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suppose given a based map @xmath9 of simply connected cw complexes . denote by @xmath10 the path component of the space of ( unbased ) maps @xmath11 consisting of those maps that are homotopic to @xmath4 . then evaluation at the basepoint of @xmath5 gives a based map @xmath12 . we refer to this map as the _ evaluation map_. we define the _ @xmath3th evaluation subgroup of @xmath4 _ to be the subgroup @xmath13 of @xmath2 . the famous gottlieb groups @xmath14 occur as the special case in which @xmath15 and @xmath16 @xcite . the gottlieb groups of a space have been much studied by homotopy theorists ( see @xcite for a survey of results and references ) . while many general results are known , explicit computation of @xmath17 appears difficult and is limited to a small number of sporadic examples . one reason that accounts in part for this difficulty is the fact that a map of spaces @xmath18 does not necessarily induce a corresponding homomorphism of gottlieb groups , since in general @xmath19 . in particular , attempts to study @xmath17 via a cell decomposition of @xmath5 are frustrated , since it is not clear what effect a cell attachment may have on the gottlieb groups . one tool for studying @xmath17 that attempts to circumvent this problem is the so - called _ @xmath8-sequence of a map _ , introduced by woo and lee in @xcite . the @xmath8-sequence of a map @xmath9 is a sequence @xmath20 of groups and homomorphisms that derives from the long exact homotopy sequence of the map @xmath4 . in this sequence , @xmath21 is the gottlieb group of @xmath5 , @xmath22 is the evaluation subgroup of @xmath4 introduced above , and the third term @xmath23 is a suitably defined relative " term . the @xmath8-sequence arises as follows . one has the following commutative diagram of spaces : @xmath24^{f _ * } \ar[d]_{\omega } & \map(x , y ; f)\ar[d]^{\omega}\\ x \ar[r]_{f } & y}\ ] ] now pass to the corresponding induced homomorphisms of homotopy groups . in a standard way , the induced homomorphisms of homotopy groups @xmath25 and @xmath26 can be fitted into the long exact homotopy sequences of the maps @xmath27 and @xmath4 respectively . then the evaluation maps induce maps of each term in the long exact sequences , resulting in a homotopy ladder . the @xmath8-sequence of the map @xmath4 is then the image of the top long exact homotopy sequence in that of the bottom . a portion of the @xmath8-sequence is shown here : @xmath28 \ar@{->>}[d]^{\omega_{\ # } } & \pi_{n}(\map(x , x;1 ) ) \ar@{->>}[d]^{\omega_{\ # } } \ar[r]^{(f_*)_{\ # } } & \pi_{n}(\map(x , y;f ) ) \ar@{->>}[d]^{\omega_{\ # } } \\ g^{rel}_{n+1}(y , x;f ) \ar@{^{(}->}[d ] \ar[r ] & g_{n}(x ) \ar@{^{(}->}[d ] \ar[r]^{f_{\ # } } & g_{n}(y , x;f ) \ar@{^{(}->}[d ] \\ \pi_{n+1}(f ) \ar[r ] & \pi_{n}(x ) \ar[r]^{f_{\ # } } & \pi_{n}(y ) } \ ] ] the homomorphisms in the @xmath8-sequence are restrictions of those in the long exact homotopy sequence of the map @xmath4 . therefore , the @xmath8-sequence forms a chain complex ( consecutive compositions are trivial ) . some general conditions are known under which the @xmath8-sequence is exact ( e.g. @xcite ) , but in general it is not exact ( e.g. @xcite ) . in this paper we bring the techniques of rational homotopy theory to bear on problems and questions concerning evaluation subgroups ( of a map ) in general , and the @xmath8-sequence in particular . our main goal is to expand the range of application of these techniques in this area . to this end , we are primarily concerned with establishing a suitable framework for considering such questions . at the same time , we obtain a number of results of interest in their own right . the paper is organized as follows : our main results are established in sections @xmath29 and @xmath30 . the basic result in section [ sec : deriv spaces ] is theorem [ thm : equivalence of squares ] , in which we identify the map induced on rational homotopy groups by the evaluation map @xmath31 . we describe this induced homomorphism as the map induced on homology by a map of complexes of derivations of the sullivan minimal models of @xmath5 and @xmath32 . theorem [ thm : equivalence of squares ] has a number of immediate corollaries . for instance , we obtain a characterization of the rationalized evaluation subgroups of a map ( corollary [ cor : rational eval subgp of f ] ) that extends a well known characterization , due to flix and halperin , of the ( rationalized ) gottlieb groups of a space in terms of derivations of its minimal model . in section [ sec : long exact sequences ] , we extend and amplify the basic result of theorem [ thm : equivalence of squares ] . we show that several related long exact sequences of rational homotopy groups are naturally expressed as long exact sequences in homology of derivation complexes of sullivan minimal models . in particular , we obtain a description , within the framework of derivation spaces , of the @xmath8-sequence of a map after rationalization . the results of this section are of interest in their own right and in several cases ( e.g. theorem [ thm : long exact seq of eval fib ] ) they are independent of the @xmath8-sequence . in section [ sec : examples ] , we use the framework established in sections @xmath29 and @xmath30 to study questions concerning the rationalized @xmath8-sequence . just as in the integral setting , the rationalized @xmath8-sequence is not exact in general . example [ ex : non - exact g - seq ] gives a simple example for which the rationalized @xmath8-sequence fails to be exact at each of the three types of term that occur . since non - exactness rationally implies non - exactness integrally , this example provides a new , complete example of the failure of exactness of the @xmath8-sequence . this example also shows that the framework established in sections @xmath29 and @xmath30 provides an effective setting in which to carry out explicit computations . by way of contrast , in theorem [ thm : exact g - seq ] we give one set of conditions under which the rationalized @xmath8-sequence is exact . in theorem [ thm : h^omega=0 ] we show that under certain circumstances , the rationalized @xmath8-sequence may be exact at all occurrences of one type of term , while failing to be exact at the other types of term . this same result establishes a relationship , albeit under rather restrictive circumstances , between the ( vanishing of a certain type of the ) @xmath33-homology of a map @xmath34 and the ( vanishing of ) negative - degree derivations of the rational cohomology of @xmath5 . the last development that we present in section [ sec : examples ] is a connection between the @xmath8-sequence of certain fibre inclusion maps and a well - known conjecture in rational homotopy theory . let @xmath35 be a fibration with base an odd - dimensional sphere . for certain types of fibre space @xmath5 , a conjecture of halperin asserts that the fibration should be rationally tncz ( see conjecture [ conj : halperin ] below ) . in theorem [ thm : halperin g - trivial ] , we show that this is the case exactly when the rationalized @xmath8-sequence of the fibre inclusion @xmath36 reduces to a certain short exact sequence . in this way , we obtain an equivalent phrasing of the conjecture of halperin , in terms of the ideas studied in this paper . finally , in a technical appendix , we give full details for several results from rational homotopy theory used in the proof of theorem [ thm : equivalence of squares ] . we next discuss existing results on rational homotopy , function spaces , and the gottlieb groups of a space that relate to this paper . our aim in this discussion is to indicate the basic results that exist in the area . at the same time , we identify how these results relate to our work , and our points of departure from them . from results in rational homotopy theory , we can identify three tributary streams " that flow into this work precisely at theorem [ thm : equivalence of squares]our first main result at varying levels of generality . there is also a fourth tributary flowing into our work , from outside rational homotopy theory , that includes the work on the @xmath8-sequence . the first tributary of antecedent results in rational homotopy theory concerns the rationalized gottlieb groups of a space . in @xcite , flix and halperin gave a characterization of the rationalized gottlieb groups of a space , in terms of derivations of the sullivan minimal model . at its most specialized level , theorem [ thm : equivalence of squares ] retrieves this characterization ( corollary [ cor : rational gottlieb group ] ) and extends it to a similar characterization of the rationalized evaluation subgroups of a general map ( corollary [ cor : rational eval subgp of f ] ) . flix and halperin went on to prove a remarkable result concerning the rationalized gottlieb groups of a finite complex ( * ? ? ? * th.iii ) . their result significantly extends results of gottlieb from @xcite , and relates the rationalized gottlieb groups with the rational lusternik - schnirelmann category . unfortunately , no analogous result seems forthcoming for the rationalized evaluation subgroups of a map . nonetheless , our characterization of the rationalized evaluation subgroups of a map is as effective for concrete computations as is the earlier characterization of the rationalized gottlieb groups . the second tributary concerns the rational homotopy type of @xmath37the classifying space for fibrations with fibre @xmath5 . although we are not concerned with this classifying space as such , the connection arises because we have an isomorphism of homotopy groups @xmath38 , and also the gottlieb groups of @xmath5 are obtained as the image in homotopy groups of the connecting homomorphism of the corresponding classifying fibration ( * ? ? ? * th.2.6 ) . at a higher level of generality than the rationalized gottlieb groups , theorem [ thm : equivalence of squares ] includes an identification of the map induced on rational homotopy groups by the evaluation map @xmath39 , and in particular it identifies the rational homotopy groups of @xmath40 . whilst the identification of these groups we give is familiar in rational homotopy theory , our proof for this obtained by restricting that of theorem [ thm : equivalence of squares]is the first direct and detailed one that has actually appeared in the literature . we support this assertion as follows : in ( * ? ? ? * sec.11 ) , sullivan sketched ( with no proof ) a model for the rational homotopy type of @xmath37 , from which the description of the rational homotopy groups of @xmath40 contained in theorem [ thm : equivalence of squares ] follows . a justification of sullivan s model for @xmath37 may be gleaned by collating results from a number of sources spread through the literature ( e.g. @xcite ) . but to date , no direct proof of sullivan s model has been given . even amongst those articles that focus specifically on the rational homotopy _ groups _ , either of @xmath37 or of @xmath41and that therefore avoid the technical problems of dealing with the rational homotopy _ type_we still do not find complete details . meier ( * ? ? ? * ( 1.4 ) , ( 2.6 ) ) outlines the basic idea , but is actually focussed on a special kind of situation in which the minimal model can be replaced by its cohomology . grivel @xcite focusses on the same special case as meier , and quotes sullivan s model directly . flix and thomas ( * ? ? ? * sec.2.3 ) give exactly the description of the rational homotopy groups of @xmath40 contained in theorem [ thm : equivalence of squares ] , but no details of the proof are given . as well as including a direct and detailed proof for the case of @xmath40 , theorem [ thm : equivalence of squares ] extends this identification of the rational homotopy groups to the general case of @xmath10 . it thus provides a natural framework for the study of rational homotopy groups of function spaces . finally , the third tributary from rational homotopy theory consists of a model , due to sullivan and haefliger , for the rational homotopy type of @xmath10 . at its full level of generality , theorem [ thm : equivalence of squares ] identifies the map induced on rational homotopy groups by @xmath42 , a general evaluation map . the precursor to the identification we give , and to our general line of proof , is the approach of thom in @xcite , although obviously there is no reference to minimal models in his work . pursuing the river analogy a little further , we may think of thom s result , if not as the source , then at least as somewhere in the headwaters . we emphasize the connection between theorem [ thm : equivalence of squares ] and thom s approach by retrieving a basic result of his in corollary [ cor : thom ] . coming further downstream , sullivan also described in ( * ? ? ? * sec.11 ) a model for the space of sections of a fibration homotopic to a given section . by specializing to the trivial fibration @xmath43 , this yields a model for the function space @xmath10and more generally a model for the rational homotopy _ type _ of the general evaluation map @xmath33 . a detailed proof for sullivan s model in this case was given by haefliger @xcite . now this model should in principle determine the rational homotopy groups of the function space ( see @xcite and @xcite , where it is used quite effectively ) . however , the model in question is a ( non - minimal ) dg algebra model . therefore , the homomorphism induced by @xmath33 on rational homotopy groups which is exactly the information we require to proceed with our development is available only indirectly , at best . by focussing on the rational homotopy _ groups_as opposed to the rational homotopy type , we have arrived in theorem [ thm : equivalence of squares ] at an entirely new characterization of the map induced on rational homotopy groups by @xmath31 . furthermore , we have been able to give a direct proof that avoids many of the technical complexities of haefliger s work and is completely independent of it . the remaining tributary flowing into our work comes from outside rational homotopy theory , and concerns classical results on the gottlieb groups of a space , and more recent results on evaluation subgroups of a map and the @xmath8-sequence . we have already mentioned some of the results in this area . in his original work on evaluation subgroups , gottlieb observed that a map of spaces does not necessarily induce a map of gottlieb groups , and gave conditions under which it does ( * ? ? ? * sec.1 ) . gottlieb briefly mentions the evaluation subgroups of a map in @xcite , but did not study them as such . a number of basic properties of the evaluation subgroup of a map are established in @xcite . as we mentioned earlier , woo and lee introduced the @xmath8-sequence of a map in @xcite . results on the @xmath8-sequence basically fall into one of three areas : conditions under which the @xmath8-sequence is exact ( e.g. ( * ? ? ? * th.12 ) and @xcite ) , examples of non - exactness ( e.g. @xcite and @xcite ) , and extensions and generalizations of evaluation subgroups and the @xmath8-sequence ( e.g. @xcite ) . these results give the stepping - off point for our work in sections 3 and 4 . using our description of the rationalized @xmath8-sequence ( theorem [ thm : g - seq of f ] ) , we extend the known exactness results to several new cases . we also give new instances of non - exactness . more significantly , by focussing on the rational setting , our methods make the production of such examples straightforward . on the other hand , our results and examples are not restricted to amplifying previous results in this area . in corollary [ cor : g - sequence halperin ] , we suggest a different kind of result that relates properties of the @xmath8-sequence to the triviality of a fibration . furthermore , some results in section 3including theorem [ thm : long exact seq of f _ * ] and theorem [ thm : long exact seq of eval fib]are of interest independently of any relation to the @xmath8-sequence . we finish this introduction by setting some notation and terminology . throughout this paper , @xmath5 and @xmath32 will denote simply connected cw complexes of finite type . by _ vector space _ we mean a rational graded vector space . by _ algebra _ , we mean the kind of commutative graded algebras over the rationals that arise in rational homotopy . that is , they are non - negatively graded , connected ( @xmath44 ) and usually simply connected ( @xmath45 ) , with cohomology of finite type . for a vector space @xmath46 , we denote the free commutative graded algebra generated by @xmath46 by @xmath47 . we use the acronym dg to denote differential graded : thus , dg vector space , dg algebra , and so - forth . for a dg algebra , the differential is of degree @xmath48 . in other situations , however , particularly when we consider the complex of derivations of a dg algebra , the differential is of degree @xmath49 . we will generally refer to a dg vector space whose differential is of degree @xmath49 as a chain complex . if @xmath50 is a map , either topological or algebraic , then @xmath51 denotes pre - composition by @xmath4 and @xmath27 denotes post - composition by @xmath4 . in any setting in which it is appropriate , we use @xmath52 to denote the map induced on homology ( or cohomology ) by @xmath4 , and @xmath26 to denote the map induced on homotopy groups by the map of spaces @xmath4 . a map of dg algebras is called a _ quasi - isomorphism _ if it induces an isomorphism on cohomology . we use @xmath33 in a generic way to denote an evaluation map , and we denote the identity map of a topological space or the identity homomorphism of an algebra by @xmath53 . we denote the rationalization of a space @xmath5 by @xmath54 and of a map @xmath4 by @xmath55 ( cf . @xcite ) . we assume that the reader is familiar with the basics of rational homotopy . our general reference for this material is @xcite . we recall , in particular , that a space @xmath5 has a _ minimal model _ @xmath56 , which is a certain type of dg algebra . namely , @xmath56 is a free algebra @xmath47 with a decomposable differential , that is , @xmath57 . furthermore , a map of spaces @xmath58 induces a map of minimal models @xmath59 . we refer to this induced map as the _ sullivan minimal model _ of the map @xmath4 . it is a complete rational homotopy invariant for a map , and in principle all rational homotopy theoretic information about @xmath4 can be retrieved from it . passing to cohomology , for example , gives @xmath60 , which corresponds to the homomorphism of rational cohomology algebras induced by @xmath4 . the results of this paper illustrate how deeper information about a space or map may be retrieved from the minimal model by making correspondingly more sophisticated constructions with the model .

