs will finally escape from the source and enter the interstellar space of the host galaxy . the proton - proton collisions between crs and nuclei in the interstellar medium will also produce high - energy neutrinos . recently , icecube collaboration reported the detection of extraterrestrial tev - pev neutrinos with a best - fit flux of @xmath3 per flavor ( aartsen et al . 2014 ) . noting the coincidence between the icecube neutrino flux and the waxman - bahcall bound ( @xmath4 ) derived from the flux of uhecrs above @xmath5 , some authors suggest that icecube neutrinos may be produced by the same source responsible these uhecrs ( waxman 2013 ; katz et al . as grbs are one candidate source of uhecrs , one may wonder whether neutrinos resulted from the cr collisions with the ism in the host galaxy can explain the icecube observations ( waxman 2013 , wang et al . 2014 ) . in this paper , we study this interesting possibility by perform a calculation of the expected neutrino flux with the knowledge about the properties of grbs and their host galaxies . one key unknown factor that decides the neutrino flux from grb host galaxies is the pion production efficiency , i.e. the energy loss of cr protons into pions due to collisions with the ism of the host galaxy . crs interact with the ism along their path before escape , so this efficiency relates with the gas column density that crs traversed . as crs are transported outward by galactic winds , the gas surface density @xmath6 represents an averaged column density of matter that crs traversed . however , for most grbs , we do not have measurements of @xmath6 at the grb explosion site as grb hosts are hardly spatially resolved . we note that the x - ray absorption column density @xmath0 , inferred from the x - ray observations of the prompt and afterglow emission , has a similar role , but @xmath0 reflects the column density along the direction of the line of sight ( rather than the averaged gas column density ) . moreover , the value of @xmath0 is derived assuming solar metallicity for the absorbing gas , while grbs seem to occur preferentially in low metallicity galaxies ( stanek et al . 2006 ; prieto et al . 2008 ) . the x - ray absorption , as measured with swift / xrt observations , mainly takes place through inner shell electrons of metals , thus it is linked to the metallicity of the ism in the host galaxies . if grb host galaxies have lower metallicity , the true absorbing gas column density should be higher than the quoted values obtained from fitting x - ray afterglows , considering this metallicity difference . we thus first study how well @xmath0 can trace the gas surface density @xmath6 in 2 . we find that @xmath0 is well correlated with the surface star - formation rate ( @xmath7 ) of the host galaxies . then taking into account the kennicutt - schmidt law that relates the surface gas density and the surface star - formation rate ( kennicutt 1998 ) , we obtain a relation between @xmath0 and @xmath6 . once @xmath6 is known for each grb , we can calculate the neutrino production efficiency and further calculate the accumulated neutrino flux from all grb host galaxies ( 3 ) . |
when the cr intensity produced by grbs is normalized with the observed uhecr flux above @xmath1 , the accumulated neutrino flux at pev energies is estimated to be about @xmath2 ( per flavor ) under the assumption that grb energy production rate follows the cosmic star - formation rate and the favorable assumption about the cr diffusion coefficient . this flux is insufficient to account for the icecube observations , but the estimate suffers from some assumptions in the calculation and thus we can not rule out this scenario at present . | c | 1503.04932 | gamma - ray bursts ( grbs ) are proposed as candidate sources of ultra - high energy cosmic rays ( uhecrs ) . we study the possibility that the pev neutrinos recently observed by icecube are produced by grb cosmic rays interacting with the interstellar gas in the host galaxies . by studying the relation between the x - ray absorption column density @xmath0 and the surface star - formation rate of grb host galaxies , we find that @xmath0 is a good indicator of the surface gas density of the host galaxies . then we are able to calculate the neutrino production efficiency of crs for grbs with known @xmath0 . we collect a sample of grbs that have both measurements of @xmath0 and accurate gamma - ray fluence , and attempt to calculate the accumulated neutrino flux based on the current knowledge about grbs and their host galaxies . when the cr intensity produced by grbs is normalized with the observed uhecr flux above @xmath1 , the accumulated neutrino flux at pev energies is estimated to be about @xmath2 ( per flavor ) under the assumption that grb energy production rate follows the cosmic star - formation rate and the favorable assumption about the cr diffusion coefficient . this flux is insufficient to account for the icecube observations , but the estimate suffers from some assumptions in the calculation and thus we can not rule out this scenario at present . | the above calculation has some uncertainties in the following aspects . first , the estimate of the energy production rate of gamma - rays @xmath97 has uncertainty ( e.g. , dermer 2012 ) . note that the factor @xmath79 is obtained by assuming that grb rate follows the cosmic sfr of porciani & madau ( 2001 ) or that of hopkins & beacom ( 2008 ) . if grb density evolves faster than the cosmic sfr , @xmath73 is smaller and then @xmath77 is larger . second , the estimate of the uhecr energy budget has uncertainty . the value can be a bit larger if one uses the telescope array or hires data . third , the power - law index @xmath75 could be softer than 2 , then the energy budget of crs at 100 pev could be larger . thus , given these uncertainties , the neutrino flux in the optimistic case could reach the observed value of icecube . on the other hand , if one consider that grb host galaxies that are not detected by optical observations are possibly smaller galaxies , such as dwarf galaxies , the pion production efficiency may be smaller and thus the neutrino flux contributed by these galaxies would be smaller . also , as shown by eq . 6 , the pion production efficiency depends on the speeds of the galactic winds . the properties of the galactic winds in grb host galaxies are not well - explored . x - ray observations of starburst galactic winds , such as m82 , usually give a higher speeds than that inferred from the optical observations ( strickland & heckman 2009 ) . if the galactic wind speeds of grb hosts are proven to be higher , the neutrino flux produced by grb hosts would decrease . the pion production efficiency also depends on the diffusive coefficient . if @xmath98 is larger than @xmath99 ( for example , @xmath100 for our galaxy ) , the accumulated neutrino flex would be lower than @xmath101 at @xmath102 , as shown in fig . 3 . in summary , we calculated the neutrino flux produced by crs accelerated by grbs while they are propagating in the host galaxies based on our current knowledge about grb and their host galaxies . these crs collide with nuclei of ism and produce neutrinos before they escape out of the galaxy . when the flux of crs produced by grbs is normalized with the observed flux of uhecrs above @xmath1 , the accumulated neutrino flux is @xmath103 per flavor under the usual assumptions about the grb properties and favorable assumptions about the cr diffusion coefficient . the estimate , however , has uncertainty due to uncertainty in our current knowledge of grb and their host galaxies and the accumulated neutrino flux could reach the observed value by icecube in the optimistic case , so we can not rule out this scenario at present . we thank zhuo li and ruoyu liu for useful discussions . this work is supported by the 973 program under grant 2014cb845800 , the nsfc under grants 11273016 and 11033002 , and the excellent youth foundation of jiangsu province ( bk2012011 ) . |
gerry brown initiated some early studies on the coexistence of different nuclear shapes . the subject has continued to be of interest and is crucial for understanding nuclear fission . perhaps a new approach in the spirit of the old calculations could better elucidate the character of the fission dynamics and explain phenomena that current theory does not model well . | i | 1611.09484 | gerry brown initiated some early studies on the coexistence of different nuclear shapes . the subject has continued to be of interest and is crucial for understanding nuclear fission . we now have a very good picture of the potential energy surface with respect to shape degrees of freedom in heavy nuclei , but the dynamics remain problematic . in contrast , the early studies on light nuclei were quite successful in describing the mixing between shapes . perhaps a new approach in the spirit of the old calculations could better elucidate the character of the fission dynamics and explain phenomena that current theory does not model well . | in the early 1960 s , bohr and mottelson pointed out some puzzling experimental data : some light nuclei thought to be spherical in shape had excited energy levels exhibiting characteristics of deformed nuclei . this was taken up first by engeland @xcite and then gerry brown , who saw an opportunity to test the realistic nuclear interactions that were being developed at the time . the nuclei @xmath0o and @xmath1o were the first subjects of study @xcite . as his graduate student , i worked on a parallel study of ca isotopes as part of my thesis project . later , a more definitive study of the ca nuclei was carried out by gerace and green @xcite . as a general conclusion , one saw that the mixing between shapes could be understood with the realistic interactions derived from nucleon - nucleon scattering data . since those early days of nuclear structure physics , the subject of nuclear deformation has matured . first of all , we now know that the shape coexistence is ubiquitous in the low - energy spectra of nuclei across the periodic table , affecting even the fission properties of the heaviest nuclei . also , we now have computational tools to describe and predict the static features of the landscape of nuclear shapes . however , the dynamics of shape change , ie . how different shapes mix together , has been a challenging problem in the theory of heavy nuclei and is still not well understood . i shall describe some work i have been engaged in recently , to develop a new approach to fission dynamics in the spirit of the old studies on light nuclei . |
three different possible sources ( treatment of resonance lifetimes , a soft equation of state and non - gaussian effects ) to understand the hbt @xmath1 puzzle are investigated . firstly , we find that different treatments of the resonance decay time can not resolve the hbt time - related puzzle , however it can modify the hbt radii at low transverse momenta to some extent to explain the data slightly . secondly , with a soft equation of state with momentum dependence , the measured transverse momentum dependent hbt radii and @xmath1 ratio can be described fairly well . | i | 0808.3457 | hbt correlations of @xmath0 pairs at fair / ags energies are investigated by using the urqmd transport model and the crab analyzing program . three different possible sources ( treatment of resonance lifetimes , a soft equation of state and non - gaussian effects ) to understand the hbt @xmath1 puzzle are investigated . firstly , we find that different treatments of the resonance decay time can not resolve the hbt time - related puzzle , however it can modify the hbt radii at low transverse momenta to some extent to explain the data slightly . secondly , with a soft equation of state with momentum dependence , the measured transverse momentum dependent hbt radii and @xmath1 ratio can be described fairly well . thirdly , non - gaussian effects are visible in the calculated correlation function . using the edgeworth expansion , one finds that the non - gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction . ( some figures in this article are in colour only in the electronic version ) | it is well - known that one can extract information on the space - time dimensions of the particle emission source ( the region of homogeneity ) in heavy - ion collisions ( hics ) by using the hanbury - brown - twiss interferometry ( hbt ) @xcite techniques . with the ongoing advances in detectors and accelerators one is able to explore collision energies for hics from less than @xmath2 gev ( sis / fair energy regime ) , @xmath3 gev ( fair / ags and sps ) up to @xmath4 gev ( rhic ) . within this broad energy region quantum chromodynamics ( qcd ) predicts a transition from a hadron gas to a quark - gluon plasma ( qgp ) , and it is expected that this new qgp state of matter exists at least temporarily in the center of hics . during the phase transition ( i.e. , in the mixed phase ) , it was proposed that a nontrivial transition in the spatio - temporal characteristics of the source exists @xcite . unfortunately , so far the excitation functions of the hbt parameters have not shown any _ obvious _ discontinuities in experiments with energies from sis , ags , sps , up to rhic @xcite . instead , several unexpected and interesting phenomena occurred , namely , the `` e - puzzle '' , the `` t - puzzle '' , and the `` non - gaussian '' effect @xcite ( for an explanation of these terms , see below ) . objectively speaking , the existing theoretical investigations are still in - sufficient and further thorough investigations are needed . in a recent work on the hbt correlation , adopting the ultra - relativistic quantum molecular dynamics ( urqmd , v2.2 ) transport model @xcite and the `` correlation after - burner '' ( crab , v3.0@xmath5 ) analyzing program @xcite , the transverse momentum , system - size , centrality , and rapidity dependence of the hbt parameters of the sources of different identical particle pairs ( two @xmath6s , two @xmath7s , and two @xmath8s ) at ags , sps and rhic energies @xcite were investigated . it was found that although the calculations are generally in line with the experimental data , discrepancies are not negligible . one of the most puzzling phenomena is that the calculated ratio of hbt radii in the outward direction ( @xmath9 ) and in sideward direction ( @xmath10 ) from central hics is always larger than that extracted from the data at all investigated energies , if the cascade mode is employed , which was named as the hbt time - related puzzle ( `` hbt t - puzzle '' ) @xcite . after considering a soft equation of state ( eos ) with momentum dependence ( dubbed as sm - eos ) for formed baryons and a simple skyrme - like ( density dependent ) potential for the `` pre - formed '' particles @xcite , the hbt radius @xmath9 is pushed down and the @xmath10 is pulled up to approach the data so that the `` hbt t - puzzle '' disappears throughout the whole energy region . meanwhile , the transverse mass ( @xmath11 ) scaling , which was predicted in ref.@xcite , and has been probed by several experiments recently @xcite , can also be much better understood with the help of `` pre - formed '' particle potentials in hics @xcite . therefore , it was concluded that the interaction ( here it is embodied with potentials ) of particles at the early stages of hics can help to solve the `` hbt t - puzzle '' . however , besides the potential effects , the resonance dynamics and decay may also influence the momentum distribution of emitted particles as well as their correlation @xcite . since this question has been left aside in our previous works , in this paper , we want to complete the discussion by investigating the effects of the handling of resonance decay times on the hbt quantities by adopting the microscopically transport model urqmd . the different contributions from the resonance decay and from the potential modification are then compared . in order to have a clearer situation , in this paper we restrict ourselves to the low energy region , i.e. , the fair / ags energy regime . in this energy region hadronic interactions dominate the dynamics . string dynamics is negligible and the quarks are still confined and the interactions between them do not need to be taken into account during the hics . a further simplification is that the available resonances at these beam energies are mainly the @xmath12s , and one can restrict the analysis of resonance modification to this hadron . due to the fact that pions have the largest abundance , they are well suited for the present analysis . negatively charged pions can be easily measured ( no contamination from misidentified k@xmath13s and protons ) and experimental data are therefore available from most experiments today . thus , we focus the present analysis on negatively charged pions . the paper is arranged as follows . in the next section , the urqmd transport model and the crab analyzing program are introduced . the different treatments of @xmath14 decay and the effects on pion production are also discussed . in section 3 , firstly , the gaussian fitting to the one- and the three - dimensional correlation functions of negatively charged pions and the non - gaussian effect are explored and discussed . secondly , we show the comparison of the transverse momentum dependence of hbt radii and @xmath1 ratios ( from the gaussian fitting ) between calculations with different treatments of the resonance decay and with(without ) mean field potentials and experimental data at ags energies . finally , in section 4 , a summary and outlook is given . |
hbt correlations of @xmath0 pairs at fair / ags energies are investigated by using the urqmd transport model and the crab analyzing program . thirdly , non - gaussian effects are visible in the calculated correlation function . using the edgeworth expansion , one finds that the non - gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction . | i | 0808.3457 | hbt correlations of @xmath0 pairs at fair / ags energies are investigated by using the urqmd transport model and the crab analyzing program . three different possible sources ( treatment of resonance lifetimes , a soft equation of state and non - gaussian effects ) to understand the hbt @xmath1 puzzle are investigated . firstly , we find that different treatments of the resonance decay time can not resolve the hbt time - related puzzle , however it can modify the hbt radii at low transverse momenta to some extent to explain the data slightly . secondly , with a soft equation of state with momentum dependence , the measured transverse momentum dependent hbt radii and @xmath1 ratio can be described fairly well . thirdly , non - gaussian effects are visible in the calculated correlation function . using the edgeworth expansion , one finds that the non - gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction . ( some figures in this article are in colour only in the electronic version ) | to summarize , the hbt correlation of @xmath0 pairs at ags energies were investigated by using the urqmd transport model and the crab analyzing program . we found that a narrower ( wider ) width of @xmath12 resonance results in larger ( smaller ) hbt radii in all directions at large @xmath127 , which can not explain the small experimental ratio between @xmath9 and @xmath10 . although a mass dependent lifetime of the resonances can not resolve this problem as well , but it pulls up the hbt ratii at small @xmath127 and hence slightly improves the hbt radii of pions . we observed that the @xmath127 dependent hbt radii and @xmath1 ratio in the ags energy region can be described fairly well with a soft equation of state with momentum dependence . this supports the idea that the interaction of particles in the early stage of the reaction ( leading to stronger correlation ) is the key to solve the hbt time - related puzzle . non - gaussian effects are visible ( although weak ) in the correlation function and might bring large uncertainties ( on the order of @xmath130 fm ) if the correlation function is fitted only by a gaussian form . to investigate the non - gaussian effect , the edgeworth expansion was used during the fitting process . it was found that the non - gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction . the decay of the intermediate- and long - lived resonances was found as the main contribution to the non - gaussian phenomenon , while the mean field potential did not increase this effect . at higher beam energies , such as sps and rhic , the non - gaussian effects as well as the broadening of vector mesons ( in connection to the na60 results @xcite ) and its influence on @xmath131 correlation deserve further investigations . in addition , other , besides pions , ( non-)identical particle correlations deserve increased attention as they might provide snapshots of the source geometry at different times of the reaction . these studies are currently underway and will be addressed in a forthcoming paper . |
hd 45166 was selected as a candidate to the v sagittae class . it s spectrum shows quite narrow emission lines of he , c , n , and o , possibly indicating a low inclination for the binary system . we performed high resolution and high stability coud spectroscopy in order to search for low amplitude radial velocity variations . # 1 1.25 in .125 in .25 in | i | astro-ph0109461 | hd 45166 was selected as a candidate to the v sagittae class . it s spectrum shows quite narrow emission lines of he , c , n , and o , possibly indicating a low inclination for the binary system . we performed high resolution and high stability coud spectroscopy in order to search for low amplitude radial velocity variations . the orbital period determined from the radial velocity curve is 0.357 days , and the radial velocity semi amplitude is k=3.8 km / s . the system inclination , determined from the mass function of the secondary star , is @xmath0 . # 1 1.25 in .125 in .25 in | the class of the v sagittae stars ( steiner & diaz 1998 ) , is composed of galactic binary systems with similar observational properties . the stars of this class are spectroscopically characterized by the simultaneous presence of the emission lines of ovi and nv and by the strength of the heii 4686 emission line , usually more than 2 times stronger than h@xmath1 . the orbital periods are distributed between 5 and 12 hr . the v sagittae stars are possible galactic counterparts of the close binary supersoft x - ray sources ( cbss ) , found in the magellanic clouds and in m31 ( steiner & diaz 1998 ) . the cbss are presently accepted to be binary systems containing massive white dwarfs with stable nuclear burning of accreted matter on its surface ( van den heuvel et al . this stable nuclear burning can occur when the mass transfer is very high ( @xmath2 yr@xmath3 ) , a situation found in systems with mass ratios ( @xmath4 ) inverted when compared to the mass ratios usually found in cataclysmic variables ( kahabka & van den heuvel 1997 ) . hd 45166 is classified in the sixth catalogue of galactic wolf - rayet stars ( van der hucht et al . 1981 ) as a low mass wr - like star of spectral type qwr + b8v . however , its spectrum shows unusually narrow emission lines for a wolf - rayet star , besides a solar chemical composition and both wn and wc features . willis & stickland ( 1983 ) confirmed the binary nature of the system with the observation of a uv photospheric absorption spectrum and reported the evidence for variability in the strengths of the niv , nv , civ and heii emission lines , probably arising in structural changes in a wind . a sdop rather than qwr interpretation is suggested , where the `` p '' designation indicates the narrow emission line spectrum . these authors report that no velocity variability in excess of @xmath5 km / s was found in the optical spectra of hd 45166 . if the amplitude of radial velocity variations is lower than 10 km / s this could mean a low inclination for the binary system , which is compatible with the narrow emission lines found in its spectra . in an effort to determine the orbital period of hd 45166 we performed high resolution and high stability coud spectroscopy at the 1.6 m telescope of the laboratrio nacional de astrofsica , brazil . a total of 42 spectra were obtained with the 1800 l / mm dispersion grating , resulting in 0.2 fwhm spectral resolution . typical rms residuals in wavelength calibrations are @xmath6 m . |
heat produced during a reset operation is meant to show a fundamental bound known as landauer limit , while simple switch operations have an expected minimum amount of produced heat equals to zero . however , in both cases , present day technology realizations dissipate far beyond these theoretical limits . in this paper we present a study based on molecular dynamics simulations , where reset and switch protocols are applied on a graphene buckled ribbon , employed here as a nano electromechanical switch working at the thermodynamic limit . | i | 1507.07450 | heat produced during a reset operation is meant to show a fundamental bound known as landauer limit , while simple switch operations have an expected minimum amount of produced heat equals to zero . however , in both cases , present day technology realizations dissipate far beyond these theoretical limits . in this paper we present a study based on molecular dynamics simulations , where reset and switch protocols are applied on a graphene buckled ribbon , employed here as a nano electromechanical switch working at the thermodynamic limit . | mechanical switches have attracted the attention of the scientific community for a long time @xcite . one interesting aspect is the non - volatile nature of bits encoded into bistable mechanical systems . this condition could in principle avoid the typical heat production associated with losses due to electric currents . in fact , excess heat production during computation is one of the main limitations that standard cmos technology is presently facing in order to develop next generations of switches . present cmos switches are orders of magnitude far from the theoretical minimum heat required for computing . this fundamental bound , known as landauer limit@xcite , arises for any physical system encoding two logic states , @xmath0 and @xmath1 , and in contact with a heat bath at temperature @xmath2 , when we intend to set the system into one given state , regardless of the knowledge of the initial state . according to the so - called landauer principle , such a reset operation must produce at least @xmath3 of heat ( with @xmath4 boltzmann constant)@xcite . however the landauer limit does not close the door to switch procedures that do not generate heat , once the initial state is known and a proper switch protocol is observed@xcite . in this paper we consider the encoding of a logical bit in a given configuration of a clamped - clamped single - layer graphene ribbon , as depicted in . to achieve two stable states , a compression is applied by bringing closer the extremes of the ribbon in the @xmath5-direction that buckles the structure in the out - of - plane direction . this compression generates an energy barrier separating the two stable states corresponding to the upward and downward buckling . to identify which logic state the ribbon represents at time @xmath6 , we monitor the coordinates of the central atom in the ribbon ( see zoomed image in ) . being @xmath7 the coordinates of the central atom , we indicate with @xmath8 ( @xmath9 ) the set of possible physical microstates with @xmath10 ( @xmath11 ) . if the system is a micro state that belongs to @xmath9 ( @xmath8 ) we say that the ribbon encodes the logical state @xmath0 ( @xmath1 ) . starting from these considerations we present a _ reset protocol _ based on electrostatic forces acting on the graphene ribbon that approaches the landauer limit . the procedure is designed to reach the theoretical thermodynamic bound without altering the compression of the ribbon . we also discuss a similar _ switch protocol _ that realizes the switch process approaching @xmath12 . |
high - accuracy rotation curves of spiral galaxies show a steep rise in the central few hundred pc region , indicating high concentration of mass toward the center . using the rotation curves , we idrectly calculate radial distributions of the surface - mass density ( smd ) , and obtain radial profiles of the mass - to - luminosity ratio ( m / l ) . we discuss the radial distribution of dark matter in spiral galaxies . psfig | i | astro-ph9910004 | high - accuracy rotation curves of spiral galaxies show a steep rise in the central few hundred pc region , indicating high concentration of mass toward the center . using the rotation curves , we idrectly calculate radial distributions of the surface - mass density ( smd ) , and obtain radial profiles of the mass - to - luminosity ratio ( m / l ) . the m / l ratio is found to vary significantly not only in the massive halo but also within the bulge and disk regions . it increases with the radius within the disk , and rapidly toward halo . in some galaxies , the m / l increases inward toward the center within the bulge , indicating a massive dark core . on these bases , we discuss the radial distribution of dark matter in spiral galaxies . psfig | the dark matter inferred from analyses of flat rotation curves dominates the mass of galaxies ( rubin et al 1980 , 1982 ; bosma 1981 ; mathewson et al 1996 ; persic et al 1996 ) . however , the distribution of dark - matter in the inner disk and bulge are not thoroughly investigated yet because of the difficulty in observing rotation curves of the innermost part of galaxies . in order to investigate the inner kinematics and rotation properties of spiral galaxies , we have shown that the co molecular line would be most useful because of its high concentration in the center as well as for its negligible extinction through nuclear gas disks ( sofue 1996 , 1997 , sofue et al 1997 , 1998 , 1999 ) . recent high - dynamic range ccd spectroscopy in optical lines has also made it possible to obtain high accuracy rotation curves for the inner regions ( rubin et al 1997 ; sofue et al 1998 ) . in this article , we review the observations of high - accuracy rotation curves of spiral galaxies , and discuss their general characteristics . using the rotation curves , we derive the distribution of surface mass density ( smd ) , and discuss the radial variation of mass - to - luminosity ratio and the dark mass fraction . |