let @xmath0 be a based map of simply connected spaces . the @xmath3th gottlieb group of @xmath5 occurs as the special case in which @xmath6 and @xmath7 . we identify the homomorphism induced on rational homotopy groups by this evaluation map , in terms of a map of complexes of derivations constructed using sullivan minimal models . our identification allows for the characterization of the rationalization of the @xmath3th evaluation subgroup of @xmath4 . this is a sequence in general not exact of groups and homomorphisms that includes the gottlieb groups of @xmath5 and the evaluation subgroups of @xmath4 . we give new examples of non - exact @xmath8-sequences and uncover a relationship between the homology of the rational @xmath8-sequence and negative derivations of rational cohomology . we also relate the splitting of the rational @xmath8-sequence of a fibre inclusion to a well - known conjecture in rational homotopy theory .

let @xmath0 be a based map of simply connected spaces . the corresponding evaluation map @xmath1 induces a homomorphism of homotopy groups whose image in @xmath2 is called the @xmath3th evaluation subgroup of @xmath4 . the @xmath3th gottlieb group of @xmath5 occurs as the special case in which @xmath6 and @xmath7 . we identify the homomorphism induced on rational homotopy groups by this evaluation map , in terms of a map of complexes of derivations constructed using sullivan minimal models . our identification allows for the characterization of the rationalization of the @xmath3th evaluation subgroup of @xmath4 . it also allows for the identification of several long exact sequences of rational homotopy groups , including the long exact sequence induced on rational homotopy groups by the evaluation fibration . as a consequence , we obtain an identification of the rationalization of the so - called @xmath8-sequence of the map @xmath4 . this is a sequence in general not exact of groups and homomorphisms that includes the gottlieb groups of @xmath5 and the evaluation subgroups of @xmath4 . we use these results to study the @xmath8-sequence in the context of rational homotopy theory . we give new examples of non - exact @xmath8-sequences and uncover a relationship between the homology of the rational @xmath8-sequence and negative derivations of rational cohomology . we also relate the splitting of the rational @xmath8-sequence of a fibre inclusion to a well - known conjecture in rational homotopy theory .

1206.3007

i

let @xmath11 be an integer and @xmath4:=\{1,2,\dots , n\}$ ] . by @xmath12}$ ] we denote the family of all subsets of @xmath4 $ ] and by @xmath13}k$ ] the family of all @xmath14-subsets of @xmath4 $ ] . a family @xmath15}$ ] is an _ antichain _ if @xmath5 for all distinct @xmath16 . an antichain @xmath17 is called _ flat _ if it is contained in two consecutive levels of @xmath12}$ ] , i.e. if @xmath18}{k}\cup\tbinom{[n]}{k+1}$ ] for some @xmath14 . more generally , for a subset @xmath19 $ ] , we call @xmath17 a _ @xmath1-antichain _ if it contains only @xmath14-sets with @xmath20 , i.e. @xmath21 where @xmath22}{k}$ ] . the _ dual _ @xmath23 of a family of sets @xmath24 is the collection @xmath25 of subsets of @xmath26 $ ] given by @xmath27\ : \ i \in a_j\}$ ] for @xmath28 $ ] . it is well known that a family of sets @xmath17 is an antichain if and only if its dual @xmath23 is a _ completely separating system _ ( css ) : a css is a collection @xmath29 of blocks of @xmath4 $ ] such that for each @xmath30 $ ] there are blocks @xmath31 with @xmath32 and @xmath33 . the dual of a flat antichain on @xmath13}{k } \cup \binom{[n]}{k-1}$ ] is a _ fair css _ : a css in which each point occurs exactly @xmath14 or @xmath34 times . the consideration of minimum size csss led to a conjecture which subsequently became the _ flat antichain theorem _ , which follows from results of lieby @xcite ( see also @xcite ) and kisvlcsey @xcite . this theorem greatly reduced the computational search space for csss . it says that for every antichain @xmath17 there is an equivalent flat antichain @xmath35 , where the equivalence relation is defined by : @xmath35 is equivalent to @xmath17 if and only if @xmath36 and @xmath37 . griggs et al . @xcite showed that the flat antichains minimize the _ blym - values _ @xmath38 within their equivalence classes , and more generally , they minimize ( maximize ) @xmath39 for every convex ( concave ) function @xmath40 . csss have applications in various areas including coding theory , search theory , and topology . see @xcite and @xcite for applications and further references for csss . a @xmath1-antichain @xmath17 is called a _ maximal @xmath1-antichain _ if there is no @xmath1-antichain @xmath35 with @xmath41 . for @xmath42 , any @xmath43-antichain is also a @xmath1-antichain , and if it is a maximal @xmath1-antichain , then it is also a maximal @xmath43-antichain . the converse is not true as can be seen by the family @xmath44 for @xmath45 , which is a maximal @xmath46-antichain but not a maximal @xmath47-antichain , since @xmath48 is an antichain properly containing @xmath17 . this example is illustrated in figure [ fig : maximality ] , showing a graph on 9 vertices whose edge set is the complement of @xmath49 in @xmath50}{2}$ ] , while the set of 4-cliques is precisely @xmath51 . -antichain which is not maximal as a @xmath47-antichain , and thus also not strongly maximal . ] we also call a @xmath1-antichain @xmath17 _ strongly maximal _ if it is maximal as an antichain , not just as @xmath1-antichain , i.e. if there is no antichain @xmath35 with @xmath41 . equivalently , @xmath17 is a strongly maximal @xmath1-antichain if it is also a maximal @xmath52-antichain , where @xmath14 and @xmath53 are the smallest and the largest element of @xmath1 , respectively . in this paper , we always assume @xmath54 and @xmath55 , and we study the problem of determining the smallest possible cardinality of a maximal @xmath1-antichain . our approach to the minimum size of a maximal antichain is based on the graph interpretation which was used in @xcite to completely resolve the problem for the case @xmath56 . to prove our asymptotic results we adapt arguments from @xcite where lower bounds for the size of maximal @xmath57-antichains were proved . the main tool in this part is the graph removal lemma . let @xmath58 be a graph on @xmath59 vertices and let @xmath60 . then there exists @xmath61 such that every graph @xmath62 on @xmath63 vertices containing at most @xmath64 copies of @xmath58 can be made @xmath58-free by removing @xmath65 edges . this was proved , using szemerdis regularity lemma , first for @xmath58 being a triangle @xcite and later in general @xcite . see @xcite for a recent proof avoiding the regularity lemma , and thus improving the bounds on @xmath66 significantly . the paper is organized as follows . in section [ sec : graph ] the problem is reformulated as a question in extremal graph theory . in section [ sec : construction ] we describe a construction for graphs , which we believe to correspond to optimal antichains . some evidence for this conjecture is provided by exhaustive search results for @xmath10 and small @xmath63 which are presented in section [ sec : small_n ] . section [ sec : asymptotics ] contains our asymptotic results : if @xmath7 our construction yields the correct leading term , and for @xmath10 we prove a first nontrivial bound . finally , in section [ sec : problems ] we suggest some open problems for further investigations .

let @xmath0 be a natural number , and let @xmath1 be a set @xmath2:=\{1,2,\dots , n\}$ ] . we study the problem to find the smallest possible size of a maximal family @xmath3 of subsets of @xmath4 $ ] such that @xmath3 contains only sets whose size is in @xmath1 , and @xmath5 for all @xmath6 , i.e. @xmath3 is an antichain . we present a general construction of such antichains for sets @xmath1 containing 2 , but not 1 . if @xmath7 our construction asymptotically yields the smallest possible size of such a family , up to an @xmath8 error . we conjecture our construction to be asymptotically optimal also for @xmath9 , and we prove a weaker bound for the case @xmath10 . our asymptotic results are straightforward applications of the graph removal lemma to an equivalent reformulation of the problem in extremal graph theory which is interesting in its own right . * keywords : * extremal set theory , sperner property , maximal antichains , flat antichains

let @xmath0 be a natural number , and let @xmath1 be a set @xmath2:=\{1,2,\dots , n\}$ ] . we study the problem to find the smallest possible size of a maximal family @xmath3 of subsets of @xmath4 $ ] such that @xmath3 contains only sets whose size is in @xmath1 , and @xmath5 for all @xmath6 , i.e. @xmath3 is an antichain . we present a general construction of such antichains for sets @xmath1 containing 2 , but not 1 . if @xmath7 our construction asymptotically yields the smallest possible size of such a family , up to an @xmath8 error . we conjecture our construction to be asymptotically optimal also for @xmath9 , and we prove a weaker bound for the case @xmath10 . our asymptotic results are straightforward applications of the graph removal lemma to an equivalent reformulation of the problem in extremal graph theory which is interesting in its own right . * keywords : * extremal set theory , sperner property , maximal antichains , flat antichains

1305.4974

i

the problem of community detection in networks has received wide attention @xcite . it has proved to be a problem of remarkable subtlety , computationally challenging and with deep connections to other areas of research including machine learning , signal processing , and spin - glass theory . a large number of algorithmic approaches to the problem have been considered , but interest in recent years has focused particularly on statistical inference methods @xcite , partly because they give excellent results , but also because they are mathematically principled and , at least in some cases , provably optimal @xcite . in this paper we study two of the most fundamental community inference methods , based on the so - called stochastic block model or its degree - corrected variant @xcite . we show that it is possible to map both methods onto the well - known minimum - cut graph partitioning problem , which allows us to adapt any of the large number of available methods for graph partitioning to solve the community detection problem . as an example , we apply the laplacian spectral partitioning method of fiedler @xcite to derive a community detection method competitive with the best currently available algorithms in terms of both speed and quality of results .

many methods have been proposed for community detection in networks . some of the most promising are methods based on statistical inference , which rest on solid mathematical foundations and return excellent results in practice . in this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum - cut graph partitioning problem , which allows us to apply any of the many well - understood partitioning algorithms to the solution of community detection problems . we illustrate the approach by adapting the laplacian spectral partitioning method to perform community inference , testing the resulting algorithm on a range of examples , including computer - generated and real - world networks . both the quality of the results and the running time rival the best previous methods .

many methods have been proposed for community detection in networks . some of the most promising are methods based on statistical inference , which rest on solid mathematical foundations and return excellent results in practice . in this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum - cut graph partitioning problem , which allows us to apply any of the many well - understood partitioning algorithms to the solution of community detection problems . we illustrate the approach by adapting the laplacian spectral partitioning method to perform community inference , testing the resulting algorithm on a range of examples , including computer - generated and real - world networks . both the quality of the results and the running time rival the best previous methods .

0804.1901

i

the location of the sun in the rim of the loop i superbubble has been inferred from radio continuum data , kinematical data on the flow of local ism away from the center of loop i , data on gas - phase abundances in local ism , and the coincidence of the velocity of ism inside and outside of the heliosphere . loop i is an evolved superbubble shell formed from stellar evolution in a subgroup of the sco - cen association , @xmath4 myrs ago ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? both the original dimensions found for the loop i bubble observed in 820 mhz @xcite , and more recent studies of ( * ? ? ? * ; * ? ? ? * h98a , h98b ) and @xcite , place the sun in or adjacent to the rim of a magnetic superbubble shell for an assumed spherical geometry . the 1.4 ghz wolleben study defines two magnetic subshells of loop i , s1 and s2 , with magnetic pole directions differing by @xmath5 . comparisons between the radio continuum filaments of loop i and optical polarization data indicate that the radio filaments at distances of @xmath6 pc trace magnetic field lines , indicating that optical polarization is a suitable tracer of magnetic shells ( h98a ) . both the kinematics and abundance pattern of local interstellar material ( lism ) suggest that the loop i remnant has expanded to the solar location @xcite . lism abundances of the refractory elements mg , fe , and ca , show the characteristic enhancement indicative of grain destruction in interstellar shocks @xcite . local interstellar gas , @xmath7 pc , and dust flow away from the center of loop i at a best - fit velocity of @xmath8 in the local standard of rest ( lsr , e.g. * ? ? ? the first spectrum of backscattered ly@xmath9 emission from interstellar hydrogen inside of the heliosphere showed that the velocity of interstellar inside of the heliosphere is comparable to lism velocities @xcite . together these data suggest that the magnetic field and spatial configuration of the lism can be used to test whether the loop i magnetic superbubble has expanded to the solar location . the @xcite model of the s1 and s2 shells provides enough detail to make preliminary comparisons between lism data and the properties of these shells . these comparisons provide interesting insights into the lism properties , and support the possibility that local ism within @xmath0 pc is dominated by the s1 and s2 shells . superbubble expansion into ambient ism with equal magnetic and thermal pressures yields roughly spherical superbubbles during early expansions stages when magnetic pressure is weak compared to the ram pressure of the expanding gas @xcite , and bubbles elongated along the ismf during late stages of evolution @xcite . the evolved shell is thicker near the ismf equatorial regions , where field strengths are larger due to flux freezing , than the polar regions of the shell where thermal pressure provides the main support for the shell . in media where magnetic pressure is weak , e.g. the ratio of thermal to magnetic pressure @xmath10 , the evolved bubble is more symmetric . supernovae in sco - cen association subgroups have contributed to the evolution of the loop i superbubble during the past @xmath11 myrs . the loop i superbubble ( and s1 , s2 ) expanded in a medium with a density gradient , because the initial supernova occurred in the molecular regions of the parent scorpius - centaurus association subgroups , while the subsequent bubble expansion occurred in the low density interior of the local bubble cavity @xcite . in this case the external plasma @xmath12 may have varied irregularly across the expanding shell , so that the topology of the present day s1 and s2 shells may deviate from axial symmetry as well as sphericity . the ismf direction at the heliosphere provides the most direct measure of whether the sun is embedded in the shell of the loop i superbubble . several phenomena trace the field direction the weak polarization of light from nearby stars ( * ? ? ? * ; * ? ? ? * hereafter f07 ) , the flield direction in the s1 subshell of loop i @xcite , the 3 khz emissions from the outer heliosheath detected by the two voyager satellites ( * ? ? ? * f07 ) , the observed angular offset between interstellar and flowing into the heliosphere @xcite , and the 10 pc difference between the distances of the solar wind termination shock detected by the two voyager satellites ( e.g. * ? ? ? the orientation of the plane midway between the hot and cold dipole moments of the cosmic microwave background is also within @xmath13 of the local ismf direction ( f07 ) . this paper searches for evidence that the s1 and s2 shells affect the distribution of nearby ism within @xmath0 pc . the topology of the s1 and s2 shells is discussed in [ sec : shells ] . section [ sec : mag ] shows that the direction of the ismf at the sun is consistent with the ismf direction in the s1 shell , similar to the location of the mid - plane between the cosmic microwave dipole moments , and consistent with the ismf direction inferred from heliosphere models . the distribution of the ism in the s1 and s2 shells are compared to column densities towards nearby stars behind the shells ( [ sec : feii ] ) . a similar comparison is made between the data and the s1 and s2 shells , however column densities appear instead to trace the strength of the local far ultraviolet ( uv ) diffuse radiation field ( [ sec : caii ] ) . an appendix outlines the ionization equilibrium of .

many studies of the loop i magnetic superbubble place the sun at the edges of the bubble . the result is that a model of loop i as composed of two spherical magnetic subshells remains a viable description of the distribution of nearby low density ism , but is not yet proven .

many studies of the loop i magnetic superbubble place the sun at the edges of the bubble . one recent study models the polarized radio continuum of loop i as two magnetic shells with the sun embedded in the rim of the s1 shell . if the sun is in such a shell , it should be apparent in both the local interstellar magnetic field and the distribution of nearby interstellar material . the properties of these subshells are compared to the interstellar magnetic field ( ismf ) and the distribution of interstellar and within @xmath0 pc of the sun . although the results are not conclusive , the ismf direction obtained from polarized stars within @xmath1 pc is consistent with the ismf direction of the s1 shell . the distribution of nearby interstellar with log @xmath2 is described equally well by a uniform distribution or an origin in spherical shell - like features . higher column densities of ( log @xmath3 ) tend to be better described by the pathlength of the sightline through the s1 and s2 subshells . column densities of the recombinant ion are found to increase with the strength of the interstellar radiation field , rather than with star distance or total pathlength through the two magnetic subshells . the ion can not be used to trace the distribution of local interstellar gas unless the spatial variations in the radiation field are included in the calculation of the ionization balance , in addition to possible abundance variations . the result is that a model of loop i as composed of two spherical magnetic subshells remains a viable description of the distribution of nearby low density ism , but is not yet proven .

0804.1901

c

the discussions in this paper are based on a search for evidence of the s1 and s2 shells in local ism data . the s1 and s2 shells are assumed to be spherical and complete . such simple assumptions are justified only in the initial stage of probing the ism distribution associated with a superbubble shell that has column densities too low for 21-cm measurements , and that has evolved into a very low density region of space . several studies model the formation of the local bubble in terms of the energy injected into the ism by supernovae in the sco - centaurus association @xcite , but the connection between the loop i radio emission and very local ism has never been established . the s1 and s2 shell models provide a basis for testing this connection . early optical polarization data @xcite indicate that the ismf direction close to the sun agrees with the s1 shell ismf direction once the uncertainties in wolleben s angle ( 2007 ) are included . in principle can be used to trace the ism distribution , since is arises in both neutral and ionized gas . detailed comparisons between line strengths towards nearby stars and the projected pathlength through the s1 and s2 shells towards that star support , but do not prove , that the lines arise in shells . both the and data indicate that the portions of the s1 and s2 shells with @xmath77 will be more highly ionized than in the opposite hemisphere . the data are not sufficient to distinguish an ionization gradient from an abundance gradient . for this reason , the shells are better traced using ions with first ionization potentials less than 13.7 ev . heating by radiation accounts for @xmath94% of the heating of the circumheliospheric ism , so shell regions exposed to the highest radiation flux should also be warmer ( an effect not explicitely included in the ca equilibrium discussion in the appendix ) . these models of the s1 and s2 shells assume spherically symmetric forms , which may be viable only for low density sightlines where magnetic and thermal pressures are comparable . interstellar data are compared mainly to the s1 shell , which has the most favorable geometry for surrounding the sun according to @xcite . the tinbergen data suggest a slow increase in polarizations with distance , and the position angles towards the nose are consistent with the optical polarization of more distant stars in loop i @xcite . the most distant shell regions , in the galactic center hemisphere , have expanded into the high - extinction gas beyond @xmath95 pc that is associated with the sco - cen association ( see e.g. figs . 1,3 in @xcite or fig . 2 in @xcite ) and show pronounced magnetic filaments ( h98a ) rather than a spherical shell geometry . heiles points out that the synchrotron - emission ridges of loop i follow the distortion of the nearby global ismf , as traced by polarization data , and that loop i is not a shell for the high density regions . the global ismf within several hundered parsecs is directed towards @xmath96 . the expansion of the nearest portions of the s1 shell in a uniform field would yield an ismf close to the sun directed upwards with respect to the galactic plane . @xcite model the properties of a magnetic superbubble @xmath97 myrs old and for the strong ismf case , where magnetic pressure dominates thermal pressure by a factor of @xmath98 . the superbubble cavity is elongated in the direction parallel to the ismf , where the shell is thinner . the shell is thicker and more extended in the radial direction , @xmath99 from the magnetic pole . the region of strongest polarization for the tinbergen sample is @xmath99 from the magnetic pole . non - uniform shell expansion , or a wrinkled shell , could explain the anomalous sightlines towards hd 120315 and hd 80007 ( see fig . [ fig : length ] compared to fig . [ fig : panels ] ) , while the tiny dense nearby leo cloud ( * ? ? ? * lauroesch private communication ) , and the exceptionally strong line towards rasalhague ( hd 159561 , @xmath9 oph ) may indicate a region of merging shells . the column densities for and are generally weaker for sightlines with @xmath100 , and stronger for stars with @xmath101 . this effect may be either from the distribution of ionized gas , or abundance variations for fe and ca . the effect is seen over small spatial scales of @xmath102 pc . if the variation is due to abundance differences , then the ism close to the sun would have two different histories , although the flow velocities are similar . the conclusions of this comparison between the s1 and s2 shells with lism markers can be briefly summarized : * the @xcite description of the loop i polarized radio continuum in terms of two shells , s1 and s2 , is viable and has sufficient detail to be tested against observational data . for example , when the the s1 and s2 shell parameters are varied within the allowed uncertainty range , the nearby cold gas filaments in leo @xcite are seen to be produced where the two shells merge or collide ( [ sec : shells ] ) . * the s1 shell magnetic field direction of @xcite , with = 42 , matchs the ismf direction derived from older polarization data @xcite of nearby stars near the ecliptic plane and heliosphere nose , but offset by up to @xmath103 from the heliosphere nose . the ismf direction implied by the s1 shell and polarization position angles together is directed towards , @xmath47 . * for low column densities , log @xmath2 , the strength of the is better described by the star distance . for higher column densities , log @xmath3 , the strength of the is better described by the pathlength of the sightline through the s1 and s2 shells . this result is based on a limited number of stars ( @xmath104 ) and requires confirmation using a larger data set ( [ sec : feii ] ) . * the illumination of the s1 shell by the strong diffuse far ultraviolet interstellar radiation field in quadrants iii and iv , @xmath77 , explains the higher column densities observed for and in these galactic quadrants ( [ sec : feii ] , [ sec : caii ] ) . an appendix evaluates the ionization equilibrium of features spaced around the shell , and shows that the local radiation field strength regulates the absorption line strengths . * the ismf direction at the heliosphere nose is within @xmath105 of the angle of the great circle that is midway between the hot and cold hemispheres of the cmb dipole moment , and that also bifurcates the heliosphere nose . * the s1/s2 shell model can be used to predict whether a star , or exoplanet system for example , is embedded in a cloud or in the local bubble plasma ( [ sec : feii ] ) . the reverse is also true , that measurements of astrosphere properties will help constrain the distribution of ism associated with the shells . * this scenario describing the influence of the magnetic superbubble s1 and s2 shells on the local ism , and as the origin of the interstellar magnetic field at the sun , is consistent with available data , but does not yet prove the s1/s2 model . two kinds of data are required to substantiate this picture : ( 1 ) additional uv observations of tracers of both neutral and ionized interstellar gas , e.g. , , and features . ( 2 ) measurements of nearby weak interstellar polarizations at 0.01% levels or better . the author would like to think nasa for research funding , in the form of grants nag5 - 13107 and nng05gd36 g to the university of chicago .

although the results are not conclusive , the ismf direction obtained from polarized stars within @xmath1 pc is consistent with the ismf direction of the s1 shell . higher column densities of ( log @xmath3 ) tend to be better described by the pathlength of the sightline through the s1 and s2 subshells .

many studies of the loop i magnetic superbubble place the sun at the edges of the bubble . one recent study models the polarized radio continuum of loop i as two magnetic shells with the sun embedded in the rim of the s1 shell . if the sun is in such a shell , it should be apparent in both the local interstellar magnetic field and the distribution of nearby interstellar material . the properties of these subshells are compared to the interstellar magnetic field ( ismf ) and the distribution of interstellar and within @xmath0 pc of the sun . although the results are not conclusive , the ismf direction obtained from polarized stars within @xmath1 pc is consistent with the ismf direction of the s1 shell . the distribution of nearby interstellar with log @xmath2 is described equally well by a uniform distribution or an origin in spherical shell - like features . higher column densities of ( log @xmath3 ) tend to be better described by the pathlength of the sightline through the s1 and s2 subshells . column densities of the recombinant ion are found to increase with the strength of the interstellar radiation field , rather than with star distance or total pathlength through the two magnetic subshells . the ion can not be used to trace the distribution of local interstellar gas unless the spatial variations in the radiation field are included in the calculation of the ionization balance , in addition to possible abundance variations . the result is that a model of loop i as composed of two spherical magnetic subshells remains a viable description of the distribution of nearby low density ism , but is not yet proven .

1510.00425

i

living entities , on scales from birds to individual cells , organize in complex patterns with collective behaviors that serve important biological functions . examples range from the flocking of birds @xcite to the sorting and organization of cells in morphogenesis @xcite . work over the last ten years has shown that many aspects of this complex organization can be captured by physical models based on a minimal set of rules or interactions , leading to the emergence of the new field of active matter @xcite . this is defined as a distinct category of non - equilibrium matter in which energy uptake , dissipation and movement take place at the level of discrete microscopic constituents . the active matter paradigm has additionally inspired the development of ingenious synthetic chemical and mechanical analogues , such as `` active '' colloids : micron - size spheres partly coated with a catalyst that promotes the decomposition of one of the components of the ambient fluid , resulting in self - propulsion of the colloidal particles @xcite . collections of such active synthetic particles have been shown to spontaneously assemble in coherent mesoscale structures with remarkable life - like properties @xcite . active systems exhibit rich emergent behaviors , where a collection of many interacting entities shows large - scale spatial or temporal organization in states with novel macroscopic properties . for instance , a dense swarm of bacteria can behave collectively as a living fluid with novel rheology @xcite , self - organize in complex regular patterns @xcite , exhibit turbulent motion @xcite , or ` freeze ' into a solid - like biofilm @xcite . this type of behavior is of course well known in inert inanimate matter that exhibits transitions between different phases upon the tuning of an external parameter , such as temperature , or the application of external forces that perturb the system at its boundaries ( e.g. , shear stresses ) or globally ( e.g. , an electric or magnetic field ) . it acquires , however , a new unexplored richness in active systems that are tuned out of equilibrium by energy generated internally by each unit . the active matter paradigm aims at describing and classifying the behavior of this new class of non - equilibrium systems . it does so by drawing on our understanding of familiar states of matter and of the transitions between them as controlled by interactions between atoms and molecules . new states of matter arise when we put together many units that are individually driven or motile . how are these new states formed ? are they controlled solely by local interactions among the active particles or is chemical signaling required to understand the emergence of these new states ? can we classify and describe them and control the transitions between such states as we know how to do with familiar inert matter ? [eq : thetai ] ) for @xmath0 and @xmath1 , reproduced from ref . @xcite with permission from the royal society of chemistry . the red region corresponds to a phase separated system . the blue region corresponds to a glass as characterized by the behavior of the msd . the glass would be replaced by a crystalline state in a monodisperse suspension . the dotted line is the mean - field spinodal line given by @xmath2 from eq . ( [ eq : phis ] ) for @xmath1 . ] recently , a number of ingenious synthetic systems have been engineered that show the emergent behavior of living active systems . these include autophoretic colloids @xcite , rollers @xcite , and droplets @xcite . the simplest realization of such `` colloidal microswimmers '' is obtained by immersing spherical janus colloids created by coating a hemisphere of a gold bead with platinum in a solution rich in hydrogen peroxide @xmath3 ) @xcite . the difference in the consumption rate of @xmath4 at the gold and platinum sides maintains an asymmetric concentration of solute on the two hemispheres , resulting in propulsion of the particles along their symmetry axis . in this and other catalytic colloidal swimmers interactions and propulsion can be tuned in a controlled way , allowing systematic studies up to moderate densities ( see fig . one remarkable phenomenon shown by these systems is spontaneous assembly in macroscopic clusters @xcite . this phenomenon is distinct from equilibrium assembly that arises from attractive interactions between the particles and has been shown to be driven by the nonequilibrium interplay of motility and crowding . the nonequilibrium pressure equation of state of active colloids has been probed experimentally via sedimentation measurements @xcite , revealing a motility - induced effective adhesion that can strongly suppress the pressure at moderate density . a review of recent experimental findings can be found in ref . @xcite and is beyond the scope of the present article that focuses on minimal models of active colloids that have in many cases predicted and then qualitatively reproduced many of the experimental observations . colloids have played a key role in condensed matter physics as model systems for atomic materials where pair interaction can be customized and equilibrium phase transitions and glassy behavior can be investigated with optical microscopy @xcite . although many active entities , from bacteria to birds , are elongated in shape and order in states with local or global liquid crystalline order leading to collective flocking , the growing body of work on synthetic active systems has shown that even spherical active particles can exhibit novel behaviors arising from the irreversible dynamics of each constituent , providing an excellent system for the quantitative testing of active matter theories . this has led to extensive theoretical and numerical studies of minimal models consisting of self - propelled spheres with purely repulsive interactions known as active brownian particles ( abp ) @xcite . these systems do not exhibit aligned or flocking states , but form active gases , liquids and solids , as summarized in the phase diagram shown in fig . [ fig : pd ] . the interplay between motility and steric effects is responsible for intriguing new phenomena , including motility - induced phase separation in the absence of any attractive interactions @xcite , casimir - type forces @xcite , and ratchet effects @xcite . the complexity of behavior that arises in these minimal models is truly remarkable . importantly , the abp model has demonstrated that many aspects of the emergent behavior of active systems do not require biochemical signaling , but are captured by physical contact interactions . it has additionally provided an excellent playground for addressing fundamental questions about the non - equilibrium statistical mechanics of active systems and whether equilibrium - like notions , such as effective temperature or equations of state , may be useful to describe them . in this article we review recent advances on the theoretical description of collections of active brownian particles ( abp ) defined as spherical self - propelled particles with purely repulsive interactions by organizing their behaviors in terms of the new active gases , liquids and solid phases formed by these systems . the work described demonstrates that some key aspects of the emergent behavior of active systems , such as the tendency to spontaneously cluster in large compact structures and to accumulate at surfaces exerting organized forces on the environment , can be described in terms of the nonequilibrium interplay of motility and crowding , without invoking attractive interactions nor biochemical signaling . we believe that minimal models of the type described here will continue to provide important tools for advancing our understanding of the nonequilibrium statistical mechanics of active matter . the rest of this paper is organized as follows . in section [ model ] the minimal model of abp is presented , emphasizing its parameters , limiting cases , and critical values . next , in section [ idealgas ] , we consider the properties of active gases in the context of recent work characterizing their mechanical properties and defining a pressure equation of state . from the dilute ideal active gas limit , tuning the rotational pclet number and increasing density beyond a critical value results in phase separation , where significant groups of active particles find their self - propulsion velocity caged due to increased interactions , yielding an active liquid coexisting with the active gas . this has been characterized by equations of mean velocity and critical density , which are presented and supported by simulation . this motility - induced phase separation ( mips ) is analyzed in section [ mips ] using continuum equations . the high - density limit , discussed in section [ crystals ] , is one in which solids and glasses of active colloids are formed , and this is distinguished from the glasses or crystalline states that results from high density collections of passive colloids . finally , a discussion and outlook is provided in section [ discussion ] , raising current questions regarding the interplay of noise and damping in the current models of active systems .

minimal models of active brownian colloids consisting of self - propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation . these systems do not exhibit aligned or flocking states , but do have a rich phase diagram , forming active gases , liquids and solids with novel mechanical properties . this article reviews recent advances in the understanding of such models , including the description of the active gas and its swim pressure , the motility - induced phase separation and the high - density crystalline and glassy behavior .