homogeneity and heterogeneity represent a well - known trade - off in the design of modular robot systems . we introduce challenges for self - reconfigurable systems , show advances of mechatronic and software design of heterogeneous platforms and discuss experiments , which intend to demonstrate usability and performance of this system . | i | 1109.2288 | homogeneity and heterogeneity represent a well - known trade - off in the design of modular robot systems . this work addresses the heterogeneity concept , its rationales , design choices and performance evaluation . we introduce challenges for self - reconfigurable systems , show advances of mechatronic and software design of heterogeneous platforms and discuss experiments , which intend to demonstrate usability and performance of this system . | modular and reconfigurable robotics represents the area of mechatronic systems with dynamically changing structures and functionalities @xcite . the principle of modularity is useful in obtaining several advanced properties such as reliability , adaptation @xcite , encapsulation of complexity @xcite , or in exploiting evolutionary and self - developmental capabilities of artificial systems @xcite . not only technological but also natural complex biological systems utilize the concept of modularity , which is known as multicellularity . currently , artificial multicellularity attracted attention of researchers in exploring new biological inspirations , homeostatic mechanisms , macroscopic regulation and other issues @xcite . state of the art solutions in both lattice - based and chain - based reconfigurable systems count primarily homogeneous platforms , e.g. @xcite , @xcite , @xcite , @xcite . there are multiple reasons for such a development : complexity of mechanic , electronic and software design , exploration of reconfiguration approaches , finding a balance between `` rigid '' and `` soft '' design principles . in this work we primarily focus on challenges and driving forces for introducing heterogeneity into modular and reconfigurable systems . homogeneity and heterogeneity provide different advantages and represent two opposite points on the scale of universality and specialization @xcite . for instance , homogeneous elements can be easily replaced , such systems are more scalable . most artificial and natural swarms consist of structurally homogeneous elements , capable of behavioral specialization , e.g. @xcite . however , increasing the complexity of the system , e.g. by aggregation into multi - robots organisms , we encountered bottlenecks in complexity of homogeneous elements , which are expressed in terms of weight , power limitation , or locomotion capabilities . this paper addresses the research and technological challenge of finding the compromise between homogeneous and heterogeneous design principles in general , and in particular within the scope of the european funded projects _ replicator _ and _ symbrion_. first of all , the degree of heterogeneity is an open - ended trade - off between complexity , scalability , cost factors , and required functionalities @xcite . finding a compromise , especially in the initial stage of development , is a tough problem @xcite . to establish a rationale for the heterogeneous design , so - called challenges for modularity and reconfiguration are introduced . these challenges define not only the design choices but also set up experiments for performance measurement . we discuss these issues in sec . [ sec : challenges ] . heterogeneity requires specific technological solutions for docking elements , energy and communication buses , mechatronics , power management and others . the developed solutions are shortly overviewed in sec . [ sec : solutions ] . special attention is paid to compatibility and common elements of this system as well as to a specialization of corresponding platforms . [ sec : manufacturing ] , [ sec : software ] and sec . [ sec : experiments ] introduce a software architecture , manufacturing issues and two experiments , which aim at a qualitative demonstration of increased performance and reliability of this system . finally , in sec . [ sec : conclusion ] we draw conclusions about achieving an optimal degree of heterogeneity . |
human agents happen to judge that a conjunction of two terms is more probable than one of the terms , in contradiction with the rules of classical probabilities this is the conjunction fallacy . one of the most discussed accounts of this fallacy is currently the quantum - like explanation , which relies on models exploiting the mathematics of quantum mechanics . the aim of this paper is to investigate the empirical adequacy of major quantum - like models which represent beliefs with quantum states . we first argue that they can be tested in three different ways , in a question order effect configuration which is different from the traditional conjunction fallacy experiment . the experimental results we get are at odds with the predictions of the quantum - like models . this strongly suggests that this quantum - like account of the conjunction fallacy fails . future possible research paths are discussed . | i | 1606.03430 | human agents happen to judge that a conjunction of two terms is more probable than one of the terms , in contradiction with the rules of classical probabilities this is the conjunction fallacy . one of the most discussed accounts of this fallacy is currently the quantum - like explanation , which relies on models exploiting the mathematics of quantum mechanics . the aim of this paper is to investigate the empirical adequacy of major quantum - like models which represent beliefs with quantum states . we first argue that they can be tested in three different ways , in a question order effect configuration which is different from the traditional conjunction fallacy experiment . we then carry out our proposed experiment , with varied methodologies from experimental economics . the experimental results we get are at odds with the predictions of the quantum - like models . this strongly suggests that this quantum - like account of the conjunction fallacy fails . future possible research paths are discussed . | conjunction fallacy was first empirically documented by tversky and kahneman ( 1982 , 1983 ) through a now renowned experiment in which subjects are presented with a description of someone called linda " : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ linda is 31 years old , single , outspoken , and very bright . she majored in philosophy . as a student , she was deeply concerned with issues of discrimination and social justice , and also participated in anti - nuclear demonstrations . " _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ then , subjects are shown a list of 8 possible outcomes describing her present employment and activities , and are asked to rank the propositions by representativeness or probability . two items were specifically tested : * linda is a bank teller " , * linda is a bank teller and is active in the feminist movement " . empirical results show that most people judge ( 2 ) more probable than ( 1 ) . in the framework of classical probabilities , this is a fallacy the conjunction fallacy , since a conjunction can not be more probable than one of its components . if linda being active in the feminist movement is denoted by @xmath0 and linda being a bank teller by @xmath1 , then @xmath2 should classically prevail . the conjunction fallacy has been shown to be particularly robust under various variations of the initial experimental protocol ( cf . tversky and kahneman 1982 , 1983 , gigerenzer 1996 , kahneman and tversky 1996 , hertwig 1997 , hertwig and chase 1998 , hertwig and gigerenzer 1999 , mellers et al . 2001 , stolartz - fantino et al . 2003 , bonini et al . 2004 , tentori et al . 2004 , hertwig et al . 2008 , moro 2009 , kahneman 2011 , erceg and galic 2014 ; for a review , cf . moro 2009 ) . it has been observed in other cases than the linda story , about topics like sports , politics , or natural events , and in scenarios in which the propositions to be ranked are not preceded with a description . the fallacy also persists when the experimental setting is changed , e.g. in between subjects " experiments in which ( 1 ) and ( 2 ) are presented to different subjects only . semantic and syntactic aspects have also been discussed , in relation with possible misunderstandings , like the implicit meaning of the words probability " and and " . careful experiments show that the conjunction fallacy persists . the conjunction fallacy questions the fact that classical probability theory can be used to describe human judgment and decision making , and it can also be viewed as a challenge to the definition of what a rational judgment is . thus , it is no surprise that the conjunction fallacy has been the subject of a big amount of research ( tentori and crupi 2012 give the number of a hundred papers devoted to it ) . it has interested psychologists , economists and philosophers alike . for instance , behavioral economists have looked at the consequences of the fallacy for understanding real life economic behavior , measuring the robustness of this bias in an economic context with incentives or in betting situations ( e.g. charness et al . 2010 , nilsson and anderson 2010 , erceg and galic 2014 ) . they have also investigated whether the cognitive abilities of subjects are related to behavioral biases in general ( and to the conjunction fallacy in particular , cf . oechssler et al . 2009 ) , and this has led to stimulating research with applications in finance . epistemologists have made confirmation and bayesianism enter the debate ( e.g. tentori and crupi 2008 and 2012 , hartmann and meijs 2012 , schupbach 2012 , shogenji 2012 ) . given that a conjunction fallacy occurs under robust experimental conditions , a natural question arises : how can this fallacy be explained ? several accounts have been argued for , but no one has reached an uncontroversial status today ( as noted by fisk 2004 , nilsson et al 2009 , jarvstad and hahn 2011 , tentori et al . first , tversky and kahneman originally suggested that a representativeness heuristic ( i.e. the probability that linda is a feminist is evaluated from the degree with which the instance of linda corresponds to the general category of feminists ) could account for some conjunction fallacy cases . but it has been argued that the representativeness concept involved is informal and ill - specified ( gigerenzer 1996 , birnbaum et al 1990 ) , and suggestions to specify it in the technical sense of a likelihood value ( shafir et al 1990 , massaro 1994 ) account for limited cases only ( crupi et al . according to another suggestion , agents actually evaluate the probability of the conjunction from some combination of the probabilities of the components , like averaging or adding ( fantino et al . 1997 , nilsson et al . however , such explanations do not resist empirical tests , as tentori et al . ( 2013 ) have argued . the latter propose an account of the conjunction fallacy based on the notion of inductive confirmation as defined in bayesian theory , and give experimental grounds for it it is one of the currently promising accounts . others have argued , also within a bayesian framework , that there are cases in which the conjunction fallacy is actually not a fallacy and can be accounted for rationally ( hintikka 2004 , von sydow 2011 , hartmann and meijs 2012 ) . finally , another prominent proposal to account for the conjunction fallacy , on which we focus here , makes uses of so - called quantum - like " models , which rely on the mathematics of a major contemporary physical theory , quantum mechanics ( franco 2009 , busemeyer et al . 2011 , yukalov and sornette 2011 , pothos and busemeyer 2013)note that only mathematical tools of quantum mechanics are exploited , and that the models are not justified by an application of quantum physics to the brain . the quantum - like account of the conjunction fallacy is particularly promising as it belongs to a more general theoretical framework of quantum - like modeling in cognition and decision making , which has been applied to many fallacies or human behavior considered as irrational ( for reviews , see pothos and busemeyer 2013 , ashtiani and azgomi 2015 , or bruza et al . 2015 ; textbooks include busemeyer and bruza 2012 , haven and khrennikov 2013 ) . for instance , quantum - like models of judgments have been proposed to account for order effect , i. e. when the answers given to two questions depend on the order of presentation of these questions ( atmanspacher and rmer 2012 , busemeyer and bruza 2012 , wang and busemeyer 2013 , wang et al . 2014 ) ; for the violation of the sure thing principle , which states that if an agent prefers choosing action a to b under a specific state of the world and also prefers choosing a to b in the complementary state , then she should choose a over b regardless of the state of the world ( busemeyer et al . 2006a , busemeyer et al . 2006b , busemeyer and wang 2007 , khrennikov and haven 2009 ; for ellsberg s paradox more specifically , cf . aerts et al . 2011 , aerts and sozzo 2013 , aerts et al . 2014 ; for allais paradox , cf . khrennikov and haven 2009 , yukalov and sornette 2010 , aerts et al . 2011 ) ; for asymmetry judgments in similarity , i.e. that a is like b " is not equivalent to b is like a " ( pothos and busemeyer 2011 ) ; for paradoxical strategies in game theory such as in the prisoner s dilemma ( piotrowski and sladowski 2003 , landsburg 2004 , pothos and busemeyer 2009 , brandenburger 2010 ) . more generally , new theoretical frameworks with quantum - like models have been offered in decision theory and bounded rationality ( danilov and lambert - mogiliansky 2008 and 2010 , lambert - mogiliansky et al . 2009 , yukalov and sornette 2011 ) . as the quantum - like account of the conjunction fallacy is one of the few promising accounts of the conjunction fallacy that are discussed today , we choose to focus on it in this paper . more specifically , we focus on the class of quantum - like models which are presented or defended in franco ( 2009 ) , busemeyer et al . ( 2011 ) , busemeyer and bruza ( 2012 ) , pothos and busemeyer ( 2013 ) and busemeyer et al . ( 2015 ) . in these models , an agent s belief is represented by a quantum state and not for instance by a measurement context . our aim is to assess the empirical adequacy of these quantum - like models that are used to account for the conjunction fallacy . we think that two points deserve particular scrutiny . first , it is not always clear which version of the models are supposed to account for particular cases of conjunction fallacies are the simplest ones , called non - degenerate , sufficient ? or are the more general ones , called degenerate , needed ? more recent works tend to favor degenerate models over non - degenerate ones , and non - degenerate models have received some recent criticisms ( cf . tentori and crupi 2013 and pothos and busemeyer 2013 , p. 315 - 316 ) , but a clear and definitive argument on the matter would be welcome . second , the models have not yet been much tested on other predictions than the ones they were intended to account for . it should be checked that they are not _ ad hoc _ by testing their empirical adequacy in general . it is understandable that these two points have not been tested beforehand , as a new general pattern of explanation for the conjunction fallacy is hard to come up with . but since the models have come to be seen as one of the most promising accounts , it becomes urgent to assess them empirically more thoroughly this is our goal in this paper . as for the first point discriminate between non - degenerate and degenerate models , we follow a suggestion made by boyer - kassem et al . ( 2016 ) to test so - called gr equations " , that are empirical predictions made by non - degenerate models . such a gr test requires a new kind of experiment : not the original linda experiment , in which agents have to rank propositions , but an order effect experiment , in which two yes - no questions are asked in one order or in the other , to different agents . existing data can not answer the question of whether the gr equations are verified , as was already noted in 2009 by franco : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ there are no experimental data on order effects in conjunction fallacy experiments , when the judgments are performed in different orders . such an experiment could be helpful to better understand the possible judgment strategies . " ( franco 2009 , 421 ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ we fill this gap here by running several order effect experiments that collect the needed data . as for the second point test new empirical predictions of the models , we consider two tests that apply to any version of the quantum - like models , whether degenerate or not , that are used in the account of the conjunction fallacy . it is well - known in the literature that quantum - like models that account for the conjunction fallacy predict an order effect for the two questions associated with the conjunction ( is linda a bank teller ? " and is linda a feminist ? " ) . actually , this predicted order effect is not a side effect of the quantum - like models , but a core feature of them : they can not account for the conjunction fallacy without it . this enables a direct test of the quantum - like account of the conjunction fallacy , that we apply to our collected experimental data . also , it has been shown that any quantum - like model of the kind involved in the account of the conjunction fallacy must make an empirical prediction called the qq equality " ( wang and busemeyer 2013 , wang et al . we thus test whether the qq equality is verified . the failure of any of these last two tests will be enough to refute the current quantum - like account of the conjunction fallacy . here also , the needed data is not available in the literature , but can be conveniently obtained from the same above - mentioned new experimental configuration , with two yes - no questions in both order . note that our methodology is novel : we are not testing the quantum - like models against data produced by traditional conjunction fallacy experiments that the model were designed to explain , but we are testing them against other data , in a new experimental framework on which the models actually make some predictions , and it is why the experimental situation we shall consider is different from the usual linda experiment . our experiment instantiates the mechanism that the quantum - like account claims agents follow : to evaluate a conjunction like feminist and bank teller " , agents are supposed to evaluate one characteristic after another , answering for themselves to two yes - no questions ( is linda a feminist ? " , is linda a bank teller ? " ) . in other words , the experiment we run somehow forces agents to follow the purported quantum - like mechanism . to have more powerful tests , we have conducted several experiments , with variations of the scenario ( linda , but also others known as bill , mr . f. and k. ) , of the protocol ( questionnaires or computer - assisted experiment ) and with or without monetary incentives . the results we obtain show that current quantum - like models are not able to account for the conjunction fallacy . the outline of the paper is the following . in section 2 , a general quantum - like model is introduced . section 3 presents the three empirical tests that will be performed : the gr equations , order effect , and the qq equality . the experimental protocol is presented in section 4 , and the results in section 5 . section 6 presents the statistical analysis , and section 7 discusses the scope of the results and the future of the research on the conjunction fallacy account . |
hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates . for imperfect template replication , we derive a simple expression for the maximum number of distinct templates @xmath0 that can coexist in a hypercycle and show that it is a decreasing function of the length @xmath1 of the templates . in the case of high replication accuracy prebiotic evolution , error threshold , template coexistence | i | 0806.2069 | hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates . for imperfect template replication , we derive a simple expression for the maximum number of distinct templates @xmath0 that can coexist in a hypercycle and show that it is a decreasing function of the length @xmath1 of the templates . in the case of high replication accuracy we find that the product @xmath2 tends to a constant value , limiting thus the information content of the hypercycle . template coexistence is achieved either as a stationary equilibrium ( stable fixed point ) or a stable periodic orbit in which the total concentration of functional templates is nonzero . for the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits . prebiotic evolution , error threshold , template coexistence | most of the modern theoretical work on prebiotic evolution was prompted by the seminal paper of @xcite which explored the fate of a population of competing macromolecules in an environment with limited resources . the main conclusion of eigen s work is that the length of a replicating polymer ( i.e. , a rna - like template ) is limited by the replication accuracy per nucleotide , and so primordial replicators would have to replicate with implausible high accuracy in order to reach the length of today s rna viruses ( about @xmath3 to @xmath4 nucleotides ) . this finding , together with the observation that distinct templates can not coexist in the competition - only scenario @xcite , come to be known as the information crisis of prebiotic evolution . in fact , this information crisis would be resolved by the coexistence of several distinct , short templates , i.e. by the splitting of the information in short modules , similarly to the division of the genome in chromosomes found in many present - day organisms . in this case , the total information content of the template pool is the product of the number of different templates and the maximum information coded per template ( roughly the template length @xmath1 ) , provided the template types have the same concentration . but template coexistence can be achieved only if some sort of cooperation between templates is imposed _ a priori _ to the molecular population . to this end @xcite proposed a cyclic reaction scheme , termed hypercycle , in which each replicator would aid in the replication of the next one , in a regulatory cycle closing on itself . an alternative proposal confines the templates in packages or prebiotic vesicles which are deemed viable provided it encloses a number @xmath5 of distinct functional templates @xcite . perhaps because hypercycles and vesicle models are more difficult to analyze than the naked - gene ( quasispecies ) scenario , the all - important question of whether these information integration systems exhibit a similar phenomenon as the error threshold of the quasispecies model was put off . only recently a re - examination of a prototypical package model the model of @xcite revealed that package models in general suffer from the same malady as the quasispecies model : in the case of imperfect replication an increase in the number @xmath5 of distinct templates confined in the vesicle must be followed by a decrease of their lengths , otherwise the package becomes unviable . as a result , the product @xmath6 ( i.e. , the total information content of the package ) tends to a constant value that depends essentially on the spontaneous mutation rate per nucleotide @xcite . our aim in this contribution is to investigate whether a similar restriction to the total amount of information in the pool of templates holds for hypercycle systems as well . the dynamics of hypercycle systems in the presence of a variety of mutant types was extensively investigated by @xcite . we refer the reader to @xcite for an emphasis on the destabilizing effects of mutant parasites and to @xcite for an analysis of the robustness conferred by spatial organization against those mutants . however , the formulation of @xcite in which the mutants form an error tail class seems more appropriate to study the error threshold phenomenon and so our analysis will build heavily on that paper . the sole motivation of this contribution is to show that the condition for the viability of the hypercycle derived in @xcite is in fact valid for all @xmath5 and not only for the regime where fixed points are stable , i.e. , for @xmath7 . this is so because we found numerically that a necessary condition for the presence of stable periodic orbits is the existence of an unstable fixed point . for the purpose of completeness , in the following section we describe the model and re - derive the main results regarding the existence of fixed point ( and hence of stable periodic solutions ) for the hypercycle system . |
we find that the product @xmath2 tends to a constant value , limiting thus the information content of the hypercycle . template coexistence is achieved either as a stationary equilibrium ( stable fixed point ) or a stable periodic orbit in which the total concentration of functional templates is nonzero . for the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits . | c | 0806.2069 | hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates . for imperfect template replication , we derive a simple expression for the maximum number of distinct templates @xmath0 that can coexist in a hypercycle and show that it is a decreasing function of the length @xmath1 of the templates . in the case of high replication accuracy we find that the product @xmath2 tends to a constant value , limiting thus the information content of the hypercycle . template coexistence is achieved either as a stationary equilibrium ( stable fixed point ) or a stable periodic orbit in which the total concentration of functional templates is nonzero . for the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits . prebiotic evolution , error threshold , template coexistence | in our analysis we have opted for the choice of parameters that most favored the stability of the hypercycle . for instance , introduction of other interactions such as the catalytic promotion of the growth of the templates in the error tail by functional templates an assumption implicit in the package models can only reduce the value of @xmath0 . ( we have verified that the catalytic coupling between functional templates and the error tail does not produce any qualitatively new result . ) similarly , the parameter setting that corresponds to the elementary hypercycle in which @xmath62 but @xmath63 results also in a reduction of @xmath0 . asymmetric hypercycles in which the templates have distinct productivities @xmath64 leads to internal competition and again to the decrease of @xmath0 @xcite . hence eq . ( [ n_max ] ) must be seen as an upper bound to the maximum number of functional templates in the hypercycle . the effect that a change @xmath65 causes on @xmath0 is given by @xmath66 in the case the functional templates have a high replication accuracy ( i.e. , @xmath67 ) we find that the product @xmath2 tends to a constant value , similarly to the findings for the package models @xcite . we stress that eq . ( [ n_max ] ) is worthful because its validity is not restricted to the regime where the nontrivial fixed point is stable : it holds also in the regime where the only stable solutions are periodic orbits . we provide only numerical evidence to support this remarkable finding which is based on the conjecture that the existence of an unstable fixed point is a necessary condition for the presence of stable periodic orbits in the system of ordinary differential equations ( [ ode_h])-([ode_e ] ) . it would be very interesting to find a proof for this conjecture . |