minimal models of active brownian colloids consisting of self - propelled spherical particles with purely repulsive interactions have recently been identified as excellent quantitative testing grounds for theories of active matter and have been the subject of extensive numerical and analytical investigation . these systems do not exhibit aligned or flocking states , but do have a rich phase diagram , forming active gases , liquids and solids with novel mechanical properties . this article reviews recent advances in the understanding of such models , including the description of the active gas and its swim pressure , the motility - induced phase separation and the high - density crystalline and glassy behavior . active matter , phase separation , active glasses , swim pressure

hep-ph0304182

i

vector mesons ( @xmath3 , @xmath4 , etc . ) play a significant role in hadronic physics . their interactions , though not constrained by low - energy theorems , apparently follow the broad pattern of vector meson dominance ( vmd ) @xcite . there have been numerous efforts to incorporate vector mesons into field - theoretical frameworks . historically , the yang - mills theory was discovered in an early attempt to treat the @xmath2 meson @xcite . more recently , interesting schemes based on `` hidden local symmetries '' ( hls ) were developed by bando _ et al . _ @xcite . in the original model @xcite , the @xmath2 meson is the boson of a spontaneously broken gauge group . the model has been extended to two hidden gauge groups @xcite ; then it also incorporates the lowest axial vector meson @xmath5 . with suitable parameters , these models can be quite successful phenomenologically , although they can not be systematically derived from qcd ( except in the limit of very light @xmath2 , if such a limit could be reached @xcite ) . in this paper we explore theories with very large , and even infinite number @xmath0 of hidden local symmetries . our motivation is twofold . first and most straightforwardly , there are excited states in the vector and axial vector channels ( @xmath6 , @xmath7 , @xmath8 , etc . @xcite ) , which must become narrow resonances in the limit of large number of colors @xmath9 . it is tempting to treat them as gauge bosons of additional broken gauge groups . , @xmath10 , etc . as a `` chain structure '' was made in ref . @xcite . ] the second motivation comes from recent theoretical developments . many strongly coupled gauge theories are found to have a dual description in terms of theories with gravity in higher dimensions @xcite . it was suggested that the string theory dual to large-@xmath9 qcd must have strings propagating in five dimensions , in which the fifth dimension has the physical meaning of the energy scale @xcite . in the framework of field theory , the fifth dimension can be `` deconstructed '' in models with a large number of gauge fields @xcite . we discovered that the continuum limit @xmath1 can lead to results that qualitatively , and in many cases even quantitatively , agree with phenomenology . most remarkably , the vector meson dominance , which in the hls theories required a tuning of parameters , becomes a natural consequence of the @xmath1 limit . another advantage of the limit @xmath1 is the possibility of matching to the asymptotic behavior of the current - current correlator known from perturbative qcd . as anticipated , a natural interpretation of this limit is a discretization , or deconstruction , of a 5-dimensional gauge theory . further , to our amusement , in the calculation of current - current correlators we found a relation very similar to the one employed in the ads / cft correspondence : the current - current correlator in 4d theory is expressed in terms of the variations of the classical 5d action with respect to the boundary values of the bulk gauge fields on the 4d boundaries . we limit our discussion to the isospin-1 sector of qcd . it is straightforward to extend the discussion to the isospin-0 sector ( @xmath11 , @xmath12 , and @xmath13 mesons ) . the detailed treatment of the @xmath14 problem , chiral anomaly , wess - zumino - witten term , and baryons is deferred to future work . the paper is organized as follows . in section [ sec : model ] we describe the open moose model . in section [ sec : observables ] we compute different physical observables : the vector meson mass spectrum , the decay constants of the pion and the vector mesons , the coupling between the vector mesons and the pions , and the pion electromagnetic form factor . we also check the validity of weinberg s spectral sum rules , and discover that the limit @xmath1 automatically leads to exact vmd for the pion formfactor . in section [ sec : continuum ] we take the limit of infinite number of the hidden groups @xmath1 . we show that the theory can be understood as a 5d yang - mills theory in an external metric and dilaton background . we establish an ads / cft - type prescription for calculating the current - current correlators . we consider two concrete realizations of the open moose in section [ sec : examples ] . we find that a `` cosh '' background metric interpolating between two ads boundaries leads to correct asymptotic behavior of the current - current correlator . this allows us to establish a relationship between hadron parameters such as @xmath15 , @xmath16 , and the qcd parameter @xmath9 . in section [ sec : baryon ] we show that the instanton , which is a quasiparticle in @xmath17 dimensions , becomes a skyrmion upon reduction to 4d , and thus describes the baryon . section [ sec : concl ] contains concluding remarks .

we derive the general formulas for the mass spectrum , the decay constants of the pion and vector mesons , and the couplings between mesons . we then consider two simple realizations , one with a flat metric and another with a `` cosh '' metric interpolating between two ads boundaries . we discover that an ads / cft - like prescription emerges in the computation of current - current correlators .

motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge / gravity duality , we consider the model of an `` open moose . '' such a model has a large number @xmath0 of hidden gauge groups as well as a global chiral symmetry . in the continuum limit @xmath1 the model becomes a 4 + 1 dimensional theory of a gauge field propagating in a dilaton background and an external space - time metric with two boundaries . we show that the model reproduces several well known phenomenological and theoretical aspects of low - energy hadron dynamics , such as vector meson dominance . we derive the general formulas for the mass spectrum , the decay constants of the pion and vector mesons , and the couplings between mesons . we then consider two simple realizations , one with a flat metric and another with a `` cosh '' metric interpolating between two ads boundaries . for the pion form factor , the single pole @xmath2-meson dominance is exact in the latter case and approximate in the former case . we discover that an ads / cft - like prescription emerges in the computation of current - current correlators . we speculate on the role of the model in the theory dual to qcd .

hep-ph0304182

c

we considered a theory of an `` open moose '' given by lagrangian ( [ l ] ) illustrated in fig . [ fig : k ] . this model describes a multiplet of massless goldstone bosons and a tower of vector and axial vector mesons . we developed a formalism for calculating the mass spectrum and the coupling constants in this theory for arbitrary parameters of the moose , @xmath34 and @xmath35 , and determine their values in the continuum limit , when the number of hidden symmetry groups @xmath0 tends to infinity . we applied this formalism to two exactly solvable realizations of the model and found that the physics of the lowest modes match quite well with the phenomenology of the @xmath83 , @xmath2 and @xmath78 mesons . we also find that the open - moose theory naturally incorporates the phenomenon of vector meson dominance . for example , the pion form factor is saturated by poles from a tower of vector mesons . moreover , since couplings between mesons are given by overlap integrals , the couplings of highly excited @xmath2 s to the pion are suppressed by the oscillations of their wave functions in the fifth dimension . this means that the pion form factor should be well approximated by the sum of contributions from a few lowest @xmath2 s . in the second example we considered ( the `` cosh '' background ) the situation is brought to an extreme : the pion form factor is saturated by a single pole @xmath2-meson dominance . we verified that both weinberg s spectral sum rules are automatically obeyed , in a nontrivial way , in any open - moose theory . one of our original motivations was to include the excited vector mesons beyond the lowest @xmath78 . with respect to that goal , we achieved only limited success , at least within the two exactly solvable models we considered . on the one hand , we do find that vector and axial vector mesons alternate in the spectrum , as it seems to be the case in qcd , at least for a few excited states . on the other hand , in both our simple models , the mass of an @xmath80-th state @xmath66 is @xmath329 at large @xmath80 , which seems to be in contradiction with the real world , and with the theoretical prejudice that @xmath330 . further study of different backgrounds might provide a model that reproduces desired features of excited mesons and help understand constraints that phenomenology and qcd theorems impose on functions @xmath220 and @xmath221 . alternatively , it is also possible that the excited vector mesons have `` stringy '' nature and can not , in principle , be incorporated into our field - theoretical scheme . by a suitable choice of background , even an exactly solvable one . but we did not find such models viable in other respects . ] the success that the model enjoys in describing the lowest states can be attributed to an apparent property of low - energy qcd : at intermediate distances correlation functions are reasonably well saturated by a single pole . in the `` cosh '' model the excited mesons ensure the correct behavior of the ( averaged ) spectral densities , thus playing the role of the continuum . this explains why some results of qcd sum rules are well reproduced . we hope that the study of the open moose theories will deepen our understanding of qcd at the fundamental level . one intriguing fact discovered in these theories is the similarity to the ads / cft correspondence . the procedure of calculating current - current correlators is essentially equivalent to the well - known ads / cft prescription : the correlators are given by the variational derivatives of the classical 5d action of the dual theory with respect to the sources living on the 4d boundary . there is overwhelming evidence that the @xmath331 supersymmetric yang - mills theory is described by a string theory . perhaps , an open moose theory is a low - energy limit of the string theory dual to qcd . in this regard , the result we found in the `` cosh '' model , @xmath332 is reassuring in view of a general expectation that such a dual theory should have a coupling proportional to @xmath333 in the t hooft limit . among the questions left for further study is the detailed phenomenology of isoscalar mesons ( @xmath11 , @xmath12 , @xmath13 , etc . ) . these mesons are described by an additional 5d abelian gauge field , which should be introduced into the action ( [ 5ds ] ) . most of our results should generalize straighforwardly to this case . however , there is an important new issue that the isoscalar sector brings into the theory . the global u(1)@xmath334 symmetry must be explicitly broken , e.g. , @xmath11 should not be massless . it is very encouraging that the 5d formulation of the theory provides a very natural mechanism for this . it is the topological 5d chern - simons term of the form @xmath335 where @xmath336 is the 5d vector field describing isoscalars . this term breaks the u(1)@xmath334 symmetry in the desired way . in particular , it is not invariant under u(1)@xmath334 transformations on the 4d boundary ( although it is invariant under local transformations in the bulk of 5d ) . it is easy to see that it also provides @xmath337 and other anomalous processes in qcd . the coefficient of the term ( [ aff ] ) can be fixed by matching to qcd chiral anomaly , and is therefore proportional to @xmath9 . the term ( [ aff ] ) also couples the @xmath12 meson field to the baryon current , providing a hard - core repulsion between baryons , and preventing the baryon / instanton from shrinking to zero size ( this effect is the origin of the stabilization of the skyrmion observed in ref . . it would be also interesting to see how the open - moose theory realizes di vecchia - veneziano - witten lagrangian @xcite and the corresponding phenomenology . other avenues for future study are the incorporation of finite quark masses , extension to three flavors and realization of the wess - zumino - witten topological term ( which does require a 5th dimension @xcite ) . * acknowledgments * the authors thank s. r. beane , g. gabadadze , w - y . keung , and especially t. imbo and m. strassler for discussions . the authors also wish to acknowledge the review talk by r. l. jaffe at the _ qcd and string theory _ workshop at the institute for nuclear theory in seattle , which provided much of the motivation for this work . m.a.s . acknowledges the hospitality of the institute for nuclear theory , university of washington , where part of this work has been done , and thanks riken bnl center and u.s . department of energy [ de - ac02 - 98ch10886 ] for providing facilities essential for the completion of this work . d.t.s . is supported , in part , by doe grant no.doe-er-41132 and the alfred p. sloan foundation . m.a.s . is supported , in part , by a doe oji grant and by the alfred p. sloan foundation .

motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge / gravity duality , we consider the model of an `` open moose . '' such a model has a large number @xmath0 of hidden gauge groups as well as a global chiral symmetry . in the continuum limit for the pion form factor , the single pole @xmath2-meson dominance is exact in the latter case and approximate in the former case .

motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge / gravity duality , we consider the model of an `` open moose . '' such a model has a large number @xmath0 of hidden gauge groups as well as a global chiral symmetry . in the continuum limit @xmath1 the model becomes a 4 + 1 dimensional theory of a gauge field propagating in a dilaton background and an external space - time metric with two boundaries . we show that the model reproduces several well known phenomenological and theoretical aspects of low - energy hadron dynamics , such as vector meson dominance . we derive the general formulas for the mass spectrum , the decay constants of the pion and vector mesons , and the couplings between mesons . we then consider two simple realizations , one with a flat metric and another with a `` cosh '' metric interpolating between two ads boundaries . for the pion form factor , the single pole @xmath2-meson dominance is exact in the latter case and approximate in the former case . we discover that an ads / cft - like prescription emerges in the computation of current - current correlators . we speculate on the role of the model in the theory dual to qcd .

astro-ph9508090

c

a low - density universe is well motivated from several dynamical observations of galaxies and clusters . the simplest such low - density models are those in which the universe is open . in the context of inflation theory , however , we need a special idea such as the one - bubble inflationary scenario in order to produce an open universe . in this paper , motivated by the one - bubble inflationary universe scenario , we have examined the cosmological predictions based on the assumption that the scalar field is initially in the bunch - davies vacuum state . the initial perturbation spectrum has been derived by considering the evolution of perturbations in an open inflationary stage . then the cmb anisotropies and the matter inhomogeneities have been examined . as the first test , we have performed a likelihood analysis for the cmb anisotropies by using the cobe dmr data . interestingly , the cobe likelihood analysis gives severe constraints on the model . models with @xmath172 , @xmath173 are excluded at confidence levels of @xmath174 , @xmath175 , respectively . in a previous analysis associated with the conformal vacuum state ( grski et al . 1995 ) , the likelihood function has another steep peak below @xmath176 . this complicates the statistical interpretation of the results ( grski et al . 1995 ) . in the case of the bunch - davies vacuum state , no such peak appears in the range of @xmath0 we are interested in , and so the likelihood analysis gives clear results . the cobe likelihood analysis is therefore a powerful probe of these open models . we have used the the cobe dmr maximum - likelihood normalization to predict the amplitude of matter fluctuations . according to this normalization method , there is little difference between the predictions of the bunch - davies vacuum and conformal vacuum cases . even for the case @xmath75 , the discrepancy of @xmath141 is a few percent . we obtain results that are similar to previous analyses : the power spectrum of the mass fluctuation fits the observations of galaxies and clusters for @xmath148 . the required bias is unacceptably high for @xmath177 , while high values of @xmath0 demand anti - biasing . for example , @xmath178 needs anti - biasing when @xmath179 . on the other hand , the @xmath4-models with harrison zeldovich spectrum have higher amplitude compared with open models . the @xmath4-model needs anti - biasing for @xmath180 even when @xmath179 . the @xmath4-model therefore needs low @xmath181 or a tilted spectrum ( ostriker steinhardt 1995 ) . for the range @xmath148 , open models give unacceptably small bulk velocities compared with the potent analysis . however , given the present quality of the velocity data and the problem of cosmic variance , one might be reluctant to draw strong conclusions from this fact . the rough estimation associated with the galaxy formation gives lower bound of @xmath0 consistent with the value discussed above . it is very interesting that the cobe likelihood analysis has given the most severe constraint on this open model . the cobe likelihood analysis strongly prefers a high value of @xmath0 . the peak value is around @xmath182 , and we can state that @xmath183 with @xmath175 confidence in this model . considering both the cobe analysis and the matter inhomogeneity , we are led to prefer a value of @xmath184 if the one - bubble inflationary scenario is correct . such a model is consistent with the press - schechter analysis of the epoch of galaxy formation and is marginally consistent with the bulk velocity data . as the cmb data continue to improve , particularly on degree scales , we should be able to test this model . it is premature to rule out low @xmath0 inflationary models on the basis of this investigation at present , because we do not include the effect of bubble nucleation in the calculation of initial density power spectrum . previous analysis indicates that the bubble nucleation effect in general excites fluctuations , and amplifies the perturbations on scales larger than curvature scale ( yamamoto , tanaka , sasaki 1995 ; hamazaki et al . one might therefore expect low - density models to fit the cobe data even more poorly once this effect is taken into account ; however , since the calculation has not been done , we can not be certain . in particular , the status of the super - curvature mode is still quite uncertain . various modifications of the open model may also be viable . we must investigate the effect of gravity waves in an open inflationary universe . one might also consider the effect of tilting the primordial power spectrum ; however , in order to improve the fit to the data one would probably need to tilt the power spectrum to have increased power on small scales , and such `` blue '' power spectra are not naturally produced by inflation . such a model is probably too contrived to be plausible . we would like thank n. sugiyama for providing us with the cmb anisotropy power spectra and for helpful discussions and comments . we are grateful to m. sasaki and t. tanaka for discussions and comments . one of us ( k.y . ) would like to thank professor j. silk and the people at the center for particle astrophysics , university of california , berkeley , where many parts of this work were done for their hospitality . he would like to thank professor h. sato for continuous encouragement . this work was supported in part by ministry of education grant - in - aid for scientific research no . 2841 . bardeen , j. m. , bond , j. r. , kaiser , n. , szalay , a. s. 1986 , apj , * 304 * , 15 . + bennett , c.l , et al . 1994 , apj , * 436 * , 423 . + bucher , m. , goldhaber , a. s. , turok , n. 1994 , putp-1507 , hep - ph/9411206 . + bucher , m. , turok , n. 1995 , putp-1518 , hep - ph/9503393 . + bunn , e.f . 1995a , ph.d . dissertation , u.c . berkeley physics department . + bunn , e.f . 1995b , in preparation . + bunn , e.f . , scott , d. , & white , m. 1995 , apj , * 441 * , l9 . + bunn , e.f . , & sugiyama , n. 1995 , apj , in press . + coleman , s. , de luccia , f. 1980 , phys . rev . * d21 * , 3305 . + dekel , a. 1994 ara @xmath157 a , 32 , 371 . + grski , k. m. 1994 , apj , * 430 * , l85 . + grski , k. m. , ratra , b. , sugiyama , n. , banday , a. j. 1995 , astro - ph/9502034 , apj , in press . + gottlber , s. , mchet , j. p. , starobinsky , a. a. 1994 , apj , * 434 * , 417 . + hamazaki , t. , sasaki , m. , tanaka , t. , yamamoto , k. 1995 , kuns1340 . + kamionkowski , m. , ratra , b. , spergel , d. n. , sugiyama , n. 1994 , apj , * 434 * , l1 . + kashlinsky , a. , tkachev , a. a. , frieman , j. 1994 , phys . lett . , * 73 * , 1582 . + kodama , h. , sasaki , m. 1984 , prog . phys . suppl . * 78 * , 1 . + liddle , a. r. , lyth , d. h. , roberts , d. , voana , p. t. 1995 , sussex - ast 95/6 - 2 , astro - ph/9506091 , mnras , in press . + linde , a. 1995 , preprint su - itp-95 - 5 , hep - th/9503097 , phys . * b * , in press . + linde , a. , mezhlumian , a. 1995 , preprint su - itp-95 - 11 , astro - ph/9506017 . + lyth , d. h. , stewart , e. d. 1990 , phys . b252 * , 336 . + lyth , d. h. , woszczyna , a. 1995 , lancaster preprint , astro - ph/9408069 . + mukhanov , v. f. , feldman , h. a. , brandenberger , r. h. 1992 , phys . rep . * 215 * , 203 . + ostriker , j. p. , steinhardt , p. j. 1995 , astro - ph/9505066 . + peacock , j. a. , dodds , s. j. 1994 , mnras , 267 , 1020 . + peebles , p. j. e. 1993 , _ principle of physical cosmology _ , princeton univ . press . + peter , p. , polarski , d. , starobinsky , a. a. 1994 , phys . rev . * d50 * , 4827 . + ratra , b. , et al . 1995 , in preparation . + ratra , b. , peebles , p. j. e. 1994a , apj , * 432 * , l5 . + ratra , b. , peebles , p. j. e. 1994b , preprint pupt-1444 . + sasaki , m. , tanaka , t. , yamamoto , k. , yokoyama , j. 1994 , prog . 90 , 1019 . + sasaki , m. , tanaka , t. , yamamoto , k. 1995 , phys . rev . * d51 * , 2979 . + scott , d. , silk , j. , white , m. 1995 , preprint . + smoot , g. f. et al . 1995 , apj . * 396 * , l1 . + stompor , r. , grski , k. m. , banday , a. j. 1995 , preprint . + sugiyama , n. 1995 , preprint cfpa - th-94 - 62 . + sugiyama , n. , gouda , n. 1992 , prog . phys . , 88 , 803 . + sugiyama , n. , silk , j. 1994 , phys . , * 73 * , 509 . + tanaka , t. , sasaki , m. , yamamoto , k. 1994 , phys . * d49 * , 1039 . + tanaka , t. , sasaki , m. 1994 , phys . * d50 * , 6444 . + tegmark , m. , & bunn , e. f. 1995 , berkeley preprint . + weinberg , s. 1989 , rev . , 61 , 1 . + white , m. , bunn , e. f. 1995 , cfpa-95-th-02 , apj , in press . + white , m. , scott , d. , silk , j. , & davis , m. 1995 , preprint . + yamamoto , k. , sasaki , m. , tanaka , t. 1995 , kuns-1309 , apj , in press . + yamamoto , k. , tanaka , t. , sasaki , m. 1995 , phys . rev . * d51 * , 2968 . power spectra of the cmb temperature anisotropy @xmath69 for ( a ) the bunch - davies vacuum open model with @xmath185 . the data were provided by n. sugiyama . these theoretical curves are normalized by the cobe likelihood . the curves are in descending order of @xmath0 as one moves down at @xmath186 . the results of several cmb experiments are also shown , taken from the paper by scott , silk , white ( 1995 ) . to compare with degree - scale observations , careful investigations are required ( ratra et al . 1995 ) . contour plot of the likelihood function @xmath112 for the bunch - davies open model . the contour range is from @xmath188 to @xmath189 , where the likelihoods are scaled so that @xmath190 corresponds to a flat harrison - zeldovich spectrum with maximum - likelihood normalization . figure 4(a ) . power spectrum of density perturbation @xmath192 for the open model with @xmath75 , @xmath76 , @xmath77 , @xmath78 , @xmath79 , for @xmath193 , respectively . we have taken @xmath194 . the points are from peacock dodds ( 1994 ) .

a likelihood analysis is performed for the cosmic microwave background anisotropies using the two - year cobe dmr data and considering models based on both the bunch - davies and conformal vacua . _ subject headings _ : cosmology : theory cosmic microwave background large scale structure = 16.0 cm = 0.0 cm # 1#20.2ex observational tests of one - bubble open inflationary cosmological models kazuhiro yamamoto@xmath2 and emory f. bunn@xmath3 + + _ kyoto 606 - 01 , japan _ + and + _ @xmath3 center for particle astrophysics , university of california , _ + _ berkeley , ca 94720 - 7304 , usa _

motivated by recent studies of the one - bubble inflationary scenario , simple open cold dark matter models are tested for consistency with cosmological observations . the initial perturbation spectrum is derived by solving for the evolution of fluctuations in an open inflationary stage . a likelihood analysis is performed for the cosmic microwave background anisotropies using the two - year cobe dmr data and considering models based on both the bunch - davies and conformal vacua . having normalized the perturbation spectrum to fit the cobe data , we reconsider the validity of the open model from the view point of cosmic structure formation . open models may be severely constrained by the cobe likelihood analysis . in particular , small values of @xmath0 are ruled out in the bunch - davies case : we find that @xmath1 at 95% confidence for this model . _ subject headings _ : cosmology : theory cosmic microwave background large scale structure = 16.0 cm = 0.0 cm # 1#20.2ex observational tests of one - bubble open inflationary cosmological models kazuhiro yamamoto@xmath2 and emory f. bunn@xmath3 + + _ kyoto 606 - 01 , japan _ + and + _ @xmath3 center for particle astrophysics , university of california , _ + _ berkeley , ca 94720 - 7304 , usa _

1701.01289

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of agent and the cooperation between agents in multi - agent system ( mas ) , a framework , named distributed constraint optimization problem ( dcop ) in terms of constraints that are known and enforced by distinct agents comes into being with it . in last decade , the research effort of dcop has been dedicated on the following three directions : 1 ) the development of dcop algorithms which are able to better balance the computational complexity and the accuracy of solution , such as large neighborhood search method @xcite ; markov chain monte carlo sampling method @xcite @xcite and distributed junction tree based method @xcite 2 ) the extension of classical dcop model in order to make it more flexible and effective for practical application , such as expected regret dcop model @xcite , multi - variable agent decomposition model @xcite and dynamic dcop model @xcite 3 ) the application of dcop in modeling environmental systems , such as sensor networks @xcite , disaster evacuation @xcite , traffic control @xcite and resource allocation @xcite . in this paper , we take more attention to the application of dcop . more precisely , we leverage dcop to solve user association problem in the downlink of multi - tier heterogeneous networks with the aim to assign mobile users to different base stations in different tiers while satisfying the qos constraint on the rate required by each user . is generally regarded as a resource allocation problem @xcite in which the resource is defined by the resource blocks ( rbs ) . in this case , the more rbs allocated to a user , the larger rate achieved by the user . the methods to solve the user association problem are divided into centralized controlled and distributed controlled . with regard to the centralized way , a central entity is set up to collect information , and then used to decide which particular bs is to serve which user according to the collected information . a classical representation of centralized method is max - sinr @xcite . distributed controlled methods attract considerable attention in last decade since they do not require a central entity and allow bss and users to make autonomous user association decisions by themselves through the interaction between bss and users . among all available methods , the methods based on lagrange dual decomposation ( ldd ) @xcite and game theory @xcite have better performance . hamidreza and vijay @xcite put forward a unified distributed algorithm for cell association followed by rbs distribution in a @xmath2-tier heterogeneous network . with aid of ldd algorithm , the users and bss make their respective decisions based on local information and a global qos , expressed in terms of minimum achievable long - term rate , is achieved . however , the constraint relaxation and the backtrack in almost each iteration are needed to avoid overload at the bss . in addition , as we will show later , the number of out - of - service users will increase since a user always selects a best - rate thereby taking up a large number of rbs and leaving less for others . nguyen and bao @xcite proposed a game theory based method in which the users are modeled as players who participate in the game of acquiring resources . the best solution is the one which can satisfy nash equilibrium ( ne ) . loosely speaking , such solution is only a local optima . in addition , it is difficult to guarantee the quality of the solution . there is no research of modeling user association problem as mas . however , some similar works have been done focusing on solving the resource management problem in the field of wireless networks or cognitive radio network @xcite by dcop framework . these methods can not be directly applied to user association problem mainly due to the scale of the models for these practical applications is relatively small . for instance , monteiro @xcite formalized the channel allocation in a wireless network as a dcop with no more than 10 agents considered in the simulation parts . however , the amount of users and resource included in a hetnet is always hundreds and thousands . in this case , a good modeling process along with a suitable dcop algorithm is necessary . according to the in - depth analysis above , it motivates us to explore a good way to solve user association problem by dcop . the main contributions of this paper are as follows : * an ecav ( each connection as variable ) model is proposed for modeling user association problem using dcop framework . in addition , we introduce a parameter @xmath0 with which we can control the scale ( the number of variables and constriants ) of the ecav model . * a dcop algorithm based on markov chain ( mc ) is proposed which is able to balance the time consumption and the quality of the solution . * the experiments are conducted which show that the results obtained by the proposed algorithm have superior accuracy compared with the max - sinr algorithm . moreover , it has better robustness than the ldd based algorithm when the number of users increases but the available resource at base stations are limited . the rest of this paper is organized as follows . in section [ preliminary ] , the definition of dcop and the system model of user association problem along with its mixed integer programming formulation are briefly introduced . in section [ formulation_with_dcop ] , we illustrate the ecav-@xmath0 model . after that , a mc based algorithm is designed in section [ markov_chain_algorithm ] . we explore the performance of the dcop framework by comparing with the max - sinr and ldd methods in section [ experimental_evaluation ] . finally , section [ conclusion ] draws the conclusion .

multi - agent systems ( mas ) is able to characterize the behavior of individual agent and the interaction between agents . thus , it motivates us to leverage the distributed constraint optimization problem ( dcop ) , a framework of modeling mas , to solve the user association problem in heterogeneous networks ( hetnets ) . two issues we have to consider when we take dcop into the application of hetnet including : ( i ) how to set up an effective model by dcop taking account of the negtive impact of the increment of users on the modeling process ( ii ) which kind of algorithms is more suitable to balance the time consumption and the quality of soltuion . aiming to overcome these issues , after that , a markov chain ( mc ) based algorithm is proposed on the basis of log - sum - exp function . in addition , it is also apparent that the dcop based method has better robustness than ldd when the number of users increases but the available resource at base stations are limited .

multi - agent systems ( mas ) is able to characterize the behavior of individual agent and the interaction between agents . thus , it motivates us to leverage the distributed constraint optimization problem ( dcop ) , a framework of modeling mas , to solve the user association problem in heterogeneous networks ( hetnets ) . two issues we have to consider when we take dcop into the application of hetnet including : ( i ) how to set up an effective model by dcop taking account of the negtive impact of the increment of users on the modeling process ( ii ) which kind of algorithms is more suitable to balance the time consumption and the quality of soltuion . aiming to overcome these issues , we firstly come up with an ecav-@xmath0 ( each connection as variable ) model in which a parameter @xmath0 with an adequate assignment ( @xmath1 in this paper ) is able to control the scale of the model . after that , a markov chain ( mc ) based algorithm is proposed on the basis of log - sum - exp function . experimental results show that the solution obtained by dcop framework is better than the one obtained by the max - sinr algorithm . comparing with the lagrange dual decomposition based method ( ldd ) , the solution performance has been improved since there is no need to transform original problem into a satisfied one . in addition , it is also apparent that the dcop based method has better robustness than ldd when the number of users increases but the available resource at base stations are limited .

1701.01737

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in this paper we studied the information overlap of chinese and western traditional media ( tm ) and social media ( sm ) . our study suggests that chinese sm covers most of the topics discussed by chinese tm and provides additional information about celebrities and locally relevant events . when comparing western and chinese tm and sm , we found a bias of china towards the west , as chinese tm reports small scaled western events , while western tm mainly focuses only on major news about china . this trend becomes particularly apparent when comparing the interest of sm users in celebrities . while western sm users barely show any interest in chinese born celebrities , chinese sm users actively discuss both chinese and western born celebrities . we also revealed several _ sensitive _ topics reported by western tm , for which we could not find a corresponding chinese article . we assume that these contain unfavourable information from the point of view of the state controlled chinese tm . gary king , jennifer pan , and margaret e roberts . reverse - engineering censorship in china : randomized experimentation and participant observation . philipp koehn , hieu hoang , alexandra birch , et al . moses : open source toolkit for statistical machine translation . in proceedings of the 45th annual meeting of the acl on interactive poster and demonstration sessions , pages 177180 . acl , 2007 . haewoon kwak , changhyun lee , hosung park , and sue moon . what is twitter , a social network or a news media ? in proceedings of the 19th international conference on world wide web , pages 591600 , 2010 . miles osborne and mark dredze . facebook , twitter and google plus for breaking news : is there a winner ? in icwsm , 2014 . sasa petrovic , miles osborne , richard mccreadie , craig macdonald , and iadh ounis . can twitter replace newswire for breaking news ? 2013 . dominik wurzer , victor lavrenko , and miles osborne . twitter - scale new event detection via k - term hashing . in proceedings of the 2015 conference on emnlp , pages 25842589 , lisbon , portugal , september 2015 . wayne xin zhao , jing jiang , et al . comparing twitter and traditional media using topic models . in european conference on information retrieval , pages 338349 , 2011 .

while the topical demographic of western media was subjects of studies in the past , less is known about chinese media . in this paper , we apply event detection and tracking technology to examine the information overlap and differences between chinese and western - traditional media and social media . our experiments reveal a biased interest of china towards the west , which becomes particularly apparent when comparing the interest in celebrities .

newswire and social media are the major sources of information in our time . while the topical demographic of western media was subjects of studies in the past , less is known about chinese media . in this paper , we apply event detection and tracking technology to examine the information overlap and differences between chinese and western - traditional media and social media . our experiments reveal a biased interest of china towards the west , which becomes particularly apparent when comparing the interest in celebrities .