hypervelocity stars ( hvss ) ejected by the massive black hole at the galactic center have unique kinematic properties compared to other halo stars . their trajectories will deviate from being exactly radial because of the asymmetry of the milky way potential produced by the flattened disk and the triaxial dark matter halo , causing a change of angular momentum that can be much larger than the initial small value at injection . [ firstpage ] black hole physics galaxy : center galaxy : halo stellar dynamics | i | 0705.3514 | hypervelocity stars ( hvss ) ejected by the massive black hole at the galactic center have unique kinematic properties compared to other halo stars . their trajectories will deviate from being exactly radial because of the asymmetry of the milky way potential produced by the flattened disk and the triaxial dark matter halo , causing a change of angular momentum that can be much larger than the initial small value at injection . we study the kinematics of hvss and propose an estimator of dark halo triaxiality that is determined only by instantaneous position and velocity vectors of hvss at large galactocentric distances ( @xmath0 ) . we show that , in the case of a substantially triaxial halo , the distribution of deflection angles ( the angle between the stellar position and velocity vector ) for hvss on bound orbits is spread uniformly over the range 10@xmath1180@xmath1 . future astrometric and deep wide - field surveys should measure the positions and velocities of a significant number of hvss , and provide useful constraints on the shape of the galactic dark matter halo . [ firstpage ] black hole physics galaxy : center galaxy : halo stellar dynamics | recent observations have revealed the existence of a population of hypervelocity stars ( hvss ) traveling in the halo of the milky way ( mw ) with galactic rest - frame velocities @xmath2 in the range between @xmath3 and @xmath4 @xcite . hvss are probably b - type main sequence stars with lifetimes @xmath5 , galactocentric distances @xmath6 kpc , and move with speeds large enough to escape from the galaxy . the significant excess of b - type stars with velocities @xmath7 and distances @xmath8 kpc observed by @xcite may also be an indication that many hvss are ejected into the halo on _ bound _ orbits . hvss were first recognized by @xcite as an unavoidable byproduct of the presence a massive black hole ( bh ) in the galactic center . only a close encounter with a relativistic potential well can accelerate a 3 - 4 @xmath9 star to such extreme velocities , and at least three different ejection mechanisms have been proposed : the interaction between background stars and an intermediate - mass black hole ( imbh ) inspiralling towards sgr a@xmath10 @xcite , the disruption of stellar binaries in the tidal field of sgr a@xmath10 @xcite , and the scattering of stars off a cluster of stellar - mass bhs orbiting sgr a@xmath10 @xcite in all these models , hvss have unique kinematics compared to other halo stars : 1 ) they have almost zero initial specific angular momentum at ejection , @xmath11 , where @xmath12 the mass of sgr @xmath13 and @xmath14 the pericenter distance of the star ; 2 ) their high speeds diminish the impact of two - body relaxation or dynamical friction effects on their motion ; and 3 ) their trajectories will deviate from being exactly radial because of the asymmetry of the milky way potential produced by the flattened disk and the triaxial dark matter ( dm ) halo , causing a change of angular momentum that can be much larger than the initial small value . ( for reference , a @xmath15 deviation of the velocity from the radial direction at @xmath16 represents a change of @xmath17 in specific angular momentum . ) proper - motion measurements of hvss may therefore become a key diagnostic tool for constraining the shape of the galactic potential @xcite . triaxial halos are a generic prediction of the hierarchical , cold dark matter ( cdm ) models of structure formation . dissipationless cosmological simulations typically predict minor - to - major density axis ratios in the range 0.4 - 0.8 ( e.g. @xcite ) , with the asphericity of the potential increasing rapidly towards the center of the halo @xcite . gas cooling tends to circularize the potential ( e.g. @xcite ) , while subsequent mergers produce highly elongated remnants ( e.g. @xcite ) . studies of weak gravitational lensing and x - ray observations of elliptical galaxies show that halos are significantly flattened , in fair agreement with results from numerical simulations @xcite . yet the coherence of tidal debris from the sagittarius dwarf galaxy appears to indicate that the inner halo of the mw is nearly spherical and therefore in conflict with cdm predictions ( ibata et al . 2001 ; but see helmi 2004 ) . in this paper , we study the kinematics of hvss in the mw as a probe of the triaxiality of the galactic halo . the outline is as follows . in [ sec : analysis ] , we analyze the motion of hvss in a flattened or triaxial gravitational potential . we provide a concise statistical estimator for the triaxiality of the galactic halo potential through the measured angular momenta of hvss . in [ sec : potential ] , we review the galactic potential model to be used in our calculations . in [ sec : simulation ] we perform numerical simulations of the motion of hvss to study their kinematics . finally , in [ sec : conclusion ] , we summarize our conclusions . |
we study the kinematics of hvss and propose an estimator of dark halo triaxiality that is determined only by instantaneous position and velocity vectors of hvss at large galactocentric distances ( @xmath0 ) . future astrometric and deep wide - field surveys should measure the positions and velocities of a significant number of hvss , and provide useful constraints on the shape of the galactic dark matter halo . | i | 0705.3514 | hypervelocity stars ( hvss ) ejected by the massive black hole at the galactic center have unique kinematic properties compared to other halo stars . their trajectories will deviate from being exactly radial because of the asymmetry of the milky way potential produced by the flattened disk and the triaxial dark matter halo , causing a change of angular momentum that can be much larger than the initial small value at injection . we study the kinematics of hvss and propose an estimator of dark halo triaxiality that is determined only by instantaneous position and velocity vectors of hvss at large galactocentric distances ( @xmath0 ) . we show that , in the case of a substantially triaxial halo , the distribution of deflection angles ( the angle between the stellar position and velocity vector ) for hvss on bound orbits is spread uniformly over the range 10@xmath1180@xmath1 . future astrometric and deep wide - field surveys should measure the positions and velocities of a significant number of hvss , and provide useful constraints on the shape of the galactic dark matter halo . [ firstpage ] black hole physics galaxy : center galaxy : halo stellar dynamics | we have studied the unique kinematics of hvss ejected from the galactic center with almost zero initial specific angular momentum . hvss can travel in the galactic halo on either bound or unbound orbits , and their spatial and velocity distribution at large galactocentric distances ( @xmath167 ) contain information on the asphericity of the halo gravitational potential . we have proposed an estimator of the triaxiality of the galactic dark matter halo that is determined solely by instantaneous position and velocity vectors of hvss , is independent of the details of the ejection mechanism , and does not require an accurate knowledge of halo mass . future astrometric and deep wide - field surveys of hvss should detect significant numbers of hvss , which could be used to determine the triaxiality of the mw halo by applying the method proposed in this paper . the new class of possibly bound hvss with velocities @xmath168 recently observed by @xcite has galactocentric distances in the range 30 - 60@xmath169 or 10 - 20@xmath169 depending on whether they are main - sequence or blue horizontal branch stars . in the first case ( main - sequence stars at large distances ) , they have a lifetime of @xmath170 and are , according to figure [ fig : alphat ] , on the initial phases of their first orbital periods . their deflection angles are expected to be rather small , supporting the fact that a significant excess of b - type stars is observed only at large positive velocities @xcite . if bound hvss are blue horizontal branch stars instead at smaller distances , the travel time of the stars can be much longer than @xmath171 as at the ejection moment the stars may not necessarily be blue horizontal branch stars but at some pre - blue - horizontal - branch stage . such stars may have experienced at least one orbital period , and many of them should be returning to the galactic center or their orbits should have been significantly bent by the asymmetric galactic potential ( fig . [ fig : alphat ] ) . this scenario appear unlikely since it does not agree with the observed positive radial velocities . it is interesting at this stage to provide an example of a statistical estimate of halo triaxiality from a mock sample . let us assign a measurement error of @xmath172 ( @xmath173 ) to the one - dimensional velocities of all stars in figure [ fig : mapjn](a ) having @xmath140 , @xmath155 , and @xmath174 ( our error analysis assumes that the distances to hvss are known to within ten percent ) . we have simulated the observed velocities of such a sample , and plot in the top panel of figure [ fig : texample ] the values of @xmath49 and @xmath175 derived for each hvs . using equations ( [ eq : tbar ] ) and ( [ eq : terror ] ) , we obtain @xmath176 and @xmath177 . for @xmath178 , we obtain @xmath176 and @xmath179 . these errors are comparable with the systematic error caused by the flattened disk ( see the slight offset of dots from the solid line in fig . [ fig : mapjn]a ) . we have tried different values of the gravitational potential parameters @xmath180 in the calculations , and found that the estimated value of @xmath181 is always consistent with the assumed halo triaxiality ( see middle and bottom panels in fig . [ fig : texample ] ) . , @xmath155 , and @xmath182 . an observational error of @xmath183 is assumed for in `` measured '' one - dimensional velocity . from top to bottom , the values of @xmath180 used in the calculations are ( 0.8 , 0.7 ) , ( 0.8 , 0.6 ) , and ( 0.8 , 0.75 ) , corresponding to a triaxiality @xmath46=0.54 , 0.32 , and 0.72 , respectively ( _ horizontal lines _ ) . a statistical analysis of the sample using eqs . ( [ eq : tbar ] ) and ( [ eq : terror ] ) yields @xmath184=(0.50 , 0.02 ) , ( 0.31 , 0.01 ) , and ( 0.64 , 0.02 ) , respectively . for clarity , only 1/3 of the sample points are drawn in the figure . ] of the simulated sample ( top panel in fig . [ fig : texample ] ) in different reference frames as a function of @xmath185 . here @xmath54 is the angle measured counter - clockwise from a reference direction ( e.g. the line from the galactic center to the sun ) to the @xmath55-axis of the halo potential , and @xmath57 is the angle formed by the observational frame with the reference direction . the variance has a minimum at @xmath186 . ] if the @xmath55-axis of the halo potential form an angle @xmath54 ( measured counter - clockwise ) with the reference axis of the observations , then ( as seen from fig . [ fig : variance ] ) the minimum variance of @xmath187 in a set of simulated samples each in a frame at angle @xmath57 from the observational reference axis ( see eq . [ eq : variance ] ) occurs for @xmath188 . our calculations show that an error of @xmath130 in the estimate of @xmath54 may cause an error of 2% in the estimate of @xmath181 . note that the axis ratios @xmath180 of the halo potential are degenerate in the defined triaxiality parameter ( eq . [ eq : tdef ] ) . after determining @xmath46 , the values of @xmath180 could be also obtained by using any value of @xmath189 ( e.g. , see fig . [ fig : mapjn]b ) , but the modeling would be sensitive to halo mass and the shape of halo potential used ( see also the determination of axis ratios in @xcite by tracing back hvs orbits ) . finally , it is possible that a few hvss in the halo may be produced by the interactions of stars with an imbh in satellite galaxies like the large magellanic cloud @xcite , and that these would contaminate the sample ejected from the galactic center . the ejection rates from the satellite dwarfs of the mw are expected to be much smaller than the rate from sgr a@xmath10 , however . such `` satellite '' hvss will also have much larger angular momenta in the galactocentric rest - frame , and should be easily distinguishable from the galactic center sample . we have benefited from discussions with francesco haardt , youjun lu , and scott tremaine . we thank alberto sesana for providing the initial velocity and spatial distributions of hvss ejected from a black hole binary . p.m. acknowledges financial support from nasa through grants nag5 - 11513 and nng04gk85 g , and from the alexander von humboldt foundation . q.y . acknowledges initial support from nasa through hubble fellowship grant hst - hf-01169.01-a awarded by the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , for nasa , under contract nas 5 - 26555 . |
i present generalized formulas for approximate corrections to qcd hard - scattering cross sections through second order in the perturbative expansion . the approximate results are based on recent two - loop calculations for soft and collinear emission near threshold and are illustrated by several applications to strong - interaction processes in hadron colliders . | i | 1109.1578 | i present generalized formulas for approximate corrections to qcd hard - scattering cross sections through second order in the perturbative expansion . the approximate results are based on recent two - loop calculations for soft and collinear emission near threshold and are illustrated by several applications to strong - interaction processes in hadron colliders . | higher - order perturbative qcd corrections are necessary to produce reliable estimates of theoretical cross sections and reduce theoretical uncertainties for hard - scattering processes . collinear and soft - gluon corrections are an important subset of the qcd corrections and they can be significant for many processes , particularly near partonic threshold . the soft and collinear corrections can be derived from factorization theorems and resummation formalisms and they require loop calculations in the eikonal approximation . in this proceedings i discuss resummation , recent calculations of soft anomalous dimensions through two loops for a number of processes , and i present master formulas for nnlo expansions of the resummed cross section . collinear and soft - gluon corrections have been calculated for many processes and i present some explicit applications to top quark and electroweak boson production . in section 2 the resummation formalism is described and expressions for the resummed cross section are presented , including two - loop expressions for some universal functions in the resummation . in section 3 we use the expansion of the resummed cross section to derive master formulas for the approximate nlo and nnlo corrections . in section 4 we describe in general the calculation of soft anomalous dimensions , and in particular the massive cusp anomalous dimension . in section 5 we present results for the soft anomalous dimension matrices for top - antitop production , in section 6 for @xmath0-channel single top quark production , in section 7 for @xmath1-channel single top quark production , in section 8 for the associated production of a top quark with a @xmath2 boson ( or a charged higgs ) , and in section 9 for electroweak boson ( @xmath2 , @xmath3 , @xmath4 ) production at large transverse momentum . |
if spacetime contains large compact extra dimensions , the fundamental mass scale of nature , @xmath0 , may be close to the weak scale , allowing gravitational physics to significantly modify electroweak symmetry breaking . operators of the form @xmath1 and @xmath2 , where @xmath3 and @xmath4 are the @xmath5 and @xmath6 field strengths and @xmath7 is the higgs field , remove the precision electroweak bound on the higgs boson mass for values of @xmath0 in a wide range : @xmath8 . within this framework , there is no preference between a light higgs boson , a heavy higgs boson , or a non - linearly realized @xmath9 symmetry beneath @xmath0 . if there is a higgs doublet , then operators of the form @xmath10 , where @xmath11 and @xmath12 are the qcd and electromagnetic field strengths , modify the production of the higgs boson by gluon - gluon fusion , and the decay of the higgs boson to @xmath13 , respectively . at run ii of the tevatron collider , furthermore , such a signal would point to gravitational physics , rather than to new conventional gauge theories at @xmath0 . _ /#1/ |#1 # 1#1 ucb pth99/13 + lbnl43085 + hep - ph/9904236 + april 1999 + * electroweak symmetry breaking and large extra dimensions * + 0.5 cm _ department of physics + university of california + berkeley , ca 94530 , usa + and + theory group + lawrence berkeley national laboratory + berkeley , ca 94530 , usa + _ .5 cm | i | hep-ph9904236 | if spacetime contains large compact extra dimensions , the fundamental mass scale of nature , @xmath0 , may be close to the weak scale , allowing gravitational physics to significantly modify electroweak symmetry breaking . operators of the form @xmath1 and @xmath2 , where @xmath3 and @xmath4 are the @xmath5 and @xmath6 field strengths and @xmath7 is the higgs field , remove the precision electroweak bound on the higgs boson mass for values of @xmath0 in a wide range : @xmath8 . within this framework , there is no preference between a light higgs boson , a heavy higgs boson , or a non - linearly realized @xmath9 symmetry beneath @xmath0 . if there is a higgs doublet , then operators of the form @xmath10 , where @xmath11 and @xmath12 are the qcd and electromagnetic field strengths , modify the production of the higgs boson by gluon - gluon fusion , and the decay of the higgs boson to @xmath13 , respectively . at run ii of the tevatron collider , a @xmath13 signal for extra dimensions will be discovered if @xmath0 is below 2.5 ( 1 ) tev for a higgs boson of mass 100 ( 300 ) gev . furthermore , such a signal would point to gravitational physics , rather than to new conventional gauge theories at @xmath0 . the discovery potential of the lhc depends sensitively on whether the gravitational amplitudes interfere constructively or destructively with the standard model amplitudes , and ranges from @xmath14 3 10 ( 2 4 ) tev for a light ( heavy ) higgs boson . @=11 caption#1[#2]#3 @=12 .7ex .7ex gev mev ev kev tev m_z m_pl ^-1 ^-1 # 1#2#3nucl . phys . * b#1 * ( 19#2 ) # 3 # 1#2#3phys . lett . * b#1 * ( 19#2 ) # 3 # 1#2#3phys . lett . * # 1b * ( 19#2 ) # 3 # 1#2#3phys . rev . * d#1 * ( 19#2 ) # 3 # 1#2#3phys . rev . lett . * # 1 * ( 19#2 ) # 3 # 1#2#3phys . rep . * # 1 * ( 19#2 ) # 3 # 1#2#3ann . rev . . astrophys . * # 1 * ( 19#2 ) # 3 # 1#2#3ann . rev . nucl . part . sci . * # 1 * ( 19#2 ) # 3 # 1#2#3mod . . lett . * # 1 * ( 19#2 ) # 3 # 1#2#3zeit . fr physik * c#1 * ( 19#2 ) # 3 # 1#2#3ap . j. * # 1 * ( 19#2 ) # 3 # 1#2#3ann . phys . * # 1 * ( 19#2 ) # 3 # 1#2#3rev . mod . phys . * # 1 * ( 19#2 ) # 3 # 1#2#3comm . math . phys . * # 1 * ( 19#2 ) # 3 _ i.e. _ _ et al . _ _ e.g. _ _ etc . _ _ c.f . _ /#1/ |#1 # 1#1 ucb pth99/13 + lbnl43085 + hep - ph/9904236 + april 1999 + * electroweak symmetry breaking and large extra dimensions * + 0.5 cm _ department of physics + university of california + berkeley , ca 94530 , usa + and + theory group + lawrence berkeley national laboratory + berkeley , ca 94530 , usa + _ .5 cm | the conventional framework for particle physics beyond the standard model ( sm ) assumes that the fundamental mass scale of nature is the planck mass : @xmath15 gev . it is then natural to ask : why are the masses of the elementary particles so small ? proposed solutions to this hierarchy problem have a common feature : new non - perturbative gauge interactions dynamically generate a much lower scale , @xmath16 , from which electroweak symmetry breaking is generated , and hence all the masses of the known elementary particles . schematically , this mass hierarchy is @xmath17 in supersymmetric theories , @xmath16 is the scale at which supersymmetry is broken , and the triggering of electroweak symmetry breaking may be mediated , for example , by gravitational - scale physics , or by gauge interactions at much lower energy scales . alternatively , @xmath16 may be the scale of a new gauge force , technicolor , which forms fermion condensates that directly break @xmath9 . finally , new strong gauge forces could bind a composite higgs boson . recently an alternative framework has been proposed @xcite in which spacetime is enlarged to contain large extra compact spatial dimensions . at distances smaller than the size of these extra dimensions the gravitational force varies more rapidly than the inverse square law , so that the fundamental mass scale of gravity can be made much smaller than @xmath18 . the conventional mass hierarchy of ( [ eq : masshier ] ) is completely avoided if this fundamental mass scale is of order the weak scale . in this case , the length scale of the extra dimensions is much larger than the scales probed experimentally at colliders , and hence this framework requires that the quarks , leptons and gauge quanta of the sm are spatially confined to a @xmath19 dimensional sub - space of the enlarged spacetime . the physics at the fundamental scale , @xmath0 , which may well be that of string theory , will be directly accessible to colliders of sufficiently high energy ; but even at lower energies this physics may be experimentally probed . at energies below the fundamental mass scale , physics is described by an effective lagrangian , which we take to be the most general set of @xmath20 invariant operators involving quark , lepton and higgs doublet fields of the sm : _ eff = _ sm + _ i c_i ^p _ i^4+p [ eq : leff ] where @xmath21 is the sm lagrangian , @xmath22 runs over all gauge invariant operators , @xmath23 , of dimension @xmath24 with @xmath25 , and @xmath26 are unknown dimensionless couplings . in this letter we study consequences of several of the dimension-6 operators . first we derive bounds on the @xmath27 from existing experimental results under very conservative assumptions about flavor - breaking in the ultraviolet theory . we then re - examine the precision electroweak bounds on the higgs boson mass . analyses within the standard model find a light higgs ; however , we will show that such results do not survive the addition of non - renormalizable operators , even if those operators are suppressed by scales as large as @xmath28 . in theories with large extra dimensions there is no good argument for a light higgs over a heavy higgs or a non - linearly realized @xmath29 symmetry , in which case ( [ eq : leff ] ) must be replaced by a chiral lagrangian . finally we examine two operators in particular and their effects on the discovery of higgs bosons : _ g & = & ^ g^a_g^a [ eq : hop1 ] + _ & = & ^ f_f^ [ eq : hop2 ] where @xmath30 and @xmath31 are the qcd and electromagnetic field strengths , and @xmath7 is the higgs doublet with re@xmath32 . the first operator contributes to higgs production at hadron colliders via gluon - gluon fusion , and the second to higgs decay to @xmath13 . there are two reasons why these effects provide a significant discovery potential for extra dimensions : first , they are competing against a sm signal which is suppressed by loop factors , and second , the sm @xmath33 is further suppressed by @xmath34 , where @xmath35 is the electromagnetic coupling constant . however we assume that the physics at scale @xmath0 which generates ( [ eq : hop1])([eq : hop2 ] ) , does so in a way that the coefficients are not suppressed by powers of the sm gauge coupling constants ( see also @xcite ) . such a behavior is certainly _ not _ expected if the theory at @xmath0 is a 4-dimensional gauge field theory : in that case operators of the form ( [ eq : hop1])([eq : hop2 ] ) would arise by integrating out heavy fields , but these fields must couple to @xmath12 and @xmath11 with the usual sm gauge couplings , and further , as shown in @xmath36 , they must be also be loop - suppressed . thus even if the gauge theory at @xmath0 were strongly - coupled , it seems unlikely that coefficients of @xmath37 could be generated . this is very important the effect of the interaction @xmath38 on the @xmath39 branching ratio has been studied , and is small for @xmath40 @xcite . thus observation of the physics we will describe in section [ sec : expt ] would provide support for an extra - dimensional theory . |
igrj18483 - 0311 was discovered with in 2003 and later classified as a supergiant fast x - ray transient . it was observed in outburst many times , but its quiescent state is still poorly known . here we present the results of , , and observations of 18483 . these data improved the x - ray position of the source , and provided new information on the timing and spectral properties of 18483 in quiescence . | i | 0905.4866 | igrj18483 - 0311 was discovered with in 2003 and later classified as a supergiant fast x - ray transient . it was observed in outburst many times , but its quiescent state is still poorly known . here we present the results of , , and observations of 18483 . these data improved the x - ray position of the source , and provided new information on the timing and spectral properties of 18483 in quiescence . we report the detection of pulsations in the quiescent x - ray emission of this source , and give for the first time a measurement of the spin - period derivative of this source . in 18483 the measured spin - period derivative of -(1.3@xmath00.3)@xmath110@xmath2 s s@xmath3 likely results from light travel time effects in the binary . we compare the most recent observational results of 18483 and 18 , the two supergiant fast x - ray transients for which a similar orbital period has been measured . x - rays : binaries - stars : individual ( 18483 , 18 ) -stars : neutron - x - rays : stars | 18483 was discovered in 2003 during deep observations of the galactic center @xcite . the mean source x - ray flux was @xmath410 mcrab in the 15 - 40 kev , and @xmath45 mcrab in the 40 - 100 kev band @xcite . the 18.5 days orbital period of the system was discovered by @xcite using _ rxte _ archival data , and was later confirmed with @xcite . data also showed that 18483 usually undergoes relatively long outbursts ( @xmath43 days ) that comprise several fast flares with typical timescales of a few hours . during these bright events , the broad band ( 3 - 50 kev ) spectrum is best fit by an absorbed cutoff power law model ( photon index @xmath5=1.4 , cut - off energy @xmath6=22 kev , and absorption column density @xmath7=9@xmath110@xmath8 @xmath9 ) . @xcite further detected a periodicity at 21.0526@xmath00.0005 s in the data , and interpreted it as the spin - period of the neutron star ( ns ) hosted in 18483 . the measured pulse fraction in the 4 - 20 kev energy band was 48@xmath07%=(@xmath10-@xmath11)/(@xmath10+@xmath11 ) , where @xmath10 and @xmath11 are the measured count rates at the maximum and at the minimum of the folded light curve , respectively . ] . /xrt observations in 2006 detected the source at a flux level of 4.2@xmath110@xmath12 erg/@xmath13/s and provided a source position of @xmath14=18@xmath1548@xmath1617@xmath1717 and @xmath18=-3@xmath1910@xmath2015@xmath2154 ( estimated accuracy 3@xmath213 , * ? ? ? this allowed @xcite to identify the optical counterpart of the x - ray source , a b0.5ia star at a distance of 3 - 4 kpc , and to estimate its mass and radius ( @xmath22=33 @xmath23 and @xmath24=33.8 @xmath25 , respectively ) . these authors also suggested that an eccentricity 0.43@xmath26@xmath27@xmath260.68 could explain the 3-day duration of the outbursts ( as reported by * ? ? ? * ) . based on these results , it was concluded that 18483 most likely belongs to the class of supergiant fast x - ray transients ( sfxts , * ? ? ? * ; * ? ? ? * ; * ? ? ? however , due to the longer duration of its outbursts ( a few days as opposed to a few hours ) and a factor of @xmath410 lower luminosity swings between outburst and quiescence , @xcite classified 18483 as an `` intermediate '' sfxt , rather than a standard sfxt ( see * ? ? ? * for the definition of standard and intermediate sfxts ) . in this paper we analyze a 18 ks observation of 18483 in quiescence , and report the results of the spectral and timing analysis of this observation . we found that the pulse fraction of the source x - ray emission decreased significantly with respect to that measured while the source was in outburst , and provide for the first time an estimate of the spin - period derivative of this source . we also analyzed all the available /xrt observations of 18483 , and studied the orbital variations of the source x - ray flux . a 1 ks observation is also analyzed and provided an improved position of the x - ray source . the results from this study are then compared with those obtained recently on 18 , the other sfxt with a similar orbital period to that of 18483 . so far , the orbital period has been measured with certainty only in other two sfxts , i.e. igrj16479 - 4514 ( 3.3194 d * ? ? ? * ) , and igrj11215 - 5952 @xcite . |