1109.2177

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improvements in techniques for cooling of atomic gases in atomic traps make their use very promising for practical applications in various areas of fundamental science and technology such as metrology , development of frequency standards , and quantum information problems @xcite . the largest number of applications envisioned for cold and ultracold atomic ensembles have at their foundation the interaction between the medium and electromagnetic radiation . this interaction also underlies many methods for diagnostics of the states of these ensembles . recently , dense atomic clouds , in which the average interatomic distances are comparable with the optical wavelength , have attracted much attention . this interest is in part generated by such fundamental and practically important physical effects as anderson ( strong ) localization of light @xcite and lasing in a disordered medium @xcite which can take place in dense ensembles . the aim of recent studies in this field was to observe these effects experimentally and to describe them theoretically . one challenging problem in the area of disordered atomic systems is that the studied atomic ensembles normally consist of a large number of atoms in samples that are produced with a low duty cycle . the larger number of atoms is required in order to obtain sufficient signal to noise to study the subtle effects of interest . such experiments require realistic modeling in order to extract the essential physics of the observed processes . however , it is challenging to treat these problems as a multi - atom scattering process , and such studies have been limited to several thousand atoms @xcite ; this should be compared with the characteristic @xmath0 atom - sized samples of recent experiments . alternative theoretical approaches , even if approximate in nature , are then desirable . the present paper is devoted to the theoretical description of optical properties of dense and cold atomic clouds . the problem of a dense atomic ensemble belongs obviously to the field of macroscopic electrodynamics . the main approach here is based on usage of such averaged characteristics as the field strength and atomic polarization . the key point in a macroscopic approach is in finding the susceptibility or dielectric constant of the dense ensemble . the influence of density of the medium on its susceptibility can be analyzed on the basis of the idea of a local field and , following from it , the lorentz - lorenz formula @xcite . this formula is sufficient to solve completely the problem of the dependence on density only if the difference between the polarizability of a free atom and its polarizability in the medium can be neglected @xcite . as we will show below , for the considered cold atomic ensemble this is not the case . the resonant dipole - dipole interatomic interaction causes atomic level shifts and broadening and thereby essentially modifies the atomic polarizability . an explicit analytical expression for the susceptibility , which takes into account this modification , was obtained earlier in @xcite . the calculation in @xcite was based on the relevant macroscopic statistical description of the polarization response of the medium to an external field . part of the approximations made in @xcite are valid only for relatively low density ensembles and thus the corresponding results have a restricted range of applicability . constitutive relations connecting atomic polarization and an external field can be obtained consistently only in the framework of a microscopic approach based on the notion of the discrete structure of matter consisting of separate atoms . a consistent microscopic approach has been already applied for analysis of influence of interatomic interactions on spontaneous decay of an impurity atom embedded in a dielectric @xcite . quite a number of works were devoted to collective decay in dense homogeneous multiatomic media and to properties of spontaneous emission of such media initially excited by a weak external field ( see , for example @xcite and references therein ) . in these works the main attention was focused on the influence of the density of the ensemble on its afterglow , i.e. on secondary radiation . in the present paper we consider the influence of interatomic interaction on the properties of the ensemble itself . we study the spatial distribution of atomic polarization created by weak monochromatic light in a cold atomic ensemble . we show that in the case of a uniform random atomic distribution amplitude of polarization averaged over space configurations decreases exponentially beyond the boundary regions . its phase increases linearly with distance into the medium . on this ground we determine numerically the wavelength of the light in the dense atomic clouds , its extinction coefficient as well as complex index of refraction and dielectric constant of the medium . we also analyze the dispersion of the permittivity for different atomic densities . note that similar problems arise in classical electrodynamics when studying light scattering from a medium with random dielectric inclusions @xcite . such inclusions strongly influence light propagation in such media , giving rise manifold internal scattering and essentially modifying its averaged dielectric constant . an important feature of the present work is in taking into account the polarization properties of light . nearly all the mentioned above papers on multiatomic systems used only a two - level model for the atoms . this prevents a correct consideration of the light polarization , adequate description of the resonance dipole - dipole interaction at small distances and , as a consequence , correct calculation of shifts and broadenings of atomic levels . we also do not use a model of an averaged continuous medium in our calculations . that is , the influence on the intrinsic spatial disorder of the atoms in the ensemble is considered . as a specific illustration of this , recent approaches to atomic physics - based localization studies have considered systems of reduced dimensionality . one way to achieve this for light localization is to optically create a quasi one dimensional system through modification of spatially larger samples . such optical channels , with wavelength - scale transverse dimensions , can be created through quantum optical techniques based on electromagnetically induced transparency , for instance . alternatively , a strongly focused far - off - resonance laser can generate a type of optical wave guide through the dense sample , allowing quasi one dimensional localization for a much weaker , but near - resonance probe beam . theoretical modeling the average properties of such generated optical wave guides , essential to interpretation of experiments , may be done using the effective optical responses of the resulting medium , as we discuss in the current paper . the remainder of this paper is organized as follows . in section 2 we describe our basic physical assumptions and the calculational approach . section 3 presents results of numerical simulations . we conclude with a brief synopsis of the results , highlighting the main points of the present report .

on the basis of general theoretical results developed previously in jetp 112 , 246 ( 2011 ) we analyze the atomic polarization created by weak monochromatic light in an optically thick , dense and cold atomic ensemble . we show that the amplitude of the polarization averaged over a uniform random atomic distribution decreases exponentially beyond the boundary regions . the phase of this polarization increases linearly with increasing penetration into the medium . on these grounds , we determine numerically the wavelength of the light in the dense atomic medium , its extinction coefficient , and the complex refractive index and dielectric constant of the medium . the dispersion of the permittivity is investigated for different atomic densities .

on the basis of general theoretical results developed previously in jetp 112 , 246 ( 2011 ) we analyze the atomic polarization created by weak monochromatic light in an optically thick , dense and cold atomic ensemble . we show that the amplitude of the polarization averaged over a uniform random atomic distribution decreases exponentially beyond the boundary regions . the phase of this polarization increases linearly with increasing penetration into the medium . on these grounds , we determine numerically the wavelength of the light in the dense atomic medium , its extinction coefficient , and the complex refractive index and dielectric constant of the medium . the dispersion of the permittivity is investigated for different atomic densities . it is shown that for dense clouds , the real part of the permittivity is negative in some spectral domains .

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the desire to create an optical directional coupler , a device composed by parallel optical waveguides close enough that leaked energy is transferred between them , led to the exploration of waveguide creation in semi - conductors via proton bombardment @xcite . at the time , power losses played an interesting role and the nascent mode coupling theory @xcite allowed the theoretical description of linear loses in such devices @xcite , @xmath2,\end{aligned}\ ] ] where the real numbers @xmath3 and @xmath4 are the effective linear loss , identical in all implanted waveguides , and the effective waveguide coupling strength , also indentical for the whole system , in that order . this , to the best of our knowledge , was the first theoretical description of an experimental @xmath1-waveguide coupler including losses in the form of a schrdinger - like equation involving a non - hermitian hamiltonian . almost twenty years later , the desire to create an intensity dependent switch working at low power levels took another team of researchers to explore twin core nonlinear couplers with gain and loss . again , coupled mode theory allowed the description of such devices @xcite , @xmath5 where we have kept the notation used before and introduce the effective real part of the refractive index , @xmath6 , and the real function @xmath7 that describes an effective kerr nonlinearity induced change in the refractive index of the @xmath8th core , positive for self - focusing and negative for self - defocusing materials . at this point in history , there existed experimental and theoretical work describing an optical dimer where the waveguides present effective loss and gain and a nonlinearity but a little something was missing . a couple of years later , a theory exploring a particular type of non - hermitian hamiltonians with real spectra was brought forward in quantum mechanics @xcite . these hamiltonians were invariant under space - time reflection , received the name of @xmath0-symmetric , and opened new avenues of research in quantum mechanics as well as other areas of physics and matemathics , c.f . @xcite and references therein . in optics , it took a few years more to propose two seminal ideas . the first one regarded single elements and showed , in particular , that an optical planar slab waveguide composed of two media with linear gain and loss can be described by a schrdinger - like equation under dynamics dictated by a @xmath9-symmetric hamiltonian , where the optical refractive index played the role of quantum - like potential and propagation distance that of time @xcite . the second one dealt with composite systems , where a mature mode coupling theory produced a theory of coupled optical pt - symmetric structures @xcite . in the ten years following those first proposals for an optical realization of @xmath9-symmetry , work has been reported on slab waveguides @xcite , bragg scatterers @xcite , as well as linear @xcite and nonlinear @xcite coupled waveguides , to mention just a few . research in this field is slowly getting to information technologies applications with recent proposals of all - optical @xmath0-symmetric logic gates @xcite and amplitude - to - phase converters @xcite . here , we will provide a review of the optical @xmath0-symmetric dimer . first , in section 2 , we will introduce a two - waveguide coupler where component waveguides show effective complex refractive indices with identical real part . starting from this device , we will recover the effective mode coupling differential equation set for the linear @xmath0-symmetric dimer , which describes a nonunitary optical device showing symmetric effective loss and gain feasible of passive and active optical realizations . then , we will recover the dispersion relation for the dimer that shows three regimes , one with real eigenvalues , the @xmath0-symmetric regime , another with fully degenerate eigenvalues equal to zero , the fully degenerate regime , and a third one with purely imaginary eigenvalues , the broken symmetry regime . we will construct an analytic propagator that will show asymmetric amplifying oscillator , power amplification , and exponential amplification behaviors in each of these regimes . we will also show that it is possible to uncouple the mode coupling differential equation set of the @xmath0-symmetric dimer . the resulting second order differential equations and boundary conditions for the field amplitudes propagating through each waveguides take the form of nonlocal oscillators with positive potential , free particle traveling through a nonlocal medium , and nonlocal oscillators with inverted potential , in each of the regimes . in the final part of section 2 , we will bring forward the renormalized field approach that helps us cast the linear @xmath0-symmetric dimer as a nonlinear dimer with imaginary kerr nonlinearity , either in a self- or a cross - modulation scheme , and allows us to realize an asymptotic behavior that depends just on the gain to coupling strength ratio of the device . in section 3 , we will discuss the linear @xmath0-symmetric dimer when both waveguides show the same effective self - focusing kerr nonlinearity . we will show the stable nonlinear modes of the device , discuss its dynamics in terms of the passive kerr two - waveguide coupler that allows for coherent and localized oscillations between the waveguide field modes , and show that the inclusion of symmetric gain and loss breaks these dynamics producing localization in the gain waveguide without showing an asymptotic behavior . in section 4 , we will extend the linear @xmath0-symmetric dimer to planar @xmath1-waveguide couplers using finite dimensional matrix representations of a complexified version of @xmath10 . we have previously shown @xcite that the @xmath0-symmetric dimer and its extensions to planar @xmath1-waveguide couplers possess an @xmath11 symmetry realized in a finite dimensional non - unitary irreducible representation . this representation is accomplished through complexification of @xmath10 , @xmath12 , and it allows us to provide the dispersion relation and a closed form analytic propagator , which have the same regimes and dynamics found for the dimer . we will show that the renormalized field approach provides us with an asymptotic behavior that is independent of the initial field distribution and depends just on the waveguide number and the effective gain to coupling ratio . then , in section 5 , we will introduce a modified version of the ehrenfest theorem suitable for non - hermitian hamiltonians and show how it can help us define the dynamics of an @xmath13-dimensional generalized stokes vector for the planar @xmath1-waveguide couplers discussed in section 4 . in section 6 , we will go back to the dimer but consider the propagation of quantum fields . in the quantum regime , spontaneous generation and absorption of electromagnetic radiation should be considered when using media with linear gain or loss . we will show the solution for the quantum linear @xmath0-symmetric dimer and discuss the generation of light from vacuum due to spontaneous processes in the absence of fields impinging at the device . finally , we will produce a brief summary and discuss future avenues regarding non - hermitian optical systems .

optics has proved a fertile ground for the experimental simulation of quantum mechanics . we focus on the optical @xmath0-symmetric dimer , a two - waveguide coupler were the materials show symmetric effective gain and loss , and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view . we go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar @xmath1-waveguide couplers that are the optical realization of lorentz group in 2 + 1 dimensions .

optics has proved a fertile ground for the experimental simulation of quantum mechanics . most recently , optical realizations of @xmath0-symmetric quantum mechanics have been shown , both theoretically and experimentally , opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry . here , we focus on the optical @xmath0-symmetric dimer , a two - waveguide coupler were the materials show symmetric effective gain and loss , and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view . we go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar @xmath1-waveguide couplers that are the optical realization of lorentz group in 2 + 1 dimensions . furthermore , we provide a formulation to describe light propagation through waveguide couplers described by non - hermitian mode coupling matrices based on a non - hermitian generalization of ehrenfest theorem .

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in this paper we have used parametric expressions to calculate the isothermal susceptibility , specific heat , coexistence curve , and correlation length along the critical isochore and coexistence curve from the asymptotic region to the crossover region . all the critical leading amplitude ratios were contained in the model as listed in table [ table : ratios ] . using only two adjustable parameters in these theoretical expressions for the critical contributions , we fit the theory to recently obtained experimental data for the isothermal susceptibility , specific heat , and early experimental data of the coexistence curve and light scattering intensity . the agreement between the theory and experimental measurements is good . further improvements to the minimal renormalization scheme are desired , especially the five - loop borel resummations throughout the whole range of @xmath212 . more accurate borel resummations at the fixed point should also lead to improved calculations of @xmath213 and @xmath214 so that the resultant critical exponents can be compared with other published values ( see appendix [ dix : const ] ) . theoretical insights on non - critical contributions are also needed in order to formulate more accurate analytical expressions for the background contributions . while the present minimal subtraction renormalization model describes quite well to experimental measurements along the critical isochore and coexistence curve , it is not as yet a model for a complete equation - of - state . recently , agayan _ et al_. have developed a phenomenological crossover parametric model ( cpm ) equation - of - state that is also based upon rg theory @xcite . within this model , the internal constants were adjusted such that the critical leading amplitude ratios agreed with the values in the fisher and zinn column in table [ table : ratios ] . this cpm model was developed to fit simple fluids as well as complex fluid systems that exhibit non - monotonic crossover behavior . this non - monotonic crossover behavior could be described by the cpm approach using a finite cut - off wavelength as an additional fitting parameter . however , in simple fluid systems , like @xmath1he , crossover behavior of different physical quantities can be well described within the framework of the field theoretical @xmath0 model without the finite cut - off wavenumber . nasa supported microgravity flight experiments @xcite ( http://miste.jpl.nasa.gov ) , which are under preparation , will take experimental data of the susceptibility , specific heat , and coexistence curve in the asymptotic region . combining these microgravity measurements in the asymptotic region with ground - based measurements in the crossover region should permit a rigorous test of the predictions of recent renormalization theories . we are indebted to dr . r. haussmann and prof . j. rudnick for supporting the early development of this work and for many stimulating discussions . we are also grateful to prof . h. meyer for a critical reading of the manuscript and to dr . m. weilert for his contribution in performing the experiments . the research described in this paper was carried out at the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration .

parametric expressions are used to calculate the isothermal susceptibility , specific heat , order parameter , and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region . these expressions are based on the minimal - subtraction renormalization scheme within the @xmath0 model . using two adjustable parameters in these expressions , we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve , and early measurements of coexistence curve and light scattering intensity along the critical isochore of @xmath1he near its liquid - vapor critical point .

parametric expressions are used to calculate the isothermal susceptibility , specific heat , order parameter , and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region . these expressions are based on the minimal - subtraction renormalization scheme within the @xmath0 model . using two adjustable parameters in these expressions , we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve , and early measurements of coexistence curve and light scattering intensity along the critical isochore of @xmath1he near its liquid - vapor critical point . the theory provides good agreement with these experimental measurements within the reduced temperature range @xmath2 .