we report the detection of pulsations in the quiescent x - ray emission of this source , and give for the first time a measurement of the spin - period derivative of this source . in 18483 the measured spin - period derivative of -(1.3@xmath00.3)@xmath110@xmath2 s s@xmath3 likely results from light travel time effects in the binary . we compare the most recent observational results of 18483 and 18 , the two supergiant fast x - ray transients for which a similar orbital period has been measured . | c | 0905.4866 | igrj18483 - 0311 was discovered with in 2003 and later classified as a supergiant fast x - ray transient . it was observed in outburst many times , but its quiescent state is still poorly known . here we present the results of , , and observations of 18483 . these data improved the x - ray position of the source , and provided new information on the timing and spectral properties of 18483 in quiescence . we report the detection of pulsations in the quiescent x - ray emission of this source , and give for the first time a measurement of the spin - period derivative of this source . in 18483 the measured spin - period derivative of -(1.3@xmath00.3)@xmath110@xmath2 s s@xmath3 likely results from light travel time effects in the binary . we compare the most recent observational results of 18483 and 18 , the two supergiant fast x - ray transients for which a similar orbital period has been measured . x - rays : binaries - stars : individual ( 18483 , 18 ) -stars : neutron - x - rays : stars | in this paper we reported on all available quiescent observations of 18483 , one of the two sfxts for which the spin and orbital periods have been measured with certainty ( the other is igrj11215 - 5952 with @xmath34=186.78 s , but see sect . [ sec : intro ] ) . we report the detection of pulsations in the quiescent x - ray emission of this source , and give for the first time a measurement of its spin - period derivative . to our knowledge , the spin - period has so far been detected unambiguously in two other sfxts ( @xmath34=228 s , and 4.7 s in igrj16465 - 4507 and igrj1841.0 - 0536 , respectively ; * ? ? ? * ; * ? ? ? * ) ; however , the orbital period of these sources is not known . on the contrary , in the case of 18 the orbital period is known , but the spin - period remains to be discovered . recently it has been suggested that a measurement of the ns spin and orbital periods can be the key to distinguish between different models proposed for sfxt sources @xcite . in fact , all these models involve a ns accreting from the intense wind of its supergiant companion , but several different mechanisms have been invoked in order to explain the very large luminosity swings observed during their transitions between outburst and quiescence @xcite . in particular , @xcite suggested that , if very slow spinning nss ( @xmath34@xmath701000 s ) in relatively close orbits ( few tens of days ) are hosted in sfxts , then a magnetic gating mechanism can be invoked in order to explain such luminosity swings . in this case the ns magnetic field would be in the `` magnetar '' range ( i.e. @xmath7010@xmath71 - 10@xmath72 g ; * ? ? ? on the contrary , faster spin - periods might indicate that the large luminosity swings of sfxts are caused by a centrifugal rather than a magnetic gating ( a similar mechanism was suggested to explain the pronounced activity of be x - ray pulsar transient systems ; * ? ? ? * ) . alternatively , the observed variations in the x - ray luminosity of sfxts might also be caused by drastic changes in the mass accretion rate onto the ns due to an extremely clumpy wind or to large scale structure in the immediate surroundings of the supergiant companion . in these models , the orbital periods may be as high as hundreds of days ( see in particular * ? ? ? * ; * ? ? ? * ) . in 2008 , an observation of igrj16479 - 4514 revealed that also eclipse - like events can contribute to the luminosity swings observed in sfxts @xcite . therefore , besides a measurement of the ns spin and orbital period , also an in - depth monitoring of the x - ray flux and spectral changes at different orbital phases is required in order to distinguish between different models or scenarios for sfxt sources . to this aim , we presented in table [ tab : comparison ] an analysis of the orbital changes in the x - ray flux observed from 18483 and 18 , the only two sfxts with a comparable orbital period . in the case of 18483 only few observations have been carried out in quiescence and thus the orbital monitoring of this source is far from being complete ( following * ? ? ? * we measured the source phases from the epoch of the brightest outburst observed with at 53844.2 mjd ) . the lowest flux state of this source was caught by /xrt at phase 0.13 , i.e. relatively close to the orbital phase where the highest x - ray activity of the source has been observed in several occasions . unfortunately , the poor statistics of this /xrt observation prevented an accurate spectral analysis , and thus we could not investigate the origin of this low flux state . in the other two /xrt observations a spectral analysis could be carried out , but we did not detect any indication of a significant spectral variation . only in the observation we measured a slight increase in the spectral power law index . this suggests that x - ray flux changes in 18483 might have occurred due to genuine variations in the mass accretion rate onto the ns , rather than eclipse - like events . note that , the detection of pulsations in the data are also in agreement with the accretion scenario . this suggests that sfxts undergo low level accretion even when they are not in outburst ( see also * ? ? ? at odds with the case of 18483 , table [ tab : comparison ] shows that the different orbital phases of 18 have been fairly well monitored . unfortunately , the x - ray spectrum of this source could be well characterized only during the outburst , whereas in quiescence only the observation provided a measurement of the spectral parameters ( see table [ tab : log ] ) . in all the other observations only a rough estimate of the source flux could be obtained . note that the source was not detected by at the orbital phase 0.52 , and the 3@xmath33 upper limit on the source x - ray flux was at least an order of magnitude lower than the fluxes measured in any other orbital phases . since no spectral analysis could be carried out on 18 at this orbital phase , the origin of this low flux event could not be investigated further . in case future observations of 18 reveal that this source regularly undergoes x - ray eclipses at the orbital phase @xmath40.5 , this can help clarifying the issue of the extreme flux changes in this source . more observations of 18483 and 18 at different orbital phases with high sensitivity x - ray telescopes , like and , are clearly required in order to understand unambiguously the origin of their outburst / quiescent activity . being these two sources the only sfxts with a comparable orbital period , they are very well suited to test different models proposed to explain the behavior of sfxts . we are currently investigating the results of the application of the gated accretion model to 18483 and 18 ( bozzo et al . , 2009 , in preparation ) . in this paper , besides x - ray flux changes , we also measured a spin - period variation in 18483 . by using our best - determined spin - period , @xmath34=21.033@xmath00.004 s , and that found previously by @xcite , we obtained a spin - period derivative in 18483 of @xmath73=-(1.3@xmath00.3)@xmath110@xmath2 s s@xmath3 . this value is comparable with the spin - period derivative measured in the case of the sfxt axj1841.0 - 0535 ( -1.5@xmath110@xmath57 s / s * ? ? ? * ) and those induced by accretion torques in wind - fed binaries ( see e.g. , * ? ? ? * ) . however , in the present case we believe that the spin - period derivative most likely results from light travel time effects in the binary . in fact , in a binary system with an orbital period of @xmath418.5 days , these effects can contribute to an apparent spin - period derivative of the order of @xmath4@xmath74/@xmath75=8.6@xmath110@xmath76 s s@xmath3 , i.e. much larger than the spin - period derivative we reported above ( here @xmath74 is the orbital velocity and @xmath75 is the light velocity ; we used the mass and radius of the supergiant companion measured by * ? ? ? unfortunately , since a detailed orbital solution for this source is not yet available , we do not know if accretion torques acting onto the ns in 18483 might also have contributed to the observed spin - period derivative . note that , in principle , this can be used to study the interaction between the ns and the inflowing matter from the supergiant companion ( see e.g. * ? ? ? an orbital monitoring of 18483 is required in order to understand the origin of the measured spin - period derivative . |
in 1982 , marshall p. tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [ _ proc . 14th symp . on naval hydrodynamics _ , 1982 , pp.1951 ] . several new and puzzling issues were highlighted by tulin , notably the existence of weak and strong wave - making regimes , and the paradoxical fact that the theory seemed to be applicable to flows at low speeds , _ but not too low speeds"_. these important issues were left unanswered , and despite the novelty of the ideas , tulin s report fell into relative obscurity . now thirty years later , we will revive tulin s observations , and explain how an asymptotically consistent framework allows us to address these concerns . most notably , we will explain , using the asymptotic method of steepest descents , how the production of free - surface waves can be related to the arrangement of integration contours connected to the shape of the moving body . this approach provides an intuitive and visual procedure for studying nonlinear wave - body interactions . | i | 1510.06014 | in 1982 , marshall p. tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [ _ proc . 14th symp . on naval hydrodynamics _ , 1982 , pp.1951 ] . several new and puzzling issues were highlighted by tulin , notably the existence of weak and strong wave - making regimes , and the paradoxical fact that the theory seemed to be applicable to flows at low speeds , _ but not too low speeds"_. these important issues were left unanswered , and despite the novelty of the ideas , tulin s report fell into relative obscurity . now thirty years later , we will revive tulin s observations , and explain how an asymptotically consistent framework allows us to address these concerns . most notably , we will explain , using the asymptotic method of steepest descents , how the production of free - surface waves can be related to the arrangement of integration contours connected to the shape of the moving body . this approach provides an intuitive and visual procedure for studying nonlinear wave - body interactions . surface gravity waves , wave - structure interactions , waves / free - surface flows | the motivation for this paper stems from an important , but seemingly forgotten 1982 report by prof . marshall p. tulin presented during the @xmath0 symposium on naval hydrodynamics , titled _ an exact theory of gravity wave generation by moving bodies , its approximation and its implications _ some thirty years after its publication , tulin wrote of his original motivation for pursuing the former study : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ what were the relations and connections among these various nonlinear approximations ray , slow ship , " , second order , formal straining , and guilloton that had arisen by the end of the 1970s ? [ ... ] i had earlier in the 1970s become intrigued by the davies transformation of the nonlinear free - surface problem , which was revealed in milne - thompson s legendary banquet speech [ in 1956 ] . my hope was that my extension of the davies theory would provide an exact result in analytical form , which even in its complexity could then be subject to various approximations , the connections of which could thereby be discerned . and so it turned out . _ @xcite _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ in the 1982 paper , tulin sought to derive a rigorous mathematical reduction of the water wave equations in such a way that certain nonlinear contributions within the free surface equations could be preserved . the resultant model was analytically simple , and took the form of a single complex - valued linear differential equation . the theory was also powerful , and provided a formulation that could relate the geometry of a moving body directly with the resultant free - surface waves . however , several important and surprising issues were raised by tulin regarding the model and its interpretation , and in particular , he had noted a paradoxical behaviour of the model at low speeds . in the years that followed , perhaps owing to the difficulty of the model s derivation , tulin s fundamental questions were never re - addressed . in this paper , we shall present an asymptotically consistent derivation that corrects tulin s model , and puts to rest many of the issues previously highlighted . more specifically , we shall present an explicit solution written in terms of a single integral that properly describes the form of water waves produced by two - dimensional moving bodies at low speeds . then , by applying the asymptotic method of steepest descents , we are able to observe how the production of free - surface waves will change depending on the deformation of integration contours connected to the geometry of the moving body . this approach provides an intuitive and visual procedure for studying wave - body interactions . the essential derivation behind tulin s model begins from bernoulli s equation applied to a free surface with streamline , @xmath1 , @xmath2 where @xmath3 is the fluid speed , @xmath4 the streamline angle , @xmath5 the potential , and the non - dimensional parameter @xmath6 is the square of the froude number for upstream speed @xmath7 , gravity @xmath8 , and length scale @xmath9 . if the sinusoidal term is split according to the identity @xmath10 then can be written in complex - valued form @xmath11 where @xmath12 is an analytic function of the complex potential , @xmath13 , and the above is evaluated on @xmath1 where @xmath14 . the rather curious substitution of is attributed to @xcite , who had argued that if @xmath15 is considered to be small , then yields a linearized version of bernoulli s equation ( in @xmath16 ) that preserves the essential nonlinearity ( in @xmath17 ) describing the structure of steep gravity waves . inspired by this idea , tulin considered the extension to general free surface flows over a moving body . since the function in the curly braces of is an analytic function in @xmath18 , except at isolated points in the complex plane , then analytic continuation implies @xmath19 where by matching to uniform flow , @xmath20 and thus @xmath21 as @xmath22 . the function @xmath23 is purely imaginary on @xmath1 . in the case of flow without a body or bottom boundary , @xmath24 , but otherwise , @xmath25 will encode the effect of the obstructions through its singular behaviour in the complex plane . if the nonlinear contribution , @xmath15 , is neglected in , then the exact solution can be written as @xmath26{\mathrm{e}}^{-\frac{1}{{\epsilon } } \int^w { \mathcal{q}}(s ) \ , { \operatorname{d\!}{}}{s}}.\ ] ] this process seems to yield the exponentially small surface waves at low speeds . however , tulin noted that as @xmath27 , there would be locations on the free surface where @xmath28 , and this would lead to unbounded steepness . he wrote of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the revelation that for sufficiently strong disturbances waves arise at discrete points on the free surface which do not become exponentially small with decreasing froude number , but rather tend to unbounded steepness as @xmath29_. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ he thus proposed the following result : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ [ tulinquote ] _ the most important comment to make is that for given @xmath30 , no matter how small , this so - called low speed theory is not valid for sufficiently low speeds . it is a theory valid for low , but not too low speeds ! _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ the matter was left at that , and in the three decades following tulin s ingenious paper , the peculiarities surrounding the asymptotic breakdown of were never directly re - addressed ( though we mention the paper by @xcite which develops numerical solutions for the case @xmath31 and @xmath32 ) . note that in addition to the investigation in the limit @xmath27 , tulin had also intended to produce an _ exact _ reduction , where the @xmath15 term in was handled through a theoretically posited nonlinear coordinate transformation . however , it is never clear how this transformation is used or derived in practice , except through nonlinear computation of the full solutions . independently from tulin , e.o . tuck later presented a series of papers @xcite where he attempted to distill the wave - making properties of wave - body problems into a linear singular equation . the equation presented [ eqn ( 22 ) of @xcite ] was @xmath33 where @xmath34 is the height of the free surface , @xmath35 is a function related to the moving body , and @xmath36 is a integral operator known as the hilbert transform ( to be introduced in [ sec : form ] ) . the difficulty in solving is that the hilbert transform is a _ global _ operator , requiring values of @xmath37 over the entire domain . in the @xcite work , tuck explained how the action of @xmath36 could be viewed as similar to that of the differential operator @xmath38 . this reduction was mostly pedagogic in nature , but tuck was motivated by the fact that @xmath36 and the differential operator will act similarly in the case of sinusoidal functions . he went on to study the various properties of the singular differential equation @xmath39 that depend on the specification of the ` body ' given by @xmath35 . apparently , tuck had been unaware of tulin s ( @xcite ) work , but a chance meeting of the two occured during a conference leading to the publication of @xcite . we are fortunate enough to possess the archived questions of the meeting , where we discover that tulin had asked the following question : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ is nt it true that the two dimensional wavemaker problem can be presented in terms of an ordinary differential equation in the complex domain , at least to some higher order of approximation ? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ tuck replied that he was unsure of the generality of the reduction to problems including different geometries , but noted the connection to the @xcite reduction : _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ i do not know the answer to this question ... my f(x ) " in some way represents a very general family of wavemakers " , with structure in both spatial dimensions , and i have doubts as to whether the problem can then be converted ( exactly ) to a differential equation . on the other hand , a few years ago i in fact used the method that you describe , and it is associated with the approximation @xmath40 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ although tuck s toy reduction should only be regarded as illustrative ( the governing differential equation should rather be first order ) , what is apparent in his work is the desire to systematically reduce both the nonlinearity of bernoulli s equation , and the global effect of @xmath36 into a single ordinary differential equation . in particular , it is tuck s search for a reduction of the operator , @xmath36 , that was missing from earlier works on this topic ( including @xcite ) . certainly , tulin and tuck were not the only ones to seek simpler reductions or formulations of the nonlinear equations for wave - body interactions , and indeed , tulin relates his work to the integral models proposed by @xcite and @xcite . reviews of these and other models were presented by @xcite and @xcite , and many others . however , what distinguishes tulin and tuck s work is the shifted focus towards the analytic continuation of the flow problem into the complex domain ; indeed , tulin notes his strong motivation by the work of @xcite in his @xcite review . as we have noted in [ sec : subtulin ] , the low - froude or low speed limit of @xmath27 is the essential approximation in which analytical results can be derived . the subtleties of studying this singular limit can be traced back to a seminal report by @xcite , who detailed certain oddities with the previously developed analytical approximations of free surface flow past a submerged body . chief amongst such oddities was the fact that the individual terms of a series approximation in powers of @xmath30 would fail to predict surface waves . thus , one might decompose the surface speed into a regular series expansion and an error term , @xmath41 , with @xmath42 + { \bar{q}}.\ ] ] the challenge , ogilvie realized , was that water waves were exponentially small in @xmath30 , with @xmath43 , and thus _ beyond - all - orders _ of any individual term of the regular series . by linearizing about the zeroth order solution , @xmath44 for @xmath45 , and strategically perserving certain terms in bernoulli s equation , ogilvie developed a general analytical approximation for the exponentially small surface waves . the approximation , however , was not asymptotically consistent , and the search for a complete numerical and analytical treatment of the low froude limit would inspire many papers in the subsequent years . one of the key issues we will explore in this paper addresses the question of how many terms must be included in the linearization of in order to obtain the exponential . originally @xcite had chosen @xmath46 , but later revised to @xmath47 in @xcite ( who quoted the work of @xcite and in particular , the study by @xcite in applying the wkb method to streamline ship waves ) . cm _ historical significance _ & & _ papers _ + origin of the low - froude paradox & & @xcite + two - dimensional and three - dimensional linearizations & & @xcite , @xcite , @xcite , @xcite , @xcite , @xcite + on numerical solutions & & @xcite , @xcite , @xcite , @xcite + on exponential asymptotics applied to water waves & & @xcite , @xcite , @xcite , @xcite , @xcite + review articles & & @xcite , @xcite + we shall not pursue , in great detail , the history of the low froude problem that followed ogilvie s seminal report , but instead refer to the review papers by @xcite and , particularly , @xcite where certain aspects of the low froude difficulty are discussed . additional historical details are presented in 1 of @xcite , and a selection of papers on the problem is presented in table [ tab : res ] . the method we apply in this paper , which combines an approach of series truncation with the method of steepest descents , is unique from the previously listed works . we have three principal goals in this work . _ ( i ) we wish to demonstrate how tulin s formulation can be systematically derived and studied in the low speed limit . _ the source of tulin s puzzling results can be resolved through better understanding of two effects : first , the _ ad - hoc _ linearization of the nonlinear @xmath15 function ; and second , the role of the forcing function , @xmath23 . we clarify these details and demonstrate , through numerical solutions of the full nonlinear water wave equations , the convergence of different proposed models in the limit @xmath27 . let @xmath41 be the fluid speed corresponding to the water waves , as in . one of our principal results ( presented on p. ) is to demonstrate that the exponentially small waves , @xmath48 , are described to leading order by the first - order equation , @xmath49{\bar{q}}= r(w ; { \hat{{\mathscr{h}}}}[{\bar{\theta}}]),\ ] ] where @xmath50 and @xmath48 is then given by the sum of @xmath41 and its complex conjugate . different choices of the series truncation @xmath51 yield different versions of the right - hand side of , but only change the predicted wave amplitudes by a numerical factor . the leading order @xmath52 contains the prescription of the moving body , and can thus be related to tuck s @xmath53 function in . the formulation in terms of the speed , @xmath3 , rather than tulin s combined function @xmath54 in is more natural , but we will relate tulin s equation to our own in [ sec : tulinconnect ] and appendix [ sec : tulinconnect2 ] . _ ( ii ) we also study the associated integral form of the solution using the method of steepest descents . _ we shall demonstrate how the appearance of surface waves can be associated with sudden deformations of the integration contours if the solution to is analytically continued across critical curves ( stokes lines ) in the complex plane . this process is known as the stokes phenomenon @xcite . the novelty of this steepest descents methodology is that it will allow us to not only relate the surface waves directly to the geometry of the moving body , but it will also allow us to observe how integration contours change depending on the geometry of the obstruction . in particular , we conclude that provided there exists a solution of the full potential flow problem , there are no issues with the approximations as @xmath27 limit . _ ( iii ) our last goal is to provide a link between the tulin approximation , our corrected model , and also the current research on low - froude approximations . _ let us now turn to a brief summary of the history of the low froude problem . |
in a diquark - diquark - antiquark picture of pentaquarks , we use two interpolating currents to calculate the mass of the recently measured @xmath0 state in the framework of qcd sum rules . we show that , even though yielding similar values for @xmath1 ( and close to the experimental value ) , these currents differ from each other in what concerns the strength of the pole , convergence of the ope and sensitivity to the continuum threshold parameter . | i | hep-ph0406246 | in a diquark - diquark - antiquark picture of pentaquarks , we use two interpolating currents to calculate the mass of the recently measured @xmath0 state in the framework of qcd sum rules . we show that , even though yielding similar values for @xmath1 ( and close to the experimental value ) , these currents differ from each other in what concerns the strength of the pole , convergence of the ope and sensitivity to the continuum threshold parameter . | after the recent discovery of pentaquark states @xcite the central question to be addressed now concerns the structure of these new baryons . they could be : a ) uncorrelated quarks inside a bag @xcite ; b ) a @xmath2 molecule bound by a van - der waals force @xcite ; c ) a `` @xmath2 '' bound state in which @xmath3 and @xmath4 are not separately in color singlet states @xcite ; d ) a diquark - triquark @xmath5 bound state @xcite and e ) a diquark - diquark - antiquark ( dda ) state . this last one was advanced by jaffe and wilczek ( jw ) @xcite and is quite appealing because it can explain two unusual features of pentaquarks : their small mass and decay width . instantons generate strong attractive quark - quark interactions with the formation of low mass diquarks , which , in turn , lead to relatively low mass pentaquarks . this was verified in @xcite , @xcite and @xcite . moreover , in @xcite , it was shown that the dda configuration may lead to strongly suppressed transition amplitudes ( to meson - baryon states ) for a reasonable choice of its spatial wave function , namely , two separated extended diquark balls overlapping only partially and the antiquark at the center of the system . pentaquark configurations can be implemented in qcd sum rules ( qcdsr ) @xcite and in lattice qcd @xcite by a proper choice of the interpolating current . a current for configuration c ) has been proposed by zhu @xcite and for configuration e ) three different currents were proposed in @xcite , @xcite and @xcite . given the impulse of this field and the prospects of new measurements , we may expect that the `` pentaquark wave '' will last still for a long time . a great effort will be devoted to understand the structure of these objects . for the qcdsr community ( and for lattice qcd studies as well ) this means that more attention will have to be given to the properties of the interpolating currents . at this point , we can already compare the three calculations presented in @xcite , @xcite and @xcite for the mass of the @xmath6 . although they present different implementations of the dda scheme , they produce very similar results for the pentaquark mass . this indicates that a more careful analysis has to be performed . the purpose of the present work is twofold . we will use qcdsr to calculate the mass of the recently measured @xmath0 and we will also take the opportunity to perform a careful comparison of the results obtained with two different currents , which we will call i and ii . current i was introduced by us in @xcite and current ii is the one proposed in @xcite . as it will be seen , both currents give approximately the same mass for the @xmath0 but have different sensitivity to the continuum threshold parameter , different convergence of the operator product expansion ( ope ) and also different strength of the pole , with respect to the continuum . this comparative study , which will later be extended to the currents suggested in @xcite and also in @xcite , will give us a better understanding of these currents and may lead to the choice of the best current . |