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it has previously been shown that `` defects '' in a planar periodic dielectric structure can simultaneously confine optical and mechanical resonances to sub - cubic - wavelength volumes@xcite . as the co - localized resonances share the same lattice , and thus the same wavelength , the ratio of the optical to mechanical frequency of these modes is proportional to the ratio of their velocities . more recently , it was demonstrated that such co - localized resonances in a silicon structure can strongly couple , via motion - induced phase modulation of the internal optical field , resulting in sensitive optical read - out and actuation of mechanical motion at ghz frequencies@xcite . in this paper we aim to further develop the theory and design of these coupled photonic and phononic systems , laying the groundwork for what we term `` optomechanical crystals '' . here we choose a cavity - centric viewpoint of the interaction between photons and phonons , using the terminology and metrics from the field of cavity optomechanics @xcite . an alternative viewpoint , more appropriate for guided - wave structures , may also be taken in which the interactions are described from a nonlinear optics ( raman - like scattering ) perspective @xcite . we focus on two cavity devices in particular , a quasi - one - dimensional ( quasi-1d ) patterned nanobeam and a quasi - two - dimensional ( quasi-2d ) patterned nanomembrane , both of which have been studied extensively in the past@xcite for their photonic properties . the strength of the ( linear ) optomechanical coupling in such structures is found to be extremely large , approaching a limit corresponding to the transfer of photon momentum to the mechanical system every optical cycle@xcite . simultaneously , the effective motional mass@xcite of the highly confined phonon modes is small , less than few hundred femtograms for a cavity system operating at a wavelength of @xmath8 @xmath6 m and a mechanical frequency of @xmath9 ghz . this combination of parameters makes possible the optical transduction of high - frequency ( multi - ghz ) mechanical vibrations@xcite with near quantum - limited displacement sensitivity@xcite . additionally , dynamical back - action@xcite between the photon and phonon fields can be used to dampen@xcite and amplify@xcite mechanical motion , providing an optical source of coherent phonons@xcite which can then be used within other phononic circuit elements@xcite . planar optomechanical crystals then , should enable a new generation of circuits where phonons and photons can be generated , routed , and made to interact , all on a common chip platform . unlike the simple motion of a mirror on a spring in more conventional cavity optomechanical systems@xcite , the complex mechanics of optomechanical crystal structures makes it difficult to intuit the origin or strength of the optomechanical coupling . nonetheless , understanding the nature of the coupling is crucial to the engineering of optomechanical crystal devices as the degree of coupling between different optical and mechanical mode pairs can vary by orders of magnitude within the same structure , with even subtle changes in the geometry inducing large changes in the optomechanical coupling . in the experimental demonstration of a nanobeam optomechanical crystal@xcite , it was shown that the perturbation theory of maxwell s equations with shifting material boundaries @xcite provides an accurate method of estimating the optomechanical coupling of these complex motions . here we describe how this perturbation theory can be used to create an intuitive , graphical picture of the optomechanical coupling of simultaneously localized optical and mechanical modes in periodic systems . the outline of the paper is as follows . we first analyze the quasi-1d nanobeam optomechanical crystal system . this nanobeam structure provides a simple example through which the salient features of optomechanical crystals can be understood . the mechanical @xmath0 of the structure is modeled using absorbing regions that provide a radiation condition for outgoing mechanical vibrations . the various types of mechanical losses are analyzed , and methodologies for minimizing or avoiding these losses are discussed . the dispersive coupling between the optical and mechanical modes is studied next . we use the aforementioned perturbation theory to analyze the optomechanical coupling strength , and which we display as an optomechanical coupling density on the surface of the structure . we use the density of optomechanical coupling picture to illustrate how the structure can be optimized to maximize the optomechanical coupling . finally , we analyze the optomechanical coupling of a quasi-2d membrane structure , the well - known double - heterostructure photonic crystal cavity @xcite . we show how the optical and mechanical modes and their coupling can be understood in terms of the quasi - one - dimensional nanobeam example .

we analyze the properties of dispersively coupled planar photonic and phononic crystals : optomechanical crystals . in particular , the properties of co - resonant optical and mechanical cavities in quasi-1d ( patterned nanobeam ) and quasi-2d ( patterned membrane ) geometries are studied . it is shown that the mechanical @xmath0 and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry . several designs are presented with mechanical frequency @xmath1-@xmath2 ghz , optical @xmath0-factor @xmath3 , motional masses @xmath4 100 femtograms , optomechanical coupling length @xmath5 @xmath6 m , and a radiation - limited mechanical @xmath0-factor @xmath7 .

periodically structured materials can sustain both optical and mechanical excitations which are tailored by the geometry . here we analyze the properties of dispersively coupled planar photonic and phononic crystals : optomechanical crystals . in particular , the properties of co - resonant optical and mechanical cavities in quasi-1d ( patterned nanobeam ) and quasi-2d ( patterned membrane ) geometries are studied . it is shown that the mechanical @xmath0 and optomechanical coupling in these structures can vary by many orders of magnitude with modest changes in geometry . an intuitive picture is developed based upon a perturbation theory for shifting material boundaries that allows the optomechanical properties to be designed and optimized . several designs are presented with mechanical frequency @xmath1-@xmath2 ghz , optical @xmath0-factor @xmath3 , motional masses @xmath4 100 femtograms , optomechanical coupling length @xmath5 @xmath6 m , and a radiation - limited mechanical @xmath0-factor @xmath7 .

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the monte carlo simulations of thermodynamics of the three - dimensional random - field ising model performed in this study demonstrate second - order phase transition from paramagnetic to antiferromagnetic state when the spin concentration is higher than pu and firstorder phase transition from paramagnetic to mixed phase consisting of antiferromagnetic and ferromagnetic domains separated by spin - glass domains when @xmath46 , where @xmath37 and @xmath47 are vacancy and magnetic percolation thresholds , respectively . when the spin concentration is high , the system consists of antiferromagnetic domains separated by spin - glass regions . with decreasing spin concentration or increasing applied magnetic field strength , both the number and size of antiferromagnetic domains decrease , both the number and size of ferromagnetic domains increase , and the volume fraction of the spin - glass phase decreases . it is shown that random magnetic field induces a transition from antiferromagnetic to spinglass ground state when @xmath46 in the three - dimensional random - field ising model with competing interactions analyzed in this study . a. b. harris , j. phys . c 7 , 1671 ( 1993 ) . r. folk , y. holovatch , and t. yavorski . nauk 173 , 175 ( 2003 ) [ phys . 46 , 169 ( 2003 ) ] . v. s. dotsenko , usp . nauk 165 , 481 ( 1995 ) [ phys . 38 , 457 ( 1995 ) ] . y. imry and s .- k . ma , phys . 35 , 1399 ( 1975 ) . g. parisi and n. sourlas , phys . 43 , 744 ( 1979 ) . j. z. imbrie , phys . 53 , 1747 ( 1984 ) . j. bricmont and a. kupiainen , phys . 59 , 1829 ( 1987 ) . young and m. nauenberg , phys . 54 , 2429 ( 1985 ) . h. rieger and a. p. young , j. phys . a 26 , 5279 ( 1993 ) . a. t. ogielski and d. a. huse , phys . 56 , 1298 ( 1986 ) . a. t. ogielski , phys . 57 , 1251 ( 1986 ) . j. cardy , phys . b 29 , 505 ( 1984 ) . d. p. belanger and a. p. young , j. magn . magn . mater . 100 , 272 ( 1991 ) . g. s. grest , c. m. soukoulis , and k. levin , phys . rev . b 33 , 7659 ( 1986 ) . f. ye , l. zhou , s. larochelle , et al . , 89 , 157 202 ( 2002 ) . d. p. landau , phys . 28 , 449 ( 1972 ) . h. muller - krumbhaar and d. p. landau , phys . b 14 , 2014 ( 1976 ) . v. v. prudnikov , o. n. markov , and e. v. osintsev , zh . 116 , 953 ( 1999 ) [ jetp 89 , 508 ( 1999 ) ] . k. binder , z. phys . b 43 , 119 ( 1981 ) . v. s. dotsenko , usp . nauk 163 ( 6 ) , 1 ( 1993 ) [ phys . 36 , 455 ( 1993 ) ] . e. pytte , y. imry , and d. mukamel , phys . rev . lett . 46 , 1173 ( 1981 ) .

it is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second - order phase transition to first - order transition to a new phase characterized by a spin - glass ground state and metastable energy states at finite temperatures . * monte carlo simulation of a random - field ising antiferromagnet * * v. v. prudnikov and v. n. borodikhin + omsk state university , pr .

phase transitions in the three - dimensional diluted ising antiferromagnet in an applied magnetic field are analyzed numerically . it is found that random magnetic field in a system with spin concentration below a certain threshold induces a crossover from second - order phase transition to first - order transition to a new phase characterized by a spin - glass ground state and metastable energy states at finite temperatures . * monte carlo simulation of a random - field ising antiferromagnet * * v. v. prudnikov and v. n. borodikhin + omsk state university , pr . mira 55 , omsk , 644077 russia + e - mail : prudnikv@univer.omsk.su *

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the conduction electron oscillations within a metallic nanoparticle driven by an external electromagnetic field gives rise to a localized surface plasmon resonance ( lspr ) . at the resonance , a metallic particle will confine light at the nanoscale , with the electric field being enhanced in the near - field region at the surface of the particle . the field enhancement and sub - wavelength character of lsprs can be applied to modify the spontaneous emission decay rate of nanoemitters @xcite and to control various nonlinear effects , such as second harmonic generation and raman scattering @xcite . however , due to the strong radiative damping , lsprs usually exhibit broad spectral linewidths and low quality factors @xcite which hinder potential applications . if the nanoparticles are placed in an array , the dipolar interactions between the particles may induce extra resonances . in particular , when the array periodicity is on the order of particle resonance wavelength , the coupling between the diffractive orders ( dos ) of the array and the lsprs on each individual particle will result in a collective resonance called surface lattice resonance ( slr ) @xcite . slrs on plasmonic nanoparticle arrays show angle dependent dispersions and have significantly narrower linewidths compared with lsprs on the individual particles . these features make metallic nanoparticle arrays suited for tailoring the light dispersion at the nanoscale . slrs have been utilized in light harvesting @xcite , emission control @xcite , strong light - matter interaction @xcite , and plasmonic lasing @xcite . recent works have also implemented slrs in magneto - plasmonic responses in magnetic nanoparticle arrays @xcite , dark mode excitation in asymmetric dimer arrays @xcite and superlattice plasmons in hierarchical gold particle arrays @xcite . even condensation phenomena have been theoretically studied @xcite . yet another interesting aspect of slrs stems from the fact that as the dipolar radiation pattern of the lspr is non - isotropic , the effective radiative coupling in different lattice directions will depend strongly on polarization , as shown in fig . [ fig : fig1 ] . moreover , since the coupling originates from the fairly slow - decaying radiation fields between the particles , any model relying only on the nearest - neighbor coupling , that is , the tight - binding model , is not sufficient to describe the system response . this raises the question whether such systems exhibit , for example , topologically non - trivial modes often found in tight - binding models @xcite and if so , whether these modes could have novel features . recent progress in nanofabrication makes nanoparticle arrays with different lattice symmetries possible . however , more complex geometries have been experimentally investigated only under normal incident angle @xcite , thus providing no information on the system dispersion . numerical models to calculate slr dispersions , such as the discrete dipole approximation ( dda ) , have been provided @xcite , but an intuitive description from which one can straightforwardly determine the expected mode structure of also more complicated lattices has been missing . in this article , we explore the various slrs supported by metallic nanoparticle arrays with different geometries . we provide a simple description of how complex lattice geometries affect the slr dispersions with a given polarization . our model uses simple diagrams to show how the different dispersions result from the coupling between the do vectors of the lattice and the dipole orientations on the individual nanoparticles . angle - resolved extinction spectra measured from silver nanoparticle arrays with square , hexagonal , rectangular , honeycomb and lieb lattices are well explained by the simple model we provide for both te- and tm - polarizations . finite - difference time - domain ( fdtd ) simulations are also performed to verify our interpretation . the complex dependence of the mode structure on the light polarization and the dipole orientations of individual particles suggests interesting possibilities if the polarization ( the dipole orientation ) is taken as a pseudospin degree of freedom . our results show that the plasmonic nanoparticle arrays might be used for realizing novel types of spin - orbit coupling and thereby topological states of light , and provide an efficient approach for designing such systems . this prospect is discussed in the conclusions .

plasmonic nanoarrays which support collective surface lattice resonances ( slrs ) have become an exciting frontier in plasmonics . compared with the localized surface plasmon resonance ( lspr ) in individual particles , these collective modes have appealing advantages such as angle - dependent dispersions and much narrower linewidths . here numerical simulations are performed to elucidate the field profiles of the different modes . our findings extend the diversity of slrs in plasmonic nanoparticle arrays , and the theoretical framework provides a simple model for interpreting the slrs features , and vice versa , for designing the geometrical patterns .

plasmonic nanoarrays which support collective surface lattice resonances ( slrs ) have become an exciting frontier in plasmonics . compared with the localized surface plasmon resonance ( lspr ) in individual particles , these collective modes have appealing advantages such as angle - dependent dispersions and much narrower linewidths . here , we investigate systematically how the geometry of the lattice affects the slrs supported by metallic nanoparticles . we present a general theoretical framework from which the various slr modes of a given geometry can be straightforwardly obtained by a simple comparison of the diffractive order ( do ) vectors and orientation of the nanoparticle dipole given by the polarization of the incident field . our experimental measurements show that while square , hexagonal , rectangular , honeycomb and lieb lattice arrays have similar spectra near the @xmath0-point ( @xmath1 ) , they have remarkably different slr dispersions . furthermore , their dispersions are highly dependent on the polarization . numerical simulations are performed to elucidate the field profiles of the different modes . our findings extend the diversity of slrs in plasmonic nanoparticle arrays , and the theoretical framework provides a simple model for interpreting the slrs features , and vice versa , for designing the geometrical patterns .