in a previous paper ( avotina _ et al . _ phys . rev . b * 71 * , 115430 ( 2005 ) ) we have shown that in principle it is possible to image the defect positions below a metal surface by means of a scanning tunnelling microscope . the principle relies on the interference of electron waves scattered on the defects , which give rise to small but measurable conductance fluctuations . we demonstrate that the amplitude and period of the conductance oscillations are determined by the local geometry of the fermi surface . the signal results from those points for which the electron velocity is directed along the vector connecting the point contact to the defect . for a general fermi surface geometry the position of the maximum amplitude of the conductance oscillations is not found for the tip directly above the defect . we have determined optimal conditions for determination of defect positions in metals with closed and open fermi surfaces . | i | cond-mat0604344 | in a previous paper ( avotina _ et al . _ phys . rev . b * 71 * , 115430 ( 2005 ) ) we have shown that in principle it is possible to image the defect positions below a metal surface by means of a scanning tunnelling microscope . the principle relies on the interference of electron waves scattered on the defects , which give rise to small but measurable conductance fluctuations . whereas in that work the band structure was assumed to be free - electron like , here we investigate the effects of fermi surface anisotropy . we demonstrate that the amplitude and period of the conductance oscillations are determined by the local geometry of the fermi surface . the signal results from those points for which the electron velocity is directed along the vector connecting the point contact to the defect . for a general fermi surface geometry the position of the maximum amplitude of the conductance oscillations is not found for the tip directly above the defect . we have determined optimal conditions for determination of defect positions in metals with closed and open fermi surfaces . | the interference of electron waves scattered by single defects results in an oscillatory dependence of the point contact conductance @xmath0 on the applied voltage @xmath1 this effect originates from quantum interference between the principal wave that is directly transmitted through the contact and the partial wave that is scattered by the contact and the defect or several defects . such conductance oscillations have been observed in quantum point contacts @xcite and investigated theoretically in the papers ludoph , namir , avotina2,avotina3 . in our previous paper @xcite the oscillatory voltage dependence of the conductance of a tunnel point contact in the presence of a single point - like defect has been analyzed theoretically and it has been shown that this dependence can be used for the determination of defect positions below a metal surface by means of a scanning tunnelling microscope ( stm ) . in the model of a spherical fermi surface ( fs ) the amplitude of the conductance oscillations is maximal when the contact is placed directly above the defect . the oscillatory part of the conductance @xmath2 for this situation is proportional to @xmath3where @xmath4 the depth of the defect and @xmath5 and @xmath6 are the fermi wave vector and effective mass of the electrons @xcite . materials with an almost spherical fs are most suitable for this model . in most metals the dispersion relation for the charge carriers is a complicated anisotropic function of the momentum . this leads to anisotropy of the various kinetic characteristics @xcite . particularly , as shown in ref . kosevich , the current spreading may be strongly anisotropic in the vicinity of a point - contact . this effect influences the way the point - contact conductance depends on the position of the defect . for example , in the case of a au(111 ) surface the ` necks ' in the fs should cause a defect to be invisible when probed exactly from above . qualitatively , the wave function of electrons injected by a point contact for arbitrary fs @xmath7 has been analyzed by a. kosevich @xcite . he noted that at large distances from the contact the electron wave function for a certain direction @xmath8 is defined by those points on the fs for which the electron group velocity is parallel to @xmath9 unless the entire fs is convex there are several such points . the amplitude of the wave function depends on the gaussian curvature @xmath10 in these points , which can be convex @xmath11 or concave @xmath12 . the parts of the fs having different signs of curvature are separated by lines of @xmath13 ( inflection lines ) . in general there is a continuous set of electron wave vectors for which @xmath13 . the electron flux in the directions having zero gaussian curvature exceeds the flux in other directions @xcite . electron scattering by defects in metals with an arbitrary fs can be strongly anisotropic @xcite . generally , the wave function of the electrons scattered by the defect consists of several superimposed waves , which travel with different velocities . in the case of an open constant - energy surface there are directions along which the electrons can not move at all . scattering events along those directions occur only if the electron is transferred to a different sheet of the fs @xcite . in this paper we analyze the effect of anisotropy of the fs to the possibility of determination of the position of a defect below a metal surface by use of a stm . we show that the amplitude and the period of the conductance oscillations are defined by the local geometry of the fs , namely by those points for which the electron group velocity is directed along the radius vector from the contact to the defect . general formulas for the wave function and point contact conductance are obtained in sections ii and iii . in sec . iv the asymptotic forms of the wave function and the point contact conductance for large distances of the defect from the contact are found . the general results are illustrated for two specific models of the fs : an ellipsoid ( sec . v ) and a corrugated cylinder ( sec . vi ) . using these models , for which analytical dependencies of the conductance on voltage and defect position can be found , we describe the manifestation of common features of fs geometries to the conductance oscillations : anisotropy of a convex part ( ` bellies ' ) , changing of the curvature ( inflection lines ) and presence of open directions ( ` necks ' ) . |
in a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques . we present here significant improvements over this scheme . this makes our method very competitive for applications to _ ab - initio _ | i | 0809.2232 | in a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques . we present here significant improvements over this scheme . the original complex - valued formalism is turned into a purely real one . in addition , we use chebyshev polynomials expansion and fast summation techniques . this drastically reduces the scaling of the algorithm with the width of the hamiltonian spectrum , which is now of the order of the cubic root of such parameter . this makes our method very competitive for applications to _ ab - initio _ simulations , when high energy resolution is required . address = computational science , department of chemistry and applied biosciences , eth zurich , usi campus , via giuseppe buffi 13 , ch-6900 lugano , switzerland , , email=michele.ceriotti@phys.chem.ethz.ch address = computational science , department of chemistry and applied biosciences , eth zurich , usi campus , via giuseppe buffi 13 , ch-6900 lugano , switzerland address = computational science , department of chemistry and applied biosciences , eth zurich , usi campus , via giuseppe buffi 13 , ch-6900 lugano , switzerland | several fields of computational science ( nanotechnology , materials science or biochemistry just to name a few ) would greatly benefit from the possibility of performing simulations of large systems , containing hundreds of thousands of atoms . conventional electronic structure calculations require the diagonalization of matrices whose size @xmath0 is of the order of the number of electrons in the system . the @xmath1-scaling cost of this step greatly limits the range of systems which can be tackled by _ ab - initio _ techniques , despite the fast - paced progress in the computational power of modern processors . based on the theoretical foundations of the nearsightedness principle of electronic matter@xcite , several techniques have been developed in the last years to avoid the diagonalization step , by directly computing the density matrix of the system using linear scaling algorithms@xcite . one of the earliest approaches have been to compute the finite temperature density matrix , i.e. the fermi function of the system s hamiltonian , @xmath2 , by decomposing it into easier - to - compute functions of the hamiltonian@xcite , for instance chebyshev polynomials or rational functions . in a recent paper@xcite we have discussed an exact decomposition of the fermi operator which can be efficiently computed by a combination of polynomial expansion and iterative inversion techniques . in this way , we achieved an efficient scaling with @xmath3 , the width of the spectrum of the hamiltonian in units of @xmath4 . this makes the method attractive for applications to metals or low - band gap semiconductors at low electronic temperature . in this short paper we discuss a number of improvements to this scheme , which further lower the operation count , leading to a scaling @xmath5{\delta\epsilon}$ ] , which is , to the best of our knowledge , the lowest so far reported in literature . we will follow closely the scheme of our previous work@xcite , obtaining analytical estimates for the operation count of the different steps which compose our algorithm , so as to optimize them in order to achieve optimal performance . |
in ambient re - scatter communications , devices convey information by modulating and re - scattering the radio frequency signals impinging on their antennas . in this correspondence , we consider a system consisting of a modulated continuous carrier multiple - input multiple - output ( mimo ) link ( primary ) and a multi - antenna modulated re - scatter ( mrs ) node ( secondary ) , where the mrs node uses the signal generated by the primary transmitter . we also consider the impact of channel estimation errors under least squares channel estimation . | i | 1607.01284 | in ambient re - scatter communications , devices convey information by modulating and re - scattering the radio frequency signals impinging on their antennas . in this correspondence , we consider a system consisting of a modulated continuous carrier multiple - input multiple - output ( mimo ) link ( primary ) and a multi - antenna modulated re - scatter ( mrs ) node ( secondary ) , where the mrs node uses the signal generated by the primary transmitter . the receiver tries to decode both the original transmitted message and the information added by the mrs antennas . we show that the sum capacity of this system exceeds that , which the mimo system could achieve alone . we also consider the impact of channel estimation errors under least squares channel estimation . the results suggest that the estimation error has negative impact on the capacity , however , its severity can be minimised by increasing the number of receiver antennas . backscatter , re - scatter , bi - static channel , mimo , keyhole channel , modulation coding , polyphase coding . | of the limiting factors of connecting things to the internet using wireless technologies is the availability of energy . one solution is provided by the modulated back - scattering ( mbs ) systems , such as rfid , where the nodes ( tags ) modulate their information onto a carrier generated by a reader , and the reader decodes the modulated information . in the advanced forms of mbs systems , multiple - antenna techniques are applied to increase the capacity @xcite and improve the reliability @xcite . the communication range can be increased by allowing a carrier transmitter and a reader ( receiver ) to be physically separated , referred to as a bi - static mbs system @xcite . recently , a new communication technology is emerging based on the fact that the tags can re - scatter even modulated signals , often referred to as ambient mbs system @xcite . these systems enhance the use - case possibilities of mbs systems since the information is exchanged through modulating and back - scattering the rf signals without power hungry transceivers . in this correspondence , we propose a system that extends a bi - static mbs system to an ambient bi - static modulated re - scatter ( mrs ) system , which allows information transmission between a multi - antenna transmitter and a multi - antenna receiver ( primary mimo system ) . the multi - antenna mrs node ( secondary mrs system ) bear additional information on the signal emitted by the transmitter , and the receiver decodes the information of both sources as shown in fig . [ fig : channel ] . in the following sections , we provide a detailed analysis of the impact of different components on the capacity of the overall system , and a joint pilots design using hadamard matrix for channel estimation . for the system model defined in sec . [ sec : sysmod ] , we assume that the primary system uses a gaussian codebook and the secondary system uses a polyphase coding scheme . under these assumptions , in sec . [ sec : capacity_csi ] , we consider the case that the receiver has perfect channel state information ( csi ) . first , the joint capacity available for the two systems is derived . then , it is shown that the sum capacity is larger than that , which the primary system could achieve alone . the excess capacity of the system can be utilised by the primary system alone or it can be shared with the secondary system . we show that the limiting capacity of the overall system coincides with the sum of the limiting capacity of a rich scattering mimo channel @xcite and a multiple - keyhole channel @xcite . the capacity that the secondary could obtain in the case it has a single antenna is also derived . in sec . [ sec : capacity_est ] , we first propose a pilot structure that allows joint estimation of the primary and secondary channels , and then consider the impact of channel estimation error by deriving the sum capacity lower bound as a function of estimation errors . we present the simulation results in section [ sec : sim ] . section [ sec : con ] concludes this correspondence . |
in order to double the positron injection rate into the kekb ring , a two - bunch acceleration scheme has been studied at the linac , in which bunches separated by 96 ns are accelerated in 50 hz . in this scheme stabilization of the energy and orbit of each bunch is indispensable . since beam characteristics are acquired through beam - position monitors ( bpm ) , their read - out system was improved to meet two - bunch requirements . combined waveforms from bpm s these systems were successfully used in the test beams and will be employed during routine operation . | i | physics0111180 | in order to double the positron injection rate into the kekb ring , a two - bunch acceleration scheme has been studied at the linac , in which bunches separated by 96 ns are accelerated in 50 hz . in this scheme stabilization of the energy and orbit of each bunch is indispensable . thus , the beam energy and orbit feedback systems have been upgraded . since beam characteristics are acquired through beam - position monitors ( bpm ) , their read - out system was improved to meet two - bunch requirements . combined waveforms from bpm s were adjusted with delay cables avoiding overlaps so as to enable the simultaneous measurements of the beam positions of two bunches . the beam energies of two bunches were balanced by tuning the rf pulse timings , and the average energy was stabilized by adjusting the accelerating rf phases . the average beam orbits were also stabilized . slow feedback systems at the injector section for charge and bunching stabilities are being planned as well . these systems were successfully used in the test beams and will be employed during routine operation . | the electron / positron linac at kek injects 8-gev electron and 3.5-gev positron beams into kekb rings , where the cp - violation study is carried out . since the efficiency of the experiment can be increased by shortening the injection time , several mechanisms have been introduced to accomplish this@xcite . especially , much effort has been made to improve the positron injection time , since it is longer compared with that of electrons@xcite . one of such effort is a two - bunch acceleration plan , which has been studied and applied@xcite . in this scheme two bunches of positrons are accelerated in one rf pulse , which is 50 hz ; they may double the injection rate . the time space between two bunches , however , is restricted by the rf frequencies of the linac and the rings , and the smallest space is 96.29 ns , since the common frequency is 10.38 mhz . thus , a precise beam control and diagnosis are necessary . the beam diagnosis used so far has been made by employing strip - line - type beam - position monitors ( bpm ) , wire scanners for transverse profiles and streak cameras for longitudinal profiles . in order to maintain stable beams , it is essential to have the beam instrumentations work for both of the two bunches . the two - bunch read - out of bpms is especially important , because it is used in a number of orbit and energy feedback loops to stabilize the beams . |
@xmath0 of radar signals were collected . here we compare these initial measurements with the predictions of the esa master / proof99 model in order to assess the sensitivity as well as the reliability of the data . the absolute number of objects detected in the various altitude bins indicates that the coherent integration method indeed increases the detection sensitivity when compared to incoherent integration . in the data presented here integration times from @xmath1 to @xmath2 | c | astro-ph0301200 | in the effort to obtain low cost routine space debris observations in low earth orbit , esa plans to utilise the radar facilities of the european incoherent scatter scientific association . first demonstration measurements were performed from 11 to 23 february 2001 . in total @xmath0 of radar signals were collected . here we compare these initial measurements with the predictions of the esa master / proof99 model in order to assess the sensitivity as well as the reliability of the data . we find that while the determination of object size needs to be reviewed , the altitude distribution provides a good fit to the model prediction . the absolute number of objects detected in the various altitude bins indicates that the coherent integration method indeed increases the detection sensitivity when compared to incoherent integration . in the data presented here integration times from @xmath1 to @xmath2 were used . as expected , orbit information can not be obtained from the measurements if they are linked to ionospheric measurements as planned . in addition routine space debris observations provide also useful information for the validation of large - object catalogues . ( 0,0)(0,0 ) ( -50,180)pedas1-b1.4 - 0003 - 02 | the test campaign performed by sgo resulted in raw data on one large space debris object as well as in the size and altitude distribution of @xmath57 small space debris objects . the comparison with the esa master / proof99 model shows that the conversion from signal amplitudes to object sizes has to be reviewed . the more straight forward measurement of the objects altitude provides a distribution that is well in accord with the prediction by the model . as the model is regularly checked against results from other beam - park experiments , we can conclude that the demonstration measurements with the eiscat transmitter at tromsprovides reliable measurements . the absolute number of detections is significantly larger than the predicted number when assuming incoherent integration as a detection technique . thus , the coherent integration of the received signal indeed increases the detection sensitivity . as expected , we find that , when linked to ionospheric measurements , we will not obtain orbital information using the eiscat radars . this restriction can , however , easily be removed if dedicated observation time is acquired . in this case an optimum antenna pointing will allow us to determine at least doppler inclinations , which are identical to true orbit inclinations for circular orbits . as the proof tool of the new master / proof-2001 model allows to predict the distribution of doppler inclinations , this would allow us to constrain the statistical orbit properties of the small - size leo space debris population . in summary we find that the measurements performed during the demonstration campaign in february 2001 prove the value of space debris data obtained by exploiting ionospheric measurements . the mere amount of data , that will be available in case simultaneous operations with ionospheric measurements in the order of @xmath58 per year can be performed , provides an important contribution to the understanding of the evolution of leo space debris . in order to realise measurements that operate simultaneously with the ionospheric investigations , a real - time detection method has to be developed , because the volume of data that would be needed to record the raw signal from the radar for @xmath59 per year is prohibitive . with real - time detection only the object parameters as well as the signal of the passage will be recorded . a study to develop real - time measurements will be started by the end of 2002 . 2 natexlab#1#1 klinkrad , h. , j. bendisch , k. d. bunte , h. krag , h. sdunnus , and p. wegener , the master-99 space debris and meteoroid environment model . , * 28(9 ) * , 13551366 , 2001 . markkanen , j. , m. lehtinen , a. huuskonen , and v. vnnen , measurements of small - size debris with backscatter of radio waves . , sodankyl geophysical observatory , 2002 . mehrholz , d. , l. leushacke , d. banka , beam - park experiments at fgan , this issue . |
we investigate temporal evolution of infected individuals and infectious contacts , as well as degree distributions of nodes in each class . all the results demonstrate the importance of both local protection and global intervention , as well as the demographic effects . our work thus offers a more comprehensive description of disease containment . | c | 1604.03731 | in the face of serious infectious diseases , governments endeavour to implement containment measures such as public vaccination at a macroscopic level . meanwhile , individuals tend to protect themselves by avoiding contacts with infections at a microscopic level . however , a comprehensive understanding of how such combined strategy influences epidemic dynamics is still lacking . we study a susceptible - infected - susceptible epidemic model with imperfect vaccination on dynamic contact networks , where the macroscopic intervention is represented by random vaccination of the population and the microscopic protection is characterised by susceptible individuals rewiring contacts from infective neighbours . in particular , the model is formulated both in populations without and then with demographic effects ( births , deaths , and migration ) . using the pairwise approximation and the probability generating function approach , we investigate both dynamics of the epidemic and the underlying network . for populations without demography , the emerging degree correlations , bistable states , and oscillations demonstrate the combined effects of the public vaccination program and individual protective behavior . compared to either strategy in isolation , the combination of public vaccination and individual protection is more effective in preventing and controlling the spread of infectious diseases by increasing both the invasion threshold and the persistence threshold . for populations with additional demographic factors , we investigate temporal evolution of infected individuals and infectious contacts , as well as degree distributions of nodes in each class . it is found that the disease spreads faster but is more restricted in scale - free networks than in the erds - rnyi ones . the integration between vaccination intervention and individual rewiring may promote epidemic spreading due to the birth effect . moreover , the degree distributions of both networks in the steady state is closely related to the degree distribution of newborns , which leads to uncorrelated connectivity . all the results demonstrate the importance of both local protection and global intervention , as well as the demographic effects . our work thus offers a more comprehensive description of disease containment . = 1 | widespread public vaccination programmes and individual protective behavior are two key factors of disease control . ignoring either component will reduce the accuracy of our models or , ultimately , the effectiveness of containment measures . in this paper , we developed a mathematical framework to model the combined effects of public vaccination intervention and individual protective behavior on epidemic dynamics by studying an sis model with imperfect vaccination in a dynamic contact network . the model was analyzed in a closed population without demographic turnover and a varying population with births , deaths and migration . in the case of a closed population ( without demographic effects ) , we focused specifically on the combined effects of macroscopic random vaccination and microscopic contact rewiring on the system dynamics by conducting a bifurcation analysis of the model . our analysis shows that compared with either individual strategy , the combination of vaccination programme and adaptive rewiring contributes to a more effective control for the spread of infectious diseases by increasing both the invasion threshold and the persistence threshold of the epidemic . the larger the vaccination and rewiring rates are , the safer the population is from infectious diseases . the occurrence of stable epidemic cycle at a low prevalence is particularly relevant for the seasonality of influenza epidemics @xcite . moreover , the conjunction of vaccination and rewiring has significant impacts on the topology of the underlying contact network . both the degree distributions and degree correlations among different classes of nodes are characteristically distinct . in the case of a varying population with demographic development ( births , deaths and migration ) , we studied the epidemic patterns and the network topology on the basis of the dynamical behavior of nodes and links at a microscopic level , using both the probability generating function and the pairwise approximation . this modelling approach allows us to incorporate the effects of vaccination and rewiring as well as the demographic changes into network - based epidemiological models with arbitrary degree distributions . the analytical results of the temporal evolution of both the number of infective individuals and the number of infectious contacts , as well as the degree distribution of nodes in each class , have shown a good agreement with extensive computational simulations . in general , diseases in sf networks spread relatively faster yet end at a lower level of epidemic prevalence , as compared with the er networks . ironically , the combination of contact rewiring and random vaccination aiming to contain the epidemic would probably facilitate the disease spread . while the network without demography evolves to an identical topology for different initial network configurations , the network with demography develops into different structures depending on the degree distribution of the newborns . besides , the underlying network structure displays no degree correlation regardless of model parameters and initial settings . in summary , the present work manifests the significant combined effects of public vaccination intervention and individual protective behavior on both the epidemic dynamics and the underlying network structure . moreover , the strikingly different results for the two cases of population assumptions indicate the strong impacts of the demographic turnover . thus , this research provides a more comprehensive insight into disease containment strategies . the authors would like to thank the two anonymous referees for their valuable comments and suggestions which have greatly improved this paper . this work was supported by nsfc grants ( 11331009 , 11501340 ) and stcsm grant ( 13zr1416800 ) . ms was supported by an australian research council future fellowship ( ft 110100896 ) and discovery project ( dp 140100203 ) . |
in the framework of soft - collinear effective theory with glauber gluons , results and predictions for inclusive hadron suppression , based upon in - medium parton shower evolution , are presented for au+au and pb+pb collisions at rhic and lhc energies @xmath0 agev and @xmath1 atev , respectively . the @xmath2 medium - induced splitting kernels are further implemented to evaluate the attenuation of reconstructed jet cross in such reactions and to examine their centrality and radius @xmath3 dependence . building upon a previously developed method to systematically resum the jet shape at next - to - leading logarithmic accuracy , a quantitative understanding of the jet shape modification measurement in pb+pb collisions at @xmath4 atev at the lhc can be achieved . predictions for photon - tagged jet cross sections and shapes , that can shed light on the parton flavor dependence of in - medium parton shower modification , are also given . % @xmath5 , inclusive hadron suppression , qcd evolution , reconstructed jet quenching , jet shapes , @xmath6-tagged jets | c | 1601.00015 | in the framework of soft - collinear effective theory with glauber gluons , results and predictions for inclusive hadron suppression , based upon in - medium parton shower evolution , are presented for au+au and pb+pb collisions at rhic and lhc energies @xmath0 agev and @xmath1 atev , respectively . the @xmath2 medium - induced splitting kernels are further implemented to evaluate the attenuation of reconstructed jet cross in such reactions and to examine their centrality and radius @xmath3 dependence . building upon a previously developed method to systematically resum the jet shape at next - to - leading logarithmic accuracy , a quantitative understanding of the jet shape modification measurement in pb+pb collisions at @xmath4 atev at the lhc can be achieved . predictions for photon - tagged jet cross sections and shapes , that can shed light on the parton flavor dependence of in - medium parton shower modification , are also given . % @xmath5 , inclusive hadron suppression , qcd evolution , reconstructed jet quenching , jet shapes , @xmath6-tagged jets | in central and mid - peripheral pb+pb collisions at @xmath41 atev . right panel : related modification of the differential jet shapes for inclusive jets ( green band ) and photon - tagged jets ( blue band ) , with @xmath42 in central pb+pb collisions . , title="fig:",width=234 ] in central and mid - peripheral pb+pb collisions at @xmath41 atev . right panel : related modification of the differential jet shapes for inclusive jets ( green band ) and photon - tagged jets ( blue band ) , with @xmath42 in central pb+pb collisions . , title="fig:",width=279 ] in summary , we presented results for the suppression of inclusive hadron production in au+au reactions at rhic and pb+pb reactions at the lhc based upon qcd factorization and dglap evolution with @xmath2-based medium - induced splitting kernels . this method allowed us to unify the treatment of vacuum and medium - induced parton showers . in the soft gluon bremsstrahlung limit , we demonstrated the connection between this new approach and the traditional energy loss - based jet quenching phenomenology . with an emphasis on a consistent theoretical descriptions of hadron and jet observables in heavy ion collisions , we further related the in - medium modification of parton showers to the attenuation of reconstructed jet cross sections and the modification of the jet shapes in heavy ion collisions . while good description of the majority of current experimental measurements is achieved , this theoretical framework can be further tested by the upcoming lhc run ii measurements . we present predictions for charged hadron and neutral pion @xmath16 , the jet shape modification and the cross section suppression for inclusive jets and photon - tagged jets see fig . [ fig : pred ] . we fond that the cross section suppression at high @xmath20 can provide information about the cold nuclear matter effects . since photon - tagged jets are predominately quark - initiated , the cross section is expected to be less suppressed compared to inclusive jets . on the other hand , the broadening of the photon - tagged jet is more apparent . c. w. bauer , s. fleming and m. e. luke , phys . d * 63 * ( 2000 ) 014006 ; c. w. bauer , s. fleming , d. pirjol and i. w. stewart , phys . d * 63 * , 114020 ( 2001 ) . a. idilbi and a. majumder , phys . d * 80 * ( 2009 ) 054022 ; f. deramo , h. liu and k. rajagopal , phys . d * 84 * ( 2011 ) 065015 ; g. ovanesyan and i. vitev , jhep * 1106 * ( 2011 ) 080 . z. b. kang , r. lashof - regas , g. ovanesyan , p. saad and i. vitev , phys . * 114 * ( 2015 ) 9 , 092002 ; y. t. chien , a. emerman , z. b. kang , g. ovanesyan and i. vitev , arxiv:1509.02936 [ hep - ph ] ; y. t. chien and i. vitev , arxiv:1509.07257 [ hep - ph ] . a. adare _ et al . _ [ phenix collaboration ] , phys . * 101 * ( 2008 ) 232301 . b. abelev _ et al . _ [ alice collaboration ] , phys . b * 720 * ( 2013 ) 52 ; b. b. abelev _ et al . _ [ alice collaboration ] , eur . j. c * 74 * ( 2014 ) 10 , 3108 ; g. aad _ et al . _ [ atlas collaboration ] , jhep * 1509 * ( 2015 ) 050 ; s. chatrchyan _ et al . _ [ cms collaboration ] , eur . j. c * 72 * ( 2012 ) 1945 . i. vitev , phys . c * 75 * ( 2007 ) 064906 ; z. b. kang , i. vitev and h. xing , phys . rev . c * 92 * ( 2015 ) 5 , 054911 . b. abelev _ et al . _ [ alice collaboration ] , jhep * 1403 * ( 2014 ) 013 ; g. aad _ et al . _ [ atlas collaboration ] , phys . b * 719 * ( 2013 ) 220 ; g. aad _ et al . _ [ atlas collaboration ] , phys . * 114 * ( 2015 ) 7 , 072302 ; y - j . lee [ cms collaboration ] , private communication . |
in the spin - excitation - mediated pairing mechanism for superconductivity , the geometric frustration effects not only the spin configuration but also the superconducting - state properties . within the framework of the kinetic - energy - driven superconducting mechanism , the doping and temperature dependence of the meissner effect in triangular - lattice superconductors is investigated . | i | 1506.05194 | in the spin - excitation - mediated pairing mechanism for superconductivity , the geometric frustration effects not only the spin configuration but also the superconducting - state properties . within the framework of the kinetic - energy - driven superconducting mechanism , the doping and temperature dependence of the meissner effect in triangular - lattice superconductors is investigated . it is shown that the magnetic - field - penetration depth exhibits an exponential temperature dependence due to the absence of the d - wave gap nodes at the fermi surface . however , in analogy to the dome - like shape of the doping dependence of the superconducting transition temperature , the superfluid density increases with increasing doping in the lower doped regime , and reaches a maximum around the critical doping , then decreases in the higher doped regime . | investigation of oxide compounds has uncovered many unusual properties characterized by the strong electron correlation , which include unconventional superconductivity and anomalous properties in the normal - state @xcite . superconductivity in cuprate superconductors results from some special microscopic conditions @xcite : ( a ) the one - half spin cu ions situated in a square - planar arrangement and bridged by oxygen ions ; ( b ) the weak coupling between neighboring layers ; and ( c ) the charge - carrier doping in such a way that the fermi level lies near the middle of the cu - o @xmath0 bond . one common feature of cuprate superconductors is the _ square - planar _ cu arrangement @xcite . however , some oxide materials with a two - dimensional spin arrangements on non - square lattices have been synthetized @xcite . in particular , it has been reported @xcite that there is a class of cobaltate superconductors na@xmath1coo@xmath2h@xmath3o , which have a lamellar structure consisting of the two - dimensional coo@xmath3 layers separated by a thick insulating layer of na@xmath4 ions and h@xmath3o molecules , where the one - half spin co@xmath5 ions sites sit not on a square - planar , but on a _ triangular - planar lattice _ , therefore allowing a test of the effect of the geometric frustration on superconductivity @xcite . moreover , na@xmath1coo@xmath2h@xmath3o is viewed as an electron - doped mott insulator , where superconductivity appears with electron doping @xcite . furthermore , it has been found that the antiferromagnetic ( af ) spin correlation @xcite is present in na@xmath1coo@xmath2h@xmath3o , although being much weaker than those in square - lattice cuprate superconductors . in this case , a question is whether the unusual features observed on square - lattice superconductors exist also in triangular - lattice superconductors or not ? the finding of superconductivity in triangular - lattice cobaltate superconductors has raised the hope that it may help solve the unusual physics in square - lattice cuprate superconductors . on the other hand , the doped mott insulator on a triangular lattice is also of interests in its own right with many unanswered fascinating questions @xcite , where the geometric frustration was expected to destroy the af long - range order ( aflro ) and leads to a quantum spin - liquid state . superconductivity is characterized by exactly zero electrical resistance and expulsion of magnetic fields occurring in superconductors when cooled below @xmath6 . the later phenomenon is so - called meissner effect @xcite , i.e. , a superconductor is placed in an external magnetic field @xmath7 smaller than the upper critical field @xmath8 , the magnetic field @xmath7 penetrates only to a penetration depth @xmath9 and is excluded from the main body of the system . this magnetic - field - penetration depth is a fundamental parameter of superconductors , and provides a rather direct measurement of the superfluid density @xmath10 ( @xmath11 ) @xcite , which is proportional to the squared amplitude of the macroscopic wave function . in particular , the variation of the magnetic - field - penetration depth as a function of doping and temperature gives the information about the nature of quasiparticle excitations and their dynamics . moreover , the magnetic - field - penetration depth can be also used as a probe of the pairing symmetry , since it can distinguish between a fully gapped and a nodal quasiparticle excitation spectrum @xcite . the former results in the thermally activated ( exponential ) temperature dependence of the magnetic - field - penetration depth , whereas the latter one implies a power law behavior . for square - lattice superconductors , the meissner effect has been studied experimentally @xcite as well as theoretically @xcite . in particular , the electromagnetic response in square - lattice superconductors has been discussed @xcite based on the kinetic - energy - driven superconducting ( sc ) mechanism @xcite , and the obtained results of the doping and temperature dependence of the magnetic - field - penetration depth and superfluid density are well consistent with the experimental data observed on square - lattice superconductors @xcite . in triangular - lattice cobaltate superconductors , on the other hand , although the meissner effect has been investigated by virtue of systematic studies using the muon - spin - rotation measurement technique @xcite , the electromagnetic response has not been clarified starting from a microscopic sc theory , and no explicit calculations of the evolution of the superfluid density with doping and temperature has been made so far . in this paper , we try to study this issue within the framework of the kinetic - energy - driven sc mechanism . we show that the magnetic - field - penetration depth of triangular - lattice superconductors exhibits an exponential temperature dependence due to the absence of the d - wave gap nodes . however , in analogy to the case of square - lattice superconductors , the superfluid density in triangular - lattice superconductors also has a dome - like shape of the doping dependence . the rest of this paper is organized as follows . the basic formalism is presented in section [ framework ] , where we generalize the response kernel function obtained within the framework of the kinetic - energy - driven sc mechanism from the case in the previous square - lattice superconductors @xcite to the present case for triangular - lattice superconductors , and then employ this response kernel function to obtain explicitly the doping dependence of the meissner effect in triangular - lattice superconductors for all the temperature @xmath12 . based on this theoretical framework of the electromagnetic response , we then discuss the basic behavior of triangular - lattice superconductors in a weak electromagnetic field in section [ meissner - effect ] . finally , we give a summary in section [ conclusions ] . |
it is shown that the magnetic - field - penetration depth exhibits an exponential temperature dependence due to the absence of the d - wave gap nodes at the fermi surface . however , in analogy to the dome - like shape of the doping dependence of the superconducting transition temperature , the superfluid density increases with increasing doping in the lower doped regime , and reaches a maximum around the critical doping , then decreases in the higher doped regime . | c | 1506.05194 | in the spin - excitation - mediated pairing mechanism for superconductivity , the geometric frustration effects not only the spin configuration but also the superconducting - state properties . within the framework of the kinetic - energy - driven superconducting mechanism , the doping and temperature dependence of the meissner effect in triangular - lattice superconductors is investigated . it is shown that the magnetic - field - penetration depth exhibits an exponential temperature dependence due to the absence of the d - wave gap nodes at the fermi surface . however , in analogy to the dome - like shape of the doping dependence of the superconducting transition temperature , the superfluid density increases with increasing doping in the lower doped regime , and reaches a maximum around the critical doping , then decreases in the higher doped regime . | within the framework of the kinetic - energy driven superconductivity , we have performed a calculation of the doping and temperature dependence of the meissner effect in triangular - lattice superconductors for all temperatures @xmath217 throughout the sc dome . our results indicate that the magnetic - field - penetration depth shows an exponential temperature dependence due to the absence of the d - wave gap nodes at the large charge carrier fermi surface . in particular , the experimental result of the temperature dependence of the superfluid density in cobaltate superconductors can be qualitatively described in terms of the d - wave pairing state . however , as a natural consequence of the dome - like shape of the doping dependence of the charge - carrier pair gap parameter and @xmath6 , the superfluid density increases with increasing doping in the lower doped regime , and reaches a highest value ( a peak ) around the critical doping , then decreases in the higher doped regime . this work was supported by the funds from the ministry of science and technology of china under grant nos . 2011cb921700 and 2012cb821403 , and the national natural science foundation of china under grant nos . 11274044 and 11447144 jq is supported by the fundamental research funds for the central universities under grant no . frf - tp-14 - 074a2 , and the beijing higher education young elite teacher project under grant no . 0389 . a. p. ramirez , r. j. cava , j. j. krajewski , and w. f. peck , jr . , phys . rev . b * 49 * , 16082 ( 1994 ) ; 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in this article , the three point qcd sum rules is used to compute the strong coupling constants of vertices containing the strange bottomed ( charmed ) mesons with pion . the coupling constants are calculated , when both the bottom ( charm ) and pion states are off - shell . a comparison of the obtained results of coupling constants with the existing predictions is also made . key words : strong coupling constant , meson , qcd sum rules , bottom , charm . | i | 1402.0296 | in this article , the three point qcd sum rules is used to compute the strong coupling constants of vertices containing the strange bottomed ( charmed ) mesons with pion . the coupling constants are calculated , when both the bottom ( charm ) and pion states are off - shell . a comparison of the obtained results of coupling constants with the existing predictions is also made . key words : strong coupling constant , meson , qcd sum rules , bottom , charm . | during last ten years , there have been numerous published research articles devoted to the precise determination of the strong form factors and coupling constants of meson vertices via qcd sum rules ( qcdsr ) @xcite . qcdsr formalism have also been successfully used to study some of the `` exotic '' mesons made of quark- gluon hybrid ( @xmath0 ) , tetraquark states ( @xmath1 ) , molecular states of two ordinary mesons , glueballs and many others @xcite . coupling constants can provide a real possibility for studying the nature of the bottomed and charmed pseudoscalar and axial vector mesons . more accurate determination of these coupling constants play an important role in understanding of the final states interactions in the hadronic decays of the heavy mesons . our knowledge of the form factors in hadronic vertices is of crucial importance to estimate hadronic amplitudes when hadronic degrees of freedom are used . when all of the particles in a hadronic vertex are on mass - shell , the effective fields of the hadrons describe point - like physics . however , when at least one of the particles in the vertex is off - shell , the finite size effects of the hadrons become important . the following coupling constants have been determined by different research groups : @xmath2 @xcite , @xmath3@xcite , @xmath4@xcite , @xmath5@xcite , @xmath6 @xcite , @xmath7@xcite , @xmath8 @xcite , @xmath9 , @xmath10 @xcite , @xmath11 @xcite and @xmath12 , @xmath13 , @xmath14 and @xmath15@xcite , in the framework of three point qcd sum rules . it is very important to know the precise functional form of the form factors in these vertices and even to know how this form changes when one or the other ( or both ) mesons are off - shell @xcite . in this review , we focus on the method of three point qcd sum rules to calculate , the strong form factors and coupling constants associated with the @xmath16 , @xmath17 , @xmath18 , @xmath19 , @xmath20 and @xmath21 vertices , for both the bottom ( charm ) and pion states being off - shell . the three point correlation function is investigated in two phenomenological and theoretical sides . in physical or phenomenological part , the representation is in terms of hadronic degrees of freedom which is responsible for the introduction of the form factors , decay constants and masses . in qcd or theoretical part , which consists of two , perturbative and non - perturbative contributions ( in the present work the calculations contributing the quark - quark and quark - gluon condensate diagrams are considered as non - perturbative effects ) , we evaluate the correlation function in quark - gluon language and in terms of qcd degrees of freedom such as , quark condensate , gluon condensate , etc , by the help of the wilson operator product expansion(ope ) . equating two sides and applying the double borel transformations , with respect to the momentum of the initial and final states , to suppress the contribution of the higher states and continuum , the strong form factors are estimated . the outline of the paper is as follows . in section ii , by introducing the sufficient correlation functions , we obtain qcd sum rules for the strong coupling constant of the considered @xmath16 , @xmath17 and @xmath18 vertices . with the necessary changes in quarks , we can easily apply the same calculations to the @xmath19 , @xmath20 and @xmath21 vertices . in obtaining the sum rules for physical quantities , both light quark - quark and light quark - gluon condensate diagrams are considered as non - perturbative contributions . in section iii , the obtained sum rules for the considered strong coupling constants are numerically analysed . we will obtain the numerical values for each coupling constant when both the bottom ( charm ) and pion states are off - shell . then taking the average of the two off - shell cases , we will obtain final numerical values for each coupling constant . in this section , we also compare our results with the existing predictions of the other works . |
in this letter we demonstrate that the two claims of @xmath0 ovii k@xmath1 absorption lines from warm hot intergalactic medium ( whim ) along the lines of sight to the blazars h 2356 - 309 ( buote et al . , 2009 ; fang et al . , 2010 ) and mkn 501 ( ren , fang & buote , 2014 ) are likely misidentifications of the @xmath2 oii k@xmath3 line produced by a diffuse low - ionization metal medium in the galaxy s interstellar and circum - galactic mediums . we perform detailed modeling of all the available high signal - to - noise chandra letg and xmm - newton rgs spectra of h 2356 - 309 and mkn 501 and demonstrate that the @xmath0 whim absorption along these two sightlines is statistically not required . absorption lines , ism , galaxy , whim | i | 1602.03533 | in this letter we demonstrate that the two claims of @xmath0 ovii k@xmath1 absorption lines from warm hot intergalactic medium ( whim ) along the lines of sight to the blazars h 2356 - 309 ( buote et al . , 2009 ; fang et al . , 2010 ) and mkn 501 ( ren , fang & buote , 2014 ) are likely misidentifications of the @xmath2 oii k@xmath3 line produced by a diffuse low - ionization metal medium in the galaxy s interstellar and circum - galactic mediums . we perform detailed modeling of all the available high signal - to - noise chandra letg and xmm - newton rgs spectra of h 2356 - 309 and mkn 501 and demonstrate that the @xmath0 whim absorption along these two sightlines is statistically not required . our results , however , do not rule out a small contribution from the @xmath0 ovii k@xmath1 absorber along the line of sight to h 2356 - 309 . in our model the temperature of the putative @xmath4 whim filament is t@xmath5 k and the ovii column density is n@xmath6 @xmath7 , twenty times smaller than the ovii column density previously reported , and now more consistent with the expectations from cosmological hydrodynamical simulations . absorption lines , ism , galaxy , whim | according to all hydro - dynamical simulation for structure formation run in the framework of a @xmath8cdm cosmology , large concentrations of galaxies are the best tracers of the filamentary web of dark - matter that our local universe is made of . embedded into these filaments of shining ordinary matter ( stars in galaxies ) , should be hidden the , still to be found , largest reservoir of baryons in the local universe : the so called warm - hot intergalactic medium ( whim : e.g cen & ostriker , 2006 ) . this , metal enriched ( through galaxy - igm feedback ) , otherwise primordial , medium should have temperatures in the range logt@xmath9 ( in k ) , and very low baryon densities @xmath10 @xmath11 . at such temperatures , h and he are mostly fully ionized ( and so very difficult to detect ) , and the most abundant metal , oxygen , is mainly present in its stable he - like form : ovii . the strongest bound - bound transition of the ovii ion is the k@xmath1 at @xmath12 , and should thus imprint absorption lines in the soft x - ray spectra of background objects whose lines of sight cross one or more whim filaments between us and the target . however , these lines are expected to be extremely weak . expected ovii column densities along a random line of sight crossing a whim filament , are n@xmath13_few_@xmath14 @xmath7 ( e.g. cen & fang , 2006 ) , giving rise to redshifted ovii k@xmath1 absorption lines with ew@xmath15 m . for these reasons detecting the whim has proven to be very challenging . the few detections so far , for the majority of the whim at logt@xmath16 , are either highly controversial ( e.g. nicastro et al . , 2005a , b ) , or single - line and low statistical significance ( e.g. mathur , weinberg & chen , 2003 , nicastro , 2010 , zappacosta , 2012 ) . perhaps the only exception that seemed to have gathered the largest consensus ( e.g. tananbaum et al . , 2014 ) despite the large - compared to typical whim expectations - ew and associated ovii column density reported by the authors ( ew=@xmath17 m ) , is the proposed detection of a single - line ( ovii k@xmath1 ) whim filament at the redshift of the sculptor wall , reported by buote et al . ( 2009 : hereinafter b09 ) and fang et al . ( 2010 : hereinafter f10 ) along the line of sight to the blazar h 2356 - 309 . recently , the same authors reported yet another evidence for a new ovii k@xmath1 whim absorber , again at @xmath18 , along the line of sight to the blazar mkn 501 ( ren , fang & buote , 2014 : hereinafter rfb14 ) . indeed , the ovii k@xmath1 resonant line shifts to @xmath19 at @xmath20 , a redshift consistent with both the @xmath21 and @xmath22 intervals at which the sculptor wall and the hercules supercluster cross the lines of sight to h 2356 - 309 and mkn 501 , respectively . for this reason b09 , f10 and rfb14 , identified the lines detected in the letg and rgs spectra of these two blazars at @xmath23 ( the average and maximum semi - dispersion of the two measurements in the letg and rgs spectra of h 2356 - 309 , respectively : f10 ) and @xmath24 ( rfb14 ) , as redshifted ovii k@xmath1 imprinted by two whim filaments permeating the two large scale structures of galaxies , the sculptor wall and the hercules superstructures . in a companion paper ( nicastro et al . , 2015 : hereinafter n15 ) , we present a systematic study of the cold and mildly ionized interstellar ( ism ) and circum - galactic ( cgm ) medium of our galaxy through the modeling of the oi k@xmath1 ( @xmath25 ) , oii k@xmath1 ( @xmath26 ) and oii k@xmath3 ( @xmath27 ) absorption lines imprinted by our galaxy s ism / cgm in the spectra of two distinct samples of galactic and extragalactic sources . in particular , the oii k@xmath3 transition , firstly identified by gatuzz et al . , ( 2013a , b ) , is the weak ( oscillator strength @xmath28 , behar , private communication ) @xmath29 inner shell transition of the n - like ( 7 electrons ) ion of oxygen . this line is hinted at in 9 of the 20 galactic x - ray binary ( xrb ) spectra and 8 out of the 29 agn spectra of the n15 sample , and has an average rest - frame wavelength of @xmath27 . the 8 agns of the n15 sample , in whose spectra the oii k@xmath3 absorption line is hinted at , include the two blazars h 2356 - 309 ( @xmath30 , jones et al . , 2009 ) and mkn 501 ( @xmath31 , falco et al . , 2000 ) , for which the same line had been instead identified as intervening @xmath0 ovii k@xmath1 absorption tracing whim filaments ( b09 , f10 and rfb14 ) . here we re - analyze all the available high resolution x - ray spectra of the two sightlines towards h 2356 - 309 and mkn 501 and demonstrate that , even for these two sightlines , the most likely identification of the @xmath32 line is indeed that of a @xmath2 oii k@xmath3 transition imprinted by a large amount of low - ionization metal medium ( limm ) that permeates the halo of our galaxy , at large distances from the galactic plane and perhaps up to the galaxy s cgm ( n15 ) . this , at least for the line of sight to h 2356 - 309 ( the only one for which both the k@xmath1 and k@xmath3 transitions of oii are detectables ) does not completely rule out a possible contribution , at exactly the same wavelengths , by redshifted ovii k@xmath1 , but dramatically limits it to an ovii column density more than ten times lower than that claimed by b09 and f10 . |
we find this is a very efficient way to describe many aspects of rrab light curve structure : in many cases , a principal component fit with 9 parameters can describe a rrab light curve including bumps whereas a 17 parameter fourier fit is needed . as a consequence we show show statistically why the amplitude is also a good summary of the structure of these rr lyrae light curves . rr lyraes stars : fundamental parameters | i | astro-ph0407020 | in this paper , we analyze the structure of rrab star light curves using principal component analysis . we find this is a very efficient way to describe many aspects of rrab light curve structure : in many cases , a principal component fit with 9 parameters can describe a rrab light curve including bumps whereas a 17 parameter fourier fit is needed . as a consequence we show show statistically why the amplitude is also a good summary of the structure of these rr lyrae light curves . we also use our analysis to derive an empirical relation relating absolute magnitude to light curve structure . in comparing this formula to those derived from exactly the same dataset but using fourier parameters , we find that the principal component analysis approach has distinct advantages . these advantages are , firstly , that the errors on the coefficients multiplying the fitted parameters in such formulae are much smaller , and secondly , that the correlation between the principal components is significantly smaller than the correlation between fourier amplitudes . these two factors lead to reduced formal errors , in some cases estimated to be a factor of 2 , on the eventual fitted value of the absolute magnitude . this technique will prove very useful in the analysis of data from existing and new large scale survey projects concerning variable stars . rr lyraes stars : fundamental parameters | kanbur et al ( 2002 ) , hendry et al ( 1999 ) , tanvir et al ( 2004 ) introduced the use of principal component analysis ( pca ) in studying cepheid light curves . they showed that a major advantage of such an approach over the traditional fourier method is that it is much more efficient : an adequate fourier description requires , at best , a fourth order fit or 9 parameters , whilst a pca analysis requires only 3 or 4 parameters with as much as 81@xmath0 of the variation in light curve structure being explained by the first parameter . later , leonard et al ( 2003 ) used the pca approach to create cepheid light curve templates to estimate periods and mean magnitudes for hst observed cepheids . the purpose of this paper is to apply the pca technique to the study of rr lyrae light curves . the mathematical formulation and error characteristics of pca are given in k02 and will only be summarized here . |
in this paper , we analyze the structure of rrab star light curves using principal component analysis . these two factors lead to reduced formal errors , in some cases estimated to be a factor of 2 , on the eventual fitted value of the absolute magnitude . this technique will prove very useful in the analysis of data from existing and new large scale survey projects concerning variable stars . | c | astro-ph0407020 | in this paper , we analyze the structure of rrab star light curves using principal component analysis . we find this is a very efficient way to describe many aspects of rrab light curve structure : in many cases , a principal component fit with 9 parameters can describe a rrab light curve including bumps whereas a 17 parameter fourier fit is needed . as a consequence we show show statistically why the amplitude is also a good summary of the structure of these rr lyrae light curves . we also use our analysis to derive an empirical relation relating absolute magnitude to light curve structure . in comparing this formula to those derived from exactly the same dataset but using fourier parameters , we find that the principal component analysis approach has distinct advantages . these advantages are , firstly , that the errors on the coefficients multiplying the fitted parameters in such formulae are much smaller , and secondly , that the correlation between the principal components is significantly smaller than the correlation between fourier amplitudes . these two factors lead to reduced formal errors , in some cases estimated to be a factor of 2 , on the eventual fitted value of the absolute magnitude . this technique will prove very useful in the analysis of data from existing and new large scale survey projects concerning variable stars . rr lyraes stars : fundamental parameters | we have shown that the method of pca can be used to study rr lyrae light curves . it has distinct advantages over a fourier approach because * \a ) it is a more efficient way to characterize structure since fewer parameters are needed . a typical fourier fit requires 17 parameters whereas a pca fit may only need 9 . * \b ) using the pca approach , we see clearly why the amplitude is a good descriptor of rrab light curve shape . * \c ) the different pca components are orthogonal to each other whereas the fourier amplitudes are highly correlated with each other . this leads to relations linking light curve structure to absolute magnitude using pca having coefficients with smaller errors and leading to more accurate estimates of absolute magnitudes . this can reduce the formal error , in some cases , by a factor of 2 . in the present formulation of our pca approach , the input data is a fourier analysis . if these input data , that is the fourier decompositions , contain significant observational errors , the error bars on the resulting principal components will be larger . neither the pca or fourier approach can compensate fully for noisy data . in this sense , the sensitivity of pca to noisy data should be similar to fourier , though the fact that pca is an ensemble approach in which we initially remove an average term does guard against individual points having too much undue influence . as an example , table 4 of kw gives 17 outliers ( in terms of their fourier parameters ) , which kw removed in their analysis relating absolute magnitude to fourier parameters . we do _ not _ remove these outliers , yet , in terms of the final fitted magnitudes presented in figure 10 , pca and fourier produce very similar results . further , even with the inclusion of these 17 stars , the pca method still produces pca coefficients with smaller errors as given in tables 2 and 3 . kanbur et al ( 2002 ) discuss in detail the nice error properties of the pca method as applied to variable stars and give a recipe with which to calculate errors on pca coefficients . their figure 2 , albeit for cepheids , displays error bars on these coefficients . we see that even with noisy data , the progression of pca parameters with period is preserved , though of course , the error bars on the pca coefficients are larger . ngeow et al ( 2003 ) developed a simulated annealing method which can reduce numerical wiggles in fourier decomposition of sparse data . ngeow et al ( 2003 ) give specific examples of how such an approach improves fourier techinues using ogle lmc cepheids . a similar result will hold true for rr lyraes . hence this annealing technique couple with a principal component analysis should prove very useful when dealing with noisy rr lyrae data and will be treated in detail in a subsequent paper . our pca results are based on a sample of 383 stars in globular clusters . how transferable are our results and how can our results be used to obtain pc coefficients for a new rr lyrae light curve which appears to be normal ( ie no signs of blazhko effects etc . ) ? our results are transferable to the extent that the original 383 stars are a good representation of the entire population of rrab stars , including variation in metallicity and differences between field and cluster variables . given this caveat , we suggest two methods to reproduce the light curve of a new rrab star . firstly , it is straightforward to include the new star in the pca analysis with the existing dataset . this is our recommended approach and preserves the `` ensemble analysis '' property of our pca method . our second method will be the subject of future paper but briefly it is this . we fit the progression of the pca coefficients with period , such as given in figures 4 and 5 , with simple polynomial functions . as an aside , we remark that figure 4 contains significant scatter , perhaps associated with metallicity , so that it would be best to include metallicity in such polynomial fits . for a new star , we then guess its period and read off , for that period , the value of the pca coefficients . equation ( 3 ) then allows us to generate the light curve . we iterate this until a specified error criterion is satisfied . we can then use existing formulae relating absolte magnitude to light curve structure as defined by pca . this pca template approach has been used , with considerable success , in analysing hst cepheid data ( leonard et al 2003 ) . we note from table 2 that the chi square on the fitted relations are similar for pca and fourier . does this mean that despite the smaller formal errors with pca , both methods ability to predict rrab absolte magnitudes is limited by the intrinsic properties of rrab stars themselves ? to some extent this is true . jurcsik et al ( 2004 ) , in analysing accurate data for 100 rrab stars in m3 , show that for some 16 stars , amongst which there exist some pairs whose absolute mean magnitudes differ by about 0.05 mags ( the accuracy of the photometry is about 0.02mags ) , the fourier parameters and periods are very similar . that is , an empirical method relating absolute magnitude to period and fourier parameters in one waveband could not distinguish between these stars . since , as jurcsik et al ( 2004 ) point out , their data contains a small range of both mass and metallicity , temperature is the only other variable , it may be the case that multiwavelength information is needed . it is worthwhile to investigate how pca fares with this dataset . here we give an outline that suggests that pca can be more efficient at extracting information from the light curve . for the sixteen stars which had differing absolute magnitudes but very similar fourier parameters , we can perform the following procedure : for every pair , @xmath55 , we calculate @xmath56 @xmath57 @xmath58 @xmath59 and @xmath60 where @xmath61 are the fourier amplitudes and @xmath62 are the pca coefficients and @xmath63 are the mean magnitudes . in the above , we always take the absolute value of the differences . we need to take fractional changes because the fourier amplitudes and pca coefficients have different ranges . we now plot diff3 against diff1 and diff2 . this is presented in figure 11 , where the open squares are diff1 and the closed squares are diff2 . we see that with pca ( closed squares ) , the differences between light curve structure parameters are greater than with fourier ( open squares ) . this could imply that pca can be more efficient though the limitations associated with using a single waveband are still present . a more rigorous , quantitative discussion of this , in a fisher information sense , will be given in a future paper . in other future work we plan to investigate the applicability of this method to light curve structure - metallicity relations , rrc stars and a comparison of observed and theoretical light curves using pca . .percentage of variation explained by pc components [ cols="<,^,^,^,^,^,^",options="header " , ] |
in this paper , we report on domain clustering in the ambit of an adaptive mt architecture . a standard bottom - up hierarchical clustering algorithm has been instantiated with five different distances , which have been compared , on an mt benchmark built on 40 commercial domains , in terms of dendrograms , intrinsic and extrinsic evaluations . the main outcome is that the most expensive distance is also the only one able to allow the mt engine to guarantee good performance even with few , but highly populated clusters of domains . | i | 1612.04683 | in this paper , we report on domain clustering in the ambit of an adaptive mt architecture . a standard bottom - up hierarchical clustering algorithm has been instantiated with five different distances , which have been compared , on an mt benchmark built on 40 commercial domains , in terms of dendrograms , intrinsic and extrinsic evaluations . the main outcome is that the most expensive distance is also the only one able to allow the mt engine to guarantee good performance even with few , but highly populated clusters of domains . | in this paper we have summarised our investigation on domain clustering in the ambit of an adaptive mt architecture . a standard bottom - up hierarchical clustering algorithm has been instantiated with five different distances , which have been compared , on an mt benchmark with 40 commercial domains , in terms of dendrograms , intrinsic and extrinsic evaluations . the main outcome is that the most expensive distance is also the only one which allows the mt engine with just few cluster - specific models to perform as well as the 40-domains adapted mt engine . in the close future , we are going to extend the here reported investigation as follows . first of all , instead of considering each original tm as an indivisible , single point , a finer granularity will be considered to both overcome the 0-valued clusters issue ( section [ sec : intreval ] ) and improve the performance of single - link instances of the hac algorithm . unfortunately , no further meta - information is provided inside our tms in addition to the identity of the customer who provided it . anyway , finer straightforward single points to aggregate could be : ( i ) single segments inside tms ; ( ii ) automatic clusters of sentences inside each tm . second , our evaluations treated equally all words , but a customer could consider more valued the proper translation of domain - specific terminology than of other words . for this reason , we are manually annotating domain specific terms in benchmark 1.1 for comparing the instances of the hac algorithm with respect to them . finally , we will test the clustering on much more challenging benchmarks with hundred to even thousand domains . |
in this paper , we study small-@xmath0 gravitational dynamics involving up to six objects . this is done using the fewbody numerical scattering code , which we have upgraded to treat encounters involving triple stars . we focus on outcomes that result in direct physical collisions between stars , within the low angular momentum and high absolute orbital energy regime . this study is meant as a first step in an on - going effort to extend our understanding of small-@xmath0 collisional dynamics beyond the three- and four - body problems and into the realm of larger-@xmath0 . | i | 1207.2469 | in this paper , we study small-@xmath0 gravitational dynamics involving up to six objects . we perform a large suite of numerical scattering experiments involving single , binary , and triple stars . this is done using the fewbody numerical scattering code , which we have upgraded to treat encounters involving triple stars . we focus on outcomes that result in direct physical collisions between stars , within the low angular momentum and high absolute orbital energy regime . the dependence of the collision probability on the number of objects involved in the interaction , @xmath0 , is found for fixed total energy and angular momentum . our results are consistent with a collision probability that increases approximately as @xmath1 . interestingly , this is also what is expected from the mean free path approximation in the limit of very large @xmath0 . a more thorough exploration of parameter space will be required in future studies to fully explore this potentially intriguing connection . this study is meant as a first step in an on - going effort to extend our understanding of small-@xmath0 collisional dynamics beyond the three- and four - body problems and into the realm of larger-@xmath0 . [ firstpage ] gravitation ( stars : ) binaries ( including multiples ) : close methods : statistical celestial mechanics scattering . | the gravitational three - body problem was first studied by sir isaac newton in his principia @xcite . after solving the two - body problem , newton boldly added a third body into the mix and attempted to create a similar mathematical formalism to describe the motion of three celestial bodies under their mutual gravitational attraction . the solution evaded newton until his end , leaving the problem at the mercy of his disciples . it was later taken up by euler @xcite , lagrange @xcite , jacobi @xcite , poincare @xcite , hill ( e.g. * ? ? ? * ) , henon ( e.g. * ? ? ? * ) , and a host of others , often with a focus on the earth - moon - sun system ( e.g. * ? ? ? despite the considerable efforts of numerous researchers , a simple analytic solution to the general three - body problem has never been found . @xcite discovered a uniformly convergent infinite series involving familiar functions that technically solves the three - body problem . however , in order to attain a reasonable level of accuracy , the solution must contain on the order of @xmath2 terms @xcite . more practical solutions require a number of simplifying assumptions to make the general three - body problem tractable ( e.g. * ? ? ? as a result , the most useful analytic solutions tend to be solely applicable to a very narrow subset of the total allowed parameter space . the introduction of computers within the last few decades revolutionalized our understanding of the three - body problem . this allowed for the direct integration of the equations of motion for each particle over small time steps , incrementally moving each body forward in an iterative fashion . despite the fact that this approach completely transformed our tool - set for studying the three - body problem , it too has its short - comings . for example , the times required to run the simulations to completion are often quite long . the precise definition of a `` complete encounter '' can often be ambiguous as well . quasi - stable configurations can form that remain bound for millions or even billions of years before eventually breaking apart ( e.g. * ? ? ? * ) . there is also the issue of errors in computing the trajectories of the particles in position - space which are introduced at each time - step . these arise as a result of moving one body forward at a time , instead of moving all bodies simultaneously . such errors can be minimized by taking suitably short time - steps . however , this comes at the often considerable cost of simulation run - time . when only three bodies are involved , qualitative descriptions of the outcomes of dynamical interactions are often relatively straight - forward . they include ionizations , exchanges , fly - bys , and collisions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , the number of possible outcomes quickly increases with increasing @xmath0 , where @xmath0 is the total number of objects involved in the interaction @xcite . this complicates descriptions of the interactions , and introduces a considerable challenge in developing a physical understanding of the evolution of the system . for example , nearly 100 generic outcomes are possible for encounters involving six objects . additional bodies not only increase the parameter space to be explored , they also increase integration times for computer simulations . consequently , most previous numerical scattering studies considered only single - binary and , to a lesser extent , binary - binary encounters ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? many of the numerical scattering studies conducted to date considered equal - mass particles , and devoted their attention to studying the effects of varying the initial relative velocity or impact parameter ( e.g. * ? ? ? for example , @xcite found analytic approximations for high - velocity encounters , and provided simple formulae for the corresponding cross - sections for exchanges and ionizations to occur . similar analytic formulae were derived by @xcite for encounters involving two binaries having unequal orbital energies but equal masses . an extensive analysis that considered unequal mass particles was conducted by @xcite , who studied the effects of dynamics on the stellar and remnant populations in a globular cluster . a number of other scattering experiments were designed purely to study the formation of different types of stellar exotica in globular clusters , including blue stragglers ( e.g. * ? ? ? * ) , low - mass x - ray binaries ( e.g. * ? ? ? * ) , cataclysmic variables ( e.g. * ? ? ? * ) , and millisecond pulsars ( e.g. * ? ? ? many of these also considered a range of particle masses . the effects of general relativity have also been studied in the context of the three- and four - body problems . for example , @xcite and @xcite considered interactions involving binary super - massive black holes during the mergers of galaxies , and identified several important trends arising from energy losses due to gravitational radiation . in this paper , we study gravitational interactions involving up to six objects . our goal is to better understand how the outcome of an encounter depends on the number of interacting objects . this is a first step toward extending techniques developed for the three - body problem , where the vast majority of research efforts have thus far been concentrated , to treat larger-@xmath0 encounters . to this end , we perform @xmath3 numerical scattering experiments involving single , binary and triple star systems . the number of possible encounter outcomes is a steeply increasing function of @xmath0 . this presents a considerable challenge when trying to draw parallels between encounters involving different numbers of objects . to minimize this issue , we focus only on outcomes resulting in direct physical collisions , which we consider to have occurred when the radii of any two stars overlap . in section [ method ] , we describe the set - up for our numerical scattering experiments , including the range of initial conditions considered . additionally , we develop an analytic formula for the collision probability as a function of @xmath0 , that is based on a simple analytic model originally derived for 1 + 2 encounters . in section [ results ] , we present the results of our analysis of this large suite of single - binary ( 1 + 2 ) , binary - binary ( 2 + 2 ) , single - triple ( 1 + 3 ) , binary - triple ( 2 + 3 ) , and triple - triple ( 3 + 3 ) scattering experiments . here , we fit the analytic formula to the results from these numerical scattering experiments , thereby deriving the @xmath0-dependence of the collision probability . the implications of our analysis for small-@xmath0 collisional dynamics are discussed in section [ discussion ] . concluding remarks are given in section [ summary ] . finally , in an appendix , we present a formalism for creating schematic diagrams that quantitatively depict the evolution of an interaction in energy - space , and briefly discuss some of their possible applications . |
we perform a large suite of numerical scattering experiments involving single , binary , and triple stars . the dependence of the collision probability on the number of objects involved in the interaction , @xmath0 , is found for fixed total energy and angular momentum . our results are consistent with a collision probability that increases approximately as @xmath1 . interestingly , this is also what is expected from the mean free path approximation in the limit of very large @xmath0 . | i | 1207.2469 | in this paper , we study small-@xmath0 gravitational dynamics involving up to six objects . we perform a large suite of numerical scattering experiments involving single , binary , and triple stars . this is done using the fewbody numerical scattering code , which we have upgraded to treat encounters involving triple stars . we focus on outcomes that result in direct physical collisions between stars , within the low angular momentum and high absolute orbital energy regime . the dependence of the collision probability on the number of objects involved in the interaction , @xmath0 , is found for fixed total energy and angular momentum . our results are consistent with a collision probability that increases approximately as @xmath1 . interestingly , this is also what is expected from the mean free path approximation in the limit of very large @xmath0 . a more thorough exploration of parameter space will be required in future studies to fully explore this potentially intriguing connection . this study is meant as a first step in an on - going effort to extend our understanding of small-@xmath0 collisional dynamics beyond the three- and four - body problems and into the realm of larger-@xmath0 . [ firstpage ] gravitation ( stars : ) binaries ( including multiples ) : close methods : statistical celestial mechanics scattering . | in this paper , we perform a large suite of numerical scattering experiments to study the probability of a direct physical collision occurring during single - binary , binary - binary , single - triple , binary - triple , and triple - triple interactions . we quantify the dependence of the collision probability on the number of objects involved in the interaction @xmath0 for fixed total energy and angular momentum . our results suggest that the collision probability increases approximately as @xmath1 , for @xmath17 . this result is consistent with the hypothesis that the average number of close approaches per crossing time also scales as @xmath1 , and we will fully investigate this possibility in a future study . interestingly , this same @xmath0-dependence is predicted by the mean free path approximation in the limit of very large @xmath0 . this similarity is rather intriguing , and further work investigating the connection between these two regimes in @xmath0 will be highly valuable for our understanding of collisional dynamics in the realm of not - so - small-@xmath0 . |
in this paper , we study the problem of stabilizing continuous - time switched linear systems with quantized output feedback . we assume that the observer and the control gain are given for each mode . also , the plant mode is known to the controller and the quantizer . extending the result in the non - switched case , we develop an update rule of the quantizer to achieve asymptotic stability of the closed - loop system under the average dwell - time assumption . to avoid quantizer saturation , we adjust the quantizer at every switching time . switched systems , quantized control , output feedback stabilization . | i | 1509.00536 | in this paper , we study the problem of stabilizing continuous - time switched linear systems with quantized output feedback . we assume that the observer and the control gain are given for each mode . also , the plant mode is known to the controller and the quantizer . extending the result in the non - switched case , we develop an update rule of the quantizer to achieve asymptotic stability of the closed - loop system under the average dwell - time assumption . to avoid quantizer saturation , we adjust the quantizer at every switching time . switched systems , quantized control , output feedback stabilization . | quantized control problems have been an active research topic in the past two decades . discrete - level actuators / sensors and digital communication channels are typical in practical control systems , and they yield quantized signals in feedback loops . quantization errors lead to poor system performance and even loss of stability . therefore , various control techniques to explicitly take quantization into account have been proposed , as surveyed in @xcite . on the other hand , switched system models are widely used as a mathematical framework to represent both continuous and discrete dynamics . for example , such models are applied to dc - dc converters @xcite and to car engines @xcite . stability and stabilization of switched systems have also been extensively studied ; see , e.g. , the survey @xcite , the book @xcite , and many references therein . in view of the practical importance of both research areas and common technical tools to study them , the extension of quantized control to switched systems has recently received increasing attention . there is by now a stream of papers on control with limited information for discrete - time markovian jump systems @xcite . moreover , our previous work @xcite has analyzed the stability of sampled - data switched systems with static quantizers . in this paper , we study the stabilization of continuous - time switched linear systems with quantized output feedback . our objective is to solve the following problem : given a switched system and a controller , design a quantizer to achieve asymptotic stability of the closed - loop system . we assume that the information of the currently active plant mode is available to the controller and the quantizer . extending the quantizer in @xcite for the non - switched case to the switched case , we propose a lyapunov - based update rule of the quantizer under a slow - switching assumption of average dwell - time type @xcite . the difficulty of quantized control for switched systems is that a mode switch changes the state trajectories and saturates the quantizer . in the non - switched case @xcite , in order to avoid quantizer saturation , the quantizer is updated so that the state trajectories always belong to certain invariant regions defined by level sets of a lyapunov function . however , for switched systems , these invariant regions are dependent on the modes . hence the state may not belong to such regions after a switch . to keep the state in the invariant regions , we here adjust the quantizer at every switching time , which prevent quantizer saturation . the same philosophy of emphasizing the importance of quantizer updates after switching has been proposed in @xcite for sampled - data switched systems with quantized state feedback . subsequently , related works were presented for the output feedback case @xcite and for the case with bounded disturbances @xcite . the crucial difference lies in the fact that these works use the quantizer based on @xcite and investigates propagation of reachable sets for capturing the measurement . this approach also aims to avoid quantizer saturation , but it is fundamentally disparate from our lyapunov - based approach . this paper is organized as follows . in section ii , we present the main result , theorem [ thm : stability_theorem ] , after explaining the components of the closed - loop system . section iii gives the update rule of the quantizer and is devoted to the proof of the convergence of the state to the origin . in section iv , we discuss lyapunov stability . we present a numerical example in section v and finally conclude this paper in section vi . the present paper is based on the conference paper @xcite . here we extend the conference version by addressing state jumps at switching times . we also made structural improvements in this version . _ notation : _ let @xmath0 and @xmath1 denote the smallest and the largest eigenvalue of @xmath2 . let @xmath3 denote the transpose of @xmath4 . the euclidean norm of @xmath5 is denoted by @xmath6 . the euclidean induced norm of @xmath4 is defined by @xmath7 . for a piecewise continuous function @xmath8 , its left - sided limit at @xmath9 is denoted by @xmath10 . |
in this paper it is demonstrated that based on two - dimensional distributions in semi - inclusive deep inelastic scattering ( sidis ) data , obtained recently by the hermes experiment at desy on different nuclei , which contains data for charged pions produced in @xmath0 slices as a function of @xmath1 , and in a @xmath1 slices as a function of @xmath0 , it it is possible to parametrise a ratio of multiplicities on nucleus and deuterium ( per nucleon ) @xmath2 in a form of a function of a single variable @xmath3 , which has the physical meaning of the formation time of hadron . @xmath3 is a function of two variables @xmath1 and @xmath0 . | i | 0810.4841 | in this paper it is demonstrated that based on two - dimensional distributions in semi - inclusive deep inelastic scattering ( sidis ) data , obtained recently by the hermes experiment at desy on different nuclei , which contains data for charged pions produced in @xmath0 slices as a function of @xmath1 , and in a @xmath1 slices as a function of @xmath0 , it it is possible to parametrise a ratio of multiplicities on nucleus and deuterium ( per nucleon ) @xmath2 in a form of a function of a single variable @xmath3 , which has the physical meaning of the formation time of hadron . we call this effect @xmath3 scaling . @xmath3 is a function of two variables @xmath1 and @xmath0 . it is also shown that @xmath2 can be presented in a form of a linear polynomial of @xmath3 , @xmath4 + @xmath5 , where parameters @xmath4 and @xmath6 do not depend on @xmath1 and @xmath0 . | hadronization is the process through which partons , created in an elementary interaction , turn into the hadrons . experimentally the hadronization process in free space ( vacuum ) has been studied extensively in @xmath7 annihilation and in semi - inclusive lepton - proton deep inelastic scattering ( dis ) . as a result , the spectra of hadrons produced and their kinematical dependences are rather well known . however , little is known about the space - time evolution of the process , because the products of this process can only be observed in a detector that is separated from the reaction point by a macroscopic distance . it is worth to mention that according to theoretical estimates the hadronization process occurs over length scales that vary from less than a femtometer to several tens of femtometers . the nuclear medium can serve as a detector located directly at the place where microscopic interaction happens . consequently , leptoproduction of hadrons on atomic nuclei provides a way to investigate the space - time picture of the hadronization process . the semi - inclusive dis of leptons on nuclear targets is widely used for the study of this process @xcite . it is most effective to observe at moderate energies of the virtual photon , when the formation time of the hadron is comparable with the nuclear radius . such possibility provides hermes experiment at desy , which uses electron ( positron ) beam with energy @xmath8 and fixed nuclear targets . + the most convenient observable measured experimentally for this process is the nuclear attenuation ratio , which is a ratio of multiplicities on nucleus and deuterium ( per nucleon ) for a given hadron . we shall denote it as @xmath2 . for a more profound understanding of the hadronization mechanism , it is important to find a variable which allows to present this observable in the most simple functional form . + usually it is supposed , that @xmath2 is a function of two variables @xmath1 and @xmath0 , which are the energy of photon and the fraction of this energy carried by the final hadron with energy @xmath9 ( @xmath10 ) , respectively also depends on the photon virtuality @xmath11 and on the square of the hadron transverse momentum in respect to the virtual photon direction , @xmath12 . however , from the experimental data , it is known that @xmath2 is a much sensitive function of @xmath1 and @xmath0 in comparison with @xmath11 and @xmath12 . ] . + in our preceding work @xcite we performed a fit for the evidence that the formation time @xmath3 is the best variable for @xmath2 , i.e. that it can be parametrized as a function of a single variable @xmath3 . three widely known representations for @xmath3 were used for the fit . the experimental data for pions on nitrogen and for identified hadrons on krypton nuclei obtained by the hermes experiment @xcite were used for this fit . we have demonstrated that the nuclear attenuation ratio can be presented , with good precision , as a function of a single variable @xmath3 instead of a function of two variables @xmath1 and @xmath0 . moreover , @xmath2 is a linear function of @xmath3 . we named @xmath3 a scaling variable , because it contains all @xmath1 and @xmath0 dependencies of @xmath2 . for the fit we have obtained @xmath2 as a function of @xmath3 from experimental data @xcite , where it was measured as a function of @xmath1 with the integration over @xmath0 , and as a function of @xmath0 with the integration over @xmath1 . this means , that the data were taken at an unequal binning over @xmath1 and @xmath0 . in case of @xmath1-dependence the detailed bins over the variable @xmath1 were taken , and for each value of @xmath1 the value of @xmath0 averaged over whole range of measured @xmath0 ( @xmath13 ) was taken . in case of @xmath0-dependence we also performed the above mentioned procedure . + recent work of published by the hermes experiment @xcite allows to escape this difficulty , because the data published contains , among others , the so called two - dimensional data , i.e. multiplicity ratio @xmath2 for charged pions produced in a @xmath0 slices as a function of @xmath1 , and in a @xmath1 slices as a function of @xmath0 . the data were obtained for four nuclear targets and used for a new fit of @xmath2 as a function of @xmath3 . + the main aim of this work is to show , that @xmath2 is a function of single variable @xmath3 , rather than a function of two variables @xmath1 and @xmath0 , using the new set of @xmath2 given by the two - dimensional analysis , where the data is split into more regular @xmath1 and @xmath0 bins than in case of traditional presentation in form of @xmath1 - and @xmath0 - dependencies , this will allow to verify the results of our preceding work @xcite in more favourable conditions , i.e. to confirm that in electroproduction of hadrons in nuclear medium we indeed observe scaling , where @xmath3 takes over the role of the scaling variable . + this paper is organized as follows . nuclear attenuation in an absorption model is presented in the next section . in section 3 we discuss the choice of an appropriate form for the variable @xmath3 . section 4 presents results of the fit . conclusions are given in section 5 . |
in this paper we have constructed a new class of thin - shell wormholes from black holes in hoava - lifshitz gravity . the former enjoys a number of advantages for small values of the throat radius . pac numbers : 04.40.nr , 04.20.jb , 04.20.dw | c | 1011.3600 | in this paper we have constructed a new class of thin - shell wormholes from black holes in hoava - lifshitz gravity . particular emphasis is placed on those aspects that allow a comparison of hoava - lifshitz to einstein gravity . the former enjoys a number of advantages for small values of the throat radius . pac numbers : 04.40.nr , 04.20.jb , 04.20.dw | this paper discusses a new class of thin - shell wormholes from black holes in hoava - lifshitz gravity by employing the asymptotically flat kehagias - sfetsos ( ks ) solution with various values of the coupling constant @xmath25 and the mass @xmath117 . in all cases the radius of the outer event horizon in the ks case turns out to be less than that in the schwarzschild case . a wormhole designer from an advanced civilization would find several advantages in the ks case over the schwarzschild case : for small values of the throat radius @xmath32 , the negative energy density of the thin shell is well below that in the schwarzschild case . the lateral pressure is also less . a particularly interesting finding is that for small values of @xmath33 , the amount of exotic matter required can be much less for a ks than for a schwarzschild wormhole , a considerable advantage given the problematical nature of exotic matter . as @xmath33 gets large , however , the properties of the ks wormhole approach those of the schwarzschild wormhole . a similar conclusion holds for the equation of state , assumed to be of the form @xmath118 : while @xmath119 for small @xmath33 , in both gravitational theories @xmath63 as @xmath120 . while both types of wormholes are attractive , the acceleration toward the center is less for the ks case than for the schwarzschild case , a particular advantage for a traveler . the final topic is a discussion of the stability to linearized radial perturbations in terms of a parameter @xmath94 , normally interpreted as the speed of sound , but which may be just a convenient parameter . it was found that stable solutions exist in the ks case for values of @xmath94 that are similar to the values in the schwarzschild case . p. hoava , arxiv:0811.2217 [ hep - th ] ; p. hoava , jhep * 903 * , 20 ( 2009 ) [ arxiv:0812.4287 [ hep - th ] ] ; p. hoava , phys . d * 79 * , 084008 ( 2009 ) [ arxiv:0901.3775 [ hep - th ] ] ; p. hoava , arxiv:0902.3657 [ hep - th ] . mu - in park , jhep * 09 * , 123 ( 2009 ) . e. poisson and m. visser , phys . d * 52 * , 7318 ( 1995 ) . a. kehagias and k. sfetsos , phys . b * 678 * , 123 ( 2009 ) . h. lu , j. mei and c. n. pope , arxiv:0904.1595 [ hep - th ] . m. visser , nucl . b 328 , 203 ( 1989 ) . f.s.n . lobo and p. crawford , class . * 21 * , 391 ( 2004 ) . lobo , class . * 21 * , 4811 ( 2004 ) . eiroa and g. romero , gen . . grav . * 36 * , 651 ( 2004 ) . eiroa and c. simeone , phys . d * 70 * , 044008 ( 2004 ) . eiroa and c. simeone , phys . rev . d * 71 * , 127501 ( 2005 ) . m. thibeault , c. simeone , and e.f . eiroa , gen . . grav . * 38 * , 1593 ( 2006 ) . f.s.n . lobo , phys . d * 71 * , 124022 ( 2005 ) . f. rahaman et al . . grav . * 38 * , 1687 ( 2006 ) . eiroa and c. simeone , phys . d * 76 * , 024021 ( 2007 ) . f. rahaman et al . d * 16 * , 1669 ( 2007 ) . f. rahaman et al . * 39 * , 945 ( 2007 ) . f. rahaman et al . , chin . j. phys . * 45 * , 518 ( 2007 ) arxiv:0705.0740 [ gr - qc ] m. g. richarte and c. simeone , phys . d * 76 * , 087502 ( 2007 ) . j. p. s. lemos and f.s.n . lobo , phys . rev d * 78 * , 044030 ( 2008 ) . f. rahaman et al . , acta phys . polon . b * 40 * , 1575 ( 2009 ) arxiv : gr - qc/0804.3852 . f. rahaman et al . , a * 24 * , 53 ( 2009 ) arxiv : gr - qc/0806.1391 . eiroa , phys . d * 78 * , 024018 ( 2008 ) . eiroa , m.g . richarte , and c. simeone , phys . a * 373 * 1 ( 2008 ) . f. rahaman , k a rahman , sk.a rakib , peter k.f . kuhfittig , int . 49 * , 2364 ( 2010 ) . e - print : arxiv:0909.1071 [ gr - qc ] a.a . usmani , z. hasan , f. rahaman , sk.a . rakib , , saibal ray , peter k.f . kuhfittig , gen . . gravit . * 42 * , 2901 ( 2010 ) e - print : arxiv:1001.1415 [ gr - qc ] m. visser , _ lorentzian wormholes@xmath121from einstein to hawking _ ( american institute of physics , new york , 1995 ) . |
the average kinetic energy of chain - end particles of these systems is larger than that of other particles , which is similar to the behavior observed for systems made of masses connected by rigid links . the energetic motion of the end particles is , however , transient , and the system relaxes to thermal equilibrium after a while , where the average kinetic energy of each particle is the same , that is , equipartition of energy is achieved . the timescale is also estimated using the boltzmann - jeans theory and is found to be in quite good agreement with that obtained by the simulation . | r | 1003.3710 | in this study , one - dimensional systems of masses connected by springs , i.e. , spring - chain systems , are investigated numerically . the average kinetic energy of chain - end particles of these systems is larger than that of other particles , which is similar to the behavior observed for systems made of masses connected by rigid links . the energetic motion of the end particles is , however , transient , and the system relaxes to thermal equilibrium after a while , where the average kinetic energy of each particle is the same , that is , equipartition of energy is achieved . this is in contrast to the case of systems made of masses connected by rigid links , where the energetic motion of the end particles is observed in equilibrium . the timescale of relaxation estimated by simulation increases rapidly with increasing spring constant . the timescale is also estimated using the boltzmann - jeans theory and is found to be in quite good agreement with that obtained by the simulation . | next , we briefly summarize the relation between our numerical simulation and thermal equilibrium . under most of the initial conditions considered for the present simulations , the system undergoes chaotic motion . since the model has no conserved quantities other than the total energy , one may think that the states of the system attained in the course of a long - duration are well approximated by a microcanonical distribution . in that case , the distribution of the state of each particle in the chain can be approximated by a canonical distribution at a certain temperature , by considering the other particles in the chain as a heat bath . that is , the long - term average of kinetic energy of each particle , @xmath40 , is equal to thermal average @xmath41 . then , according to the principle of equipartition of energy , the average kinetic energy of each particle is the same : @xmath42 where @xmath43 , @xmath44 , @xmath45 is the boltzmann constant , and @xmath46 is the temperature . since our aim is to investigate the property of relaxation to equipartition , we define the following quantity in order to measure how close the system is to equipartition : @xmath47 ^ 2 \ , .\ ] ] if @xmath48 , then @xmath49 for all @xmath5 . similar quantities have been used to measure the degree of equipartition in studies on a supercooled liquid @xcite , self - gravitating systems @xcite , and proteins @xcite . vs. @xmath50 for @xmath51 . plots are measured at 10 successive times : @xmath53 ( blue circles ) , @xmath54 ( red squares ) , @xmath55 ( yellow diamonds ) , @xmath56 ( green triangles ) , and @xmath57 ( blue inverted triangles ) . the time step of integration @xmath58 . the initial conditions are @xmath59 , @xmath60 , @xmath61 , and @xmath62 , @xmath63 @xmath64 . ] figure [ fig : ki - vs - t - for - k-1e4 ] shows the time evolution of the profile of @xmath65 . it is clearly observed that in the initial stage of the time evolution , the average kinetic energy of all particles is not equal ; rather , particles near both the ends of the chain have a larger average @xmath66 . the profile is similar to that of the rigid link , i.e. , the planar chain model @xcite . then , as time progresses , differences in average @xmath66 among particles gradually decrease and tend to zero , and equipartition is achieved . for @xmath67 ( blue circles ) , @xmath68 ( red squares ) , @xmath69 ( yellow diamonds ) , and @xmath70 ( green triangles ) . the other parameters and initial conditions are the same as those mentioned in the caption of fig . [ fig : ki - vs - t - for - k-1e4 ] . the dashed line represents @xmath71 . ] figure [ fig : delta - vs - t - k1e4 ] shows the relaxation of @xmath72 [ eq . ( [ eq : delta ] ) ] for the data considered in fig . [ fig : ki - vs - t - for - k-1e4 ] . we observe that the system relaxes to equilibrium with the progress of time . the physical process of relaxation can be understood by examining the kinetic energy in greater detail . we rewrite the hamiltonian as @xmath73 where @xmath74 ( blue circles ) and @xmath75 ( red squares ) . @xmath52 , @xmath76 , and @xmath77 . @xmath78 the initial conditions are @xmath79 , @xmath60 , @xmath61 , @xmath80 ( @xmath81 ) , and @xmath63 @xmath82 . ] if equipartition is achieved , @xmath83 , because the model has the same number of springs and angles . figure [ fig : delta - kvib - krot - vs - t ] shows the temporal evolution of @xmath84 and @xmath85 for @xmath86 . here , the time average with two arguments , @xmath87 , is defined as @xmath88 and @xmath89 ^ 2 \ , .\ ] ] we find that the system relaxed to equipartition on a timescale similar to that on which the rotational energy @xmath90 transformed into vibrational energy @xmath91 . as mentioned earlier , the aim of this study is to examine the property of relaxation to equipartition of energy for the model expressed in eq . ( [ eq : spring - chain ] ) . first , for each sample orbit starting from different initial condition , we define the relaxation time @xmath92 as the time required for @xmath72 to decay below a critical value @xmath93 . we define the average relaxation time over @xmath94 orbits as @xmath95 this time is a measure of the relaxation time to equipartition . dependence of average relaxation time @xmath13 . at each @xmath11 value , 15 samples are taken . threshold value @xmath96 . the time step @xmath97 of integration is scaled as @xmath98 . the error bars represent standard deviations of @xmath92 for 15 samples . the dashed line shows @xmath99 obtained by fitting . ] figure [ fig : log - trelax - vs - sqrt - k ] shows the plot of the dependence of @xmath13 on the spring constant @xmath11 . we observe that as the stiffness of the spring increases , the relaxation time increases rapidly . that is , systems with hard springs or a steep potential show rigid - like behavior of energetic particles near the chainends for a very long time , as shown in fig . [ fig : ki - vs - t - for - k-1e4 ] , before relaxing to equipartition . here , we mention a technical detail about the numerical integration used for obtaining the plot in fig . [ fig : log - trelax - vs - sqrt - k ] . with increasing spring constant @xmath11 , the period of bond - stretching vibration decreases in proportion to @xmath100 . therefore , for large values of @xmath11 , the magnitude of the time step of numerical integration should be reduced . we confirmed that @xmath13 converges at @xmath101 for @xmath102 . thus , we used @xmath98 for each @xmath11 . on changing the initial conditions , the relaxation time @xmath103 changes , and we obtain a distribution of @xmath92 , denoted as @xmath104 . for @xmath105 ( blue circles ) and @xmath86 ( red squares ) for each value of @xmath11 , the numbers of samples are 200 . both distributions are shown on a semi - log scale . the dashed lines show @xmath106 . for @xmath105 , @xmath107 and @xmath108 . for @xmath86 , @xmath109 and @xmath110 . ] figure [ fig : hist - trelax ] shows the distribution of @xmath13 for @xmath111 and @xmath105 . for both cases , the histograms show exponential decay expressed as @xmath112 which suggests the existence of a characteristic timescale for the relaxation . next , we analyze the results of the abovementioned calculation using the concept of the boltzmann - jeans theory ( also known as boltzmann - jeans conjecture ) @xcite . the essence of this theory is roughly described as follows . ( for a detailed description of the theory please refer to @xcite . ) suppose we have a system described by a hamiltonian , which has two subsystems @xmath113 and @xmath114 , their typical time scale being @xmath115 and @xmath116 , respectively . here , subscripts @xmath117 and @xmath118 denote `` fast '' and `` slow , '' respectively . let us call @xmath113 and @xmath114 as a `` fast subsystem '' and `` slow subsystem , '' respectively . if the timescales of the fast and slow subsystems differ greatly , i.e. , @xmath119 , then the timescale for the occurrence of energy exchange between these two subsystems is on the order of @xmath120 that is , energy exchange occurs after a long time . in the case of the spring - chain system [ eq . ( [ eq : spring - chain ] ) ] with a large spring constant @xmath11 , the fast and slow subsystems correspond to bond vibration and relative rotation , respectively . since the typical timescale of bond vibration is on the order of @xmath121 and that of rotation is assumed to be constant , we have @xmath122 since the relaxation to equipartition occurs by energy transfer from rotation to vibration ( as we observed before ) , we can consider that @xmath123 mentioned above is essentially the same as the relaxation time @xmath13 : @xmath124 now , we examine whether @xmath13 obtained by the simulation obeys eq . ( [ eq : timescale - relax ] ) . the result is already shown in fig . [ fig : log - trelax - vs - sqrt - k ] . @xmath125 is proportional to @xmath126 ; therefore the interpretation by the boltzmann - jeans theory is appropriate . this theory can also be used for interpreting the histogram of @xmath92 . since @xmath13 is defined from the average of a number of samples , we have @xmath127 where @xmath128 is the distribution of @xmath92 . if we adopt the exponential form for the distribution @xmath129 [ eq . ( [ eq : hist - exp ] ) ] , then @xmath130 where @xmath131 is the coefficient that appears in eq . ( [ eq : hist - exp ] ) . combining eqs . ( [ eq : timescale - relax ] ) and ( [ eq : t - relax - alpha ] ) , the relation between the coefficient @xmath131 and the spring constant should be @xmath132 a comparison between the estimation [ eq . ( [ eq : alpha - vs - k ] ) ] and data is shown in figure [ fig : alpha - vs - k ] , from which we find that they are in good agreement . vs @xmath11 , obtained from 300 samples . the dashed line shows @xmath133 , where @xmath134 and @xmath135 . ] thus , the fact that relaxation to equilibrium takes quite a long time to occur can be interpreted as the outcome of the boltzmann - jeans theory . |
in this study , we performed monte carlo simulations of the @xmath0-potts model on quasiperiodic decagonal lattices ( qdl ) to assess the critical behavior of these systems . using the single histogram technique in conjunction with the finite - size scaling analysis , we estimate the infinite lattice critical temperatures and the leading critical exponents for @xmath1 and @xmath2 states . our estimates for the critical exponents on qdl are in good agreement with the exact values on 2d periodic lattices , supporting the claim that both the @xmath1 and @xmath2 potts model on quasiperiodic lattices belong to the same universality class as those on 2d periodic lattices . | c | 1405.7265 | in this study , we performed monte carlo simulations of the @xmath0-potts model on quasiperiodic decagonal lattices ( qdl ) to assess the critical behavior of these systems . using the single histogram technique in conjunction with the finite - size scaling analysis , we estimate the infinite lattice critical temperatures and the leading critical exponents for @xmath1 and @xmath2 states . our estimates for the critical exponents on qdl are in good agreement with the exact values on 2d periodic lattices , supporting the claim that both the @xmath1 and @xmath2 potts model on quasiperiodic lattices belong to the same universality class as those on 2d periodic lattices . | we performed monte carlo simulations of the @xmath0-potts model on qdl to estimate the infinite critical temperature and the leading critical exponents for both @xmath1 and @xmath2 states . our analysis reveals that for both @xmath1 and @xmath2 states , the infinite lattice critical temperature is higher than that of the square lattice , which can be attributed to the different geometric structure between the two models . for the @xmath1 potts model , the leading critical exponents @xmath7 , @xmath122 and @xmath123 are , within the error precision , in good agreement with the corresponding values for the 2d periodic lattices , whereas for the @xmath2 potts model , all the critical exponents are found to be very close to the exact values on the 2d periodic lattices . this provides strong evidence to support the claim that @xmath1 and @xmath2 potts model on quasiperiodic lattices belong to the same universality class as those on 2d periodic lattices . future work will involve numerical studies on 3d quasiperiodic lattices so that the icosahedral phase found in alloys such as @xmath3-@xmath243 , @xmath3-@xmath4 and @xmath3-@xmath244 can also be better investigated . |
, the order of hermite expansion for the equilibrium distribution function is found not to be correlated with the approximation order in terms of the knudsen number to the bgk equation , which was previously suggested by @xcite . the numerical simulation results confirm that the high - order terms in the discrete equilibrium distribution function play a negligible role . [ firstpage ] | i | 0908.4520 | in this work , we have theoretically analyzed and numerically evaluated the accuracy of high - order lattice boltzmann ( lb ) models for capturing non - equilibrium effects in rarefied gas flows . in the incompressible limit , the lb equation is proved to be equivalent to the linearized bhatnagar - gross - krook ( bgk ) equation . therefore , when the same gauss - hermite quadrature is used , lb method closely assembles the discrete velocity method ( dvm ) . in addition , the order of hermite expansion for the equilibrium distribution function is found not to be correlated with the approximation order in terms of the knudsen number to the bgk equation , which was previously suggested by @xcite . furthermore , we have numerically evaluated the lb models for a standing - shear - wave problem , which is designed specifically for assessing model accuracy by excluding the influence of gas molecule / surface interactions at wall boundaries . the numerical simulation results confirm that the high - order terms in the discrete equilibrium distribution function play a negligible role . meanwhile , appropriate gauss - hermite quadrature has the most significant effect on whether lb models can describe the essential flow physics of rarefied gas accurately . for the same order of the gauss - hermite quadrature , the exact abscissae will also modestly influence numerical accuracy . using the same gauss - hermite quadrature , the numerical results of both lb and dvm methods are in excellent agreement for flows across a broad range of the knudsen numbers , which confirms that the lb simulation is similar to the dvm process . therefore , lb method can offer flexible models suitable for simulating continuum flows at navier stokes level and rarefied gas flows at the linearized boltzmann equation level . [ firstpage ] | rarefied gas flows have recently attracted significant research interest due to the rapid development of micro / nano - fluidic technologies . gaseous transport in micro / nano devices is often found to be non - equilibrium , and non - equilibrium phenomena have not yet been well understood @xcite . the conventional theory to describe gas flows is the navier stokes equations , which assume that the fluid is in a quasi - equilibrium state . however , for non - equilibrium flows , the navier stokes equations break down because that the molecular nature of the gas strongly affects the bulk flow behavior i.e. the gas can no longer be regarded as a fluid continuum . whether gas flows are in local equilibrium or not can be classified by the non - dimensional knudsen number , kn , defined as the ratio of mean free path and the device characteristic length scale . the navier stokes equations with no - velocity - slip wall boundary condition are only appropriate when @xmath0 . however , gas flows in micro / nano - fluidic devices are often in the slip flow regime ( @xmath1 ) or the transition flow regime ( @xmath2 ) . in these regimes , the gas flow can not properly be described as a continuous flow , nor as a free molecular flow . in practice , most devices operate with a range of knudsen numbers in different parts of the device ; this makes it even more difficult to develop a generalized flow model . direct simulation monte carlo ( dsmc ) methods and direct numerical simulation of the boltzmann equation can provide accurate solutions for rarefied gas flows . however , these are computationally intractable for 3d flow systems , and impractical with the current computer technology , especially for the low speed gas flows usually encountered in micro / nano - systems . statistically , one needs to take significantly more samples of the flow field at any point for the dsmc method to resolve flows with low mach numbers . the direct simulations based on the boltzmann equation requires significant computational resources for integrating the velocity space ranging from @xmath3 to @xmath4 . in addition , it is usually difficult to solve the full boltzmann equation directly via either numerical or analytical methods . meanwhile , the continuum methods beyond the navier stokes level have failed to produce satisfactory results for gas flows in the transition flow regime @xcite . it is well - known that continuum expressions for the viscous stress and heat flux in gases may be derived from the fundamental boltzmann equation via either a kn - series solution ( known as the chapman - enskog approach ) or by an expansion of the distribution function as a series of hermite tensor polynomials @xcite . to first order ( i.e. for near - equilibrium flows ) both approaches yield the navier stokes equations . however , the solution methods can be continued to second and higher orders , incorporating more and more of the salient characteristics of a non - equilibrium flow . the classical second - order stress and heat flux expressions are the burnett equations ( from the chapman - enskog approach ) , and the grad 13-moment equations ( from the hermite polynomial method ) @xcite . these can be seen as corrections to the navier stokes constitutive relations to make them more appropriate to continuum - transition flows . however , different physical interpretations of the solution methods at second and higher orders have recently led to a variety of sets of equations , including the bhatnagar - gross - krook ( bgk)-burnett@xcite , eu @xcite , augmented burnett @xcite , and regularized moment ( r13)@xcite equations . while each purports to be the proper high - order correction to the stress and heat flux ( there is no disagreement about the form of the navier stokes equations at first - order ) , none of these models are satisfactory @xcite . in addition , these models suffer unknown additional boundary conditions at solid walls to appropriately reflect gas molecule / wall surface interactions . the lattice boltzmann ( lb ) approach offers an alternative method for rarefied gas flow simulations . historically , the lb model was evolved from the lattice - gas automata ( lga ) for mimicking the navier stokes hydrodynamics ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . over the past two decades , the lb method has been developed to provide accurate and efficient solutions for continuum flow simulations as the validity of the model can be ensured by the chapman - enskog expansion . due to its kinetic nature , the lb model has distinct advantages over the continuum computational methods , including easy implementation of multi - physical mechanisms and the boundary conditions for fluid / wall interactions . the potential of lb models for simulating rarefied gas flows have been demonstrated ( e.g. * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? recently , the lb models were shown to be able to be derived systematically from the boltzmann - bgk equation based on the hermite expansion ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? this creates another theoretical foundation different from the chapman - enskog expansion , so that higher - order lb approximations to the boltzmann - bgk equation beyond the navier stokes level can be constructed by using the high - order hermite expansion with appropriate quadratures . this indicates that high - order lb models have the potential to capture non - equilibrium effects in rarefied flows . in addition to the systemic framework of constructing lb models , @xcite also established the link between the orders of hermite polynomials and chapman - enskog expansion . the authors concluded that the order of hermite expansion is responsible for obtaining correct velocity moments . the precise relation among the orders of hermite expansion , chapman - enskog expansion and velocity moments was described by eq.(4.7 ) in @xcite . for instance , the third - order expansion is required for accurate pressure tensor and momentum at the navier stokes level . these conclusions are key to constructing appropriate lb models for non - equilibrium gas flows . however , the numerical simulations do not support these conclusions . in contrast , the simulation data showed that the higher order terms in the equilibrium distribution function have negligible influence for low speed rarefied flows . this indicates that the hermite expansion order is not related to the order of chapman - enksog expansion , in contrary to the theoretical conclusions drawn by @xcite . in this work , we aim to answer this question whether the hermite expansion order is important for the lb method , as it is for the grad s moment method , to capture non - equilibrium effects in rarefied flows , especially at micro / nano - scales . furthermore , we will analyze theoretically and numerically the mechanisms that are important in constructing high - order lb models for rarefied gas dynamics . we will discuss the differences between the approaches of @xcite and grad s moment method . to help us to understand the modeling capability of the lb method for rarefied gas dynamics , we will also analyze the similarities and differences between the lb method and the discrete velocity method ( dvm ) of solving the bgk equation . in particular , we will prove that the hermite expansion order is not important for the flows that the linearized bgk equation can accurately describe . since the important nonlinear constitutive relations in the knudsen layer are still not captured satisfactorily @xcite , our numerical analysis will be based on a standing - shear - wave problem specifically designed by @xcite to exclude the effect of gas molecule / wall interactions , so we can concentrate on the model capabilities . |