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we demonstrate experimentally a rich variety of dispersions of distinctive slrs supported by silver nanoparticle arrays of different geometries . square , hexagonal , rectangular , honeycomb and lieb arrays show remarkably different and polarization - dependent extinction dispersions , while a @xmath23-degree rotated square array shows less sensitivity to the choice of the te- or tm - polarized incident light . while previous work has studied the case of normal incidence @xcite , the present work constitutes the first systematic study of slr dispersions for arbitrary incident angles and for various lattice geometries . we propose an efficient generic model to explain and predict the features of different plasmonic lattice geometries . using simple diagrams , we show how the do vectors of the corresponding bravais lattice and the in - plane electric dipole orientation determine the slrs supported by certain geometrical structures . in a more complex structure , the particles within one unit cell contribute to an envelope factor for each do . the modes determined in this way have excellent agreement with the measured spectra . furthermore , this model also reveals the principal propagation direction of each mode , along which the mode maintains its coherence properties . this has been verified by numerical simulations of the near - field distributions in a square lattice . the radiation fields of individual particles extend over several unit cells of the structure , making plasmonic lattices an excellent platform for studying physics beyond the nearest neighbor hopping regime . furthermore , the role of disorder can be quite different in radiatively coupled plasmonic lattices compared to photonic or plasmonic lattices with evanescent nearest neighbor coupling . totally new areas of research may open by interpreting the individual particle dipole orientation as a pseudospin degree of freedom , or more generally , as a two - level or two - band system . the hamiltonian describing any two - level system has the generic form @xmath54 , where @xmath55 is a vector of the pauli matrices , and @xmath56 determines the types of couplings and @xmath57 is a parameter . this hamiltonian describes , for instance , graphene and spin - orbit coupled systems , and with suitable couplings and symmetries , dirac points , gap openings and topological phases can be found @xcite . as we have shown , in plasmonic lattices , the dispersion depends on the polarization , i.e. , on the particle dipole orientation . this can be viewed analogously to having a non - trivial @xmath58 term ( here @xmath59 now refers to the dipole orientation pseudospin , not to the spatial coordinates of the lattice ) . the spin - orbit coupling terms proportional to @xmath60 and @xmath61 are not present here . however , we propose that they can be introduced by utilizing non - trivial particle shapes , or magnetic nanoparticles @xcite where the two polarization ( dipole orientation ) directions are coupled due to intrinsic spin - orbit coupling in the magnetic material , and such couplings could be made momentum(@xmath57 ) dependent by designing the lattice geometry . it is especially interesting to envision that such non - trivial lattice systems may lead to new types of nanoscale lasing phenomena , so far observed only in simple square or rectangular lattices . this work was supported by the academy of finland through its centres of excellence programme ( project no . 284621 , no . 263347 and no . 272490 ) and by the european research council ( grant no . erc-2013-adg-340748-code ) . this article is based on work from cost action mp1403 nanoscale quantum optics , supported by cost ( european cooperation in science and technology ) . part of the research was performed at the micronova nanofabrication centre , supported by aalto university . 41ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12 & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrevlett.96.113002 [ * * , ( ) ] link:\doibase 10.1146/annurev.physchem.58.032806.104607 [ * * , ( ) ] link:\doibase 10.1063/1.2734503 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.97.206806 [ * * , ( ) ] link:\doibase 10.1016/j.cplett.2004.12.107 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.087403 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.101.143902 [ * * , ( ) ] link:\doibase 10.1103/physrevx.1.021019 [ * * , ( ) ] link:\doibase 10.1038/nphoton.2014.247 [ * * , ( ) ] link:\doibase 10.1021/nn502617 t [ * * , ( ) ] link:\doibase 10.1103/physrevlett.102.146807 [ * * , ( ) ] link:\doibase 10.1063/1.3693397 [ * * , ( ) ] link:\doibase 10.1364/oe.23.028206 [ * * , ( ) ] link:\doibase 10.1088/0034 - 4885/78/1/013901 [ * * , ( ) ] link:\doibase 10.1021/nl4035219 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.112.153002 [ * * , ( ) ] link:\doibase 10.1002/adma.200305221 [ * * , ( ) ] link:\doibase 10.1038/nnano.2013.99 [ * * , ( ) ] link:\doibase 10.1002/lpor.201400056 [ * * , ( ) ] link:\doibase 10.1038/ncomms7939 [ * * , ( ) ] http://arxiv.org/abs/1606.07404 [ ( ) ] , link:\doibase 10.1038/ncomms8072 [ * * , ( ) ] link:\doibase 10.1021/acsphotonics.5b00490 [ * * , ( ) ] link:\doibase 10.1021/acsphotonics.5b00727 [ * * , ( ) ] link:\doibase 10.1021/acsphotonics.5b00546 [ * * , ( ) ] link:\doibase 10.1103/physreva.90.053604 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.110.106801 [ * * , ( ) ] link:\doibase 10.1103/physrevb.90.075404 [ * * , ( ) ] link:\doibase 10.1016/s0166 - 1280(01)00545 - 0 [ * * , ( ) ] link:\doibase 10.1021/jp026731y [ * * , ( ) ] @noop _ _ ( , ) p. link:\doibase 10.1103/physrevlett.114.245503 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.114.245504 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.116.066402 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.116.183902 [ * * , ( ) ] @noop _ _ ( , ) p. link:\doibase 10.1103/revmodphys.82.3045 [ * * , ( ) ] link:\doibase 10.1038/nphoton.2014.248 [ * * , ( ) ] link:\doibase 10.1038/nphys3796 [ * * , ( ) ] link:\doibase 10.1103/physrevlett.100.013904 [ * * , ( ) ] link:\doibase 10.1103/physreva.78.033834 [ * * , ( ) ]

, we investigate systematically how the geometry of the lattice affects the slrs supported by metallic nanoparticles . our experimental measurements show that while square , hexagonal , rectangular , honeycomb and lieb lattice arrays have similar spectra near the @xmath0-point ( @xmath1 ) , they have remarkably different slr dispersions .

plasmonic nanoarrays which support collective surface lattice resonances ( slrs ) have become an exciting frontier in plasmonics . compared with the localized surface plasmon resonance ( lspr ) in individual particles , these collective modes have appealing advantages such as angle - dependent dispersions and much narrower linewidths . here , we investigate systematically how the geometry of the lattice affects the slrs supported by metallic nanoparticles . we present a general theoretical framework from which the various slr modes of a given geometry can be straightforwardly obtained by a simple comparison of the diffractive order ( do ) vectors and orientation of the nanoparticle dipole given by the polarization of the incident field . our experimental measurements show that while square , hexagonal , rectangular , honeycomb and lieb lattice arrays have similar spectra near the @xmath0-point ( @xmath1 ) , they have remarkably different slr dispersions . furthermore , their dispersions are highly dependent on the polarization . numerical simulations are performed to elucidate the field profiles of the different modes . our findings extend the diversity of slrs in plasmonic nanoparticle arrays , and the theoretical framework provides a simple model for interpreting the slrs features , and vice versa , for designing the geometrical patterns .

1606.02484

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quantum information and quantum communication have greatly impacted the development direction of modern science . on the one hand , quantum cryptograph , such as quantum key distribution @xcite , quantum secret sharing ( qss ) @xcite , quantum data hiding @xcite , quantum signature @xcite and quantum authentication @xcite can achieve high - level security than their classical counterparts @xcite . on the other hand , quantum algorithms , such as grover s search algorithm @xcite , can solve a certain problem much faster than classical algorithms @xcite . in quantum world , quantum entanglement is a crucial resource and an amazing application of entanglement is quantum teleportation @xcite , which can securely transmit a quantum state from a preparer to a remote receiver by virtue of pre - shared entangled resource . if the preparer has already known the information of the state , the transmission can be achieved by rsp @xcite with simpler measurement and less classical communication costs . the original rsp scheme only has one preparer who knows all the information of the prepared state . but for highly sensitive and important information , it might not be reliable to let one person hold everything . to solve this potential problem , joint rsp ( jrsp ) has been proposed @xcite , which involves at least two preparers . each preparer holds partial information and only if certain preparers work together can the state be remotely prepared , similar to the idea of secret sharing . however , a serious problem for most of the previous jrsp schemes @xcite is that they are probabilistic , i.e. , the success probability is less than 1 . recently , a new direction of jrsp , namely deterministic jrsp ( djrsp ) has been put forward . xiao et al . @xcite introduced the three - step strategy to increase the success probability of jrsp . by adding some classical communication and local operations , the success probability of preparation can be increased to 1 . nguyen et al . @xcite presented two djrsp schemes of general one- and two - qubit states by using epr pairs . chen et al . @xcite extended this idea to realize a djrsp of an arbitrary three - qubit state by using six epr pairs . in 2014 , we proposed a deterministic jrsp scheme of an arbitrary two - qubit state based on the six - qubit cluster state @xcite . quantum noise is an unavoidable factor in practical quantum communication system , which will severely affect the security and reliability of the system @xcite . for a rsp scheme , the entanglement shared among participants will turn a pure state into a mixed one in the presence of noise . in recent years , some rsp schemes in noisy environment have been studied . xiang et al . @xcite presented a rsp protocol for mixed state in depolarizing and dephasing channel . chen et al . @xcite investigated remote preparation of an entangled state through a mixed state channel in nonideal conditions . guan et al . @xcite studied a jrsp of an arbitrary two - qubit state in the amplitude - damping and the phase - damping noisy environment . liang et al . @xcite investigated a jrsp of a qubit state in different noises by solving lindblad master equation . sharma et al . @xcite investigated the effect of amplitude - damping and phase - damping noise on a bidirectional rsp protocol . @xcite investigated a djrsp of an arbitrary two - qubit state via four epr pairs channel which are subjected to several markovian noises . they analyzed the djrsp scheme by solving the master equation in lindblad form . in real - world implementation , quantum communication protocols usually encountered four types of noise , namely the bit - flip , phase - flip ( phase - damping ) , depolarizing , and amplitude - damping noise . in this paper , we will study noise influence of all types of noise on djrsp . taking a one - qubit ghz based djrsp scheme as an example , we will show that for different types of noise , the prepared state and the fidelity of the output state are quite different from each other . the rest of this paper is organized as follows . in sect . 2 , we show our djrsp scheme of an arbitrary one - qubit state in ideal environment . then , we investigate the effect of noise on the scheme with the four types of noise in sect . 3 , respectively . the paper is concluded in sect .

quantum secure communication brings a new direction for information security . as an important component of quantum secure communication , deterministic joint remote state preparation ( djrsp ) could securely transmit a quantum state with 100% success probability . in this paper , we study how the efficiency of djrsp is affected when qubits involved in the protocol are subjected to noise or decoherence . taking a ghz based djrsp scheme as an example ,

quantum secure communication brings a new direction for information security . as an important component of quantum secure communication , deterministic joint remote state preparation ( djrsp ) could securely transmit a quantum state with 100% success probability . in this paper , we study how the efficiency of djrsp is affected when qubits involved in the protocol are subjected to noise or decoherence . taking a ghz based djrsp scheme as an example , we study all types of noise usually encountered in real - world implementations of quantum communication protocols , i.e. , the bit - flip , phase - flip ( phase - damping ) , depolarizing , and amplitude - damping noise . our study shows that the fidelity of the output state depends on the phase factor , the amplitude factor and the noise parameter in the bit - flip noise , while the fidelity only depends on the amplitude factor and the noise parameter in the other three types of noise . and the receiver will get different output states depending on the first preparer s measurement result in the amplitude - damping noise . our results will be helpful for improving quantum secure communication in real implementation .

1606.02484

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starting with the scheme in ideal condition , we investigated the djrsp scheme in four types of noise , respectively . as shown in the paper , some information of the prepared state is lost through the noise channels . we use fidelity to describe how close are the final states to the original state and how much information has been lost in the process . the result of our study shows that the prepared state and the fidelity of the state is quite different from each other in different types of noise . for one thing , the fidelity of the prepared state in the bit - flip noise depends on the amplitude factor @xmath126 and the phase factor @xmath127 of the initial state , and the noise parameter @xmath44 . but in the other three types of noise , the fidelity only depends on the amplitude factor and the noise parameter , but have nothing to do with the phase parameter @xmath127 . for another thing , in the amplitude - damping noise , it is interesting that the receiver charlie will get different prepared output states depending on the first preparer alice s measurement result @xmath14 . but in the other three types of noise , the receiver will get the same output state , which is irrelevant to the first preparer alice s measurement result . we have considered the case where the qubits in bob s and charlie s side were affected by quantum noise . it should be noted that the qubit a in alice s side may still be affected by noise . in this case , the noise effect on the quantum channel can be represented as @xmath128 we can still calculate the noise effect on entanglement channel in different types of noise , just as mentioned sect . [ sec:3 - 2 ] . and it is also possible to consider the situation where different qubits are subjected to different types of noise . in summary , we have studied a djrsp scheme of an arbitrary single qubit in noisy environment and shown how the scheme is affected by all types of noise usually encountered in real - world . our results will be helpful for analyzing and improving quantum secure communication in real implementation . to show our method , we have considered a simple case where three participants were involved . in the future , it is also possible to analyze other situations such as multi - participants involved or multi - qubit prepared .

our study shows that the fidelity of the output state depends on the phase factor , the amplitude factor and the noise parameter in the bit - flip noise , while the fidelity only depends on the amplitude factor and the noise parameter in the other three types of noise . and the receiver will get different output states depending on the first preparer s measurement result in the amplitude - damping noise . our results will be helpful for improving quantum secure communication in real implementation .

quantum secure communication brings a new direction for information security . as an important component of quantum secure communication , deterministic joint remote state preparation ( djrsp ) could securely transmit a quantum state with 100% success probability . in this paper , we study how the efficiency of djrsp is affected when qubits involved in the protocol are subjected to noise or decoherence . taking a ghz based djrsp scheme as an example , we study all types of noise usually encountered in real - world implementations of quantum communication protocols , i.e. , the bit - flip , phase - flip ( phase - damping ) , depolarizing , and amplitude - damping noise . our study shows that the fidelity of the output state depends on the phase factor , the amplitude factor and the noise parameter in the bit - flip noise , while the fidelity only depends on the amplitude factor and the noise parameter in the other three types of noise . and the receiver will get different output states depending on the first preparer s measurement result in the amplitude - damping noise . our results will be helpful for improving quantum secure communication in real implementation .

0711.4778

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the unitary extension of chiral perturbation theory , u@xmath0pt , has been successfully applied to study many meson - baryon and meson - meson interactions . more recently , it has been used to study the lowest axial vector mesons @xmath3 , @xmath4 , @xmath5 , @xmath6 , @xmath7 , @xmath1 and @xmath8 @xcite . both works generate most of the low - lying axial vector mesons dynamically . however , there is a surprising discovery in ref . @xcite , i.e. , two poles are found in the second riemann sheet in the @xmath9 and @xmath10 channel and both are attributed to the @xmath1 . although the @xmath1 has been observed in various reactions , the most conclusive and high - statistics data of the @xmath1 come from the wa3 experiment at cern that accumulated data on the reaction @xmath11 at 63 gev . these data were analyzed by the accmor collaboration @xcite . as will be shown in this paper , the two - peak structure , with a peak at lower energy depending drastically on the reaction channel investigated , can be easily explained in our model with two poles for the @xmath1 plus the @xmath8 . with only one pole , as has been noted long time ago @xcite , there is always a discrepancy for the peak positions observed in the @xmath12 and @xmath13 invariant mass distributions .

in particular , two poles in the second riemann sheet have been associated to the nominal @xmath1 resonance . in this talk , we present a recent analysis of the wa3 data on @xmath2 at 63 gev using the u@xmath0pt amplitudes , and show that it is in favor of the existence of two @xmath1 s [ phys . rev .

recent studies based on unitary chiral perturbation theory ( u@xmath0pt ) found that the low - lying axial vector mesons can be dynamically generated due to the interaction of the pseudoscalar octet of the pion and the vector nonet of the rho . in particular , two poles in the second riemann sheet have been associated to the nominal @xmath1 resonance . in this talk , we present a recent analysis of the wa3 data on @xmath2 at 63 gev using the u@xmath0pt amplitudes , and show that it is in favor of the existence of two @xmath1 s [ phys . rev . d 75 , 014017 ( 2007 ) ] . = 11.6pt

astro-ph0609469

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blue - shifted , broad absorption lines ( bal ) are observed in the ultraviolet spectra of about 10 - 20% luminous quasars . these lines are formed in partially ionized outflows with velocities up to 0.1 c. the outflow is likely driven by intensive radiation of the quasar probably along the equatorial directions to the extension at least larger than the broad emission line region , and is likely several 10 parsecs . disk wind and material evaporating from the putative dust torus are two plausible scenarios for the origin of the gas . it is usually believed that bal region exists in every quasar , but only covers a small fraction of quasar sky ( weymann et al . 1991 ; reichard et al . 2003 ; green et al . 2001 ; hamann , korista & morris 1993 , hereafter hkm93 ) . the outflow may carry a significant fraction of power released by the accretion process and momentum into the host galaxy of the quasar , so that it will influence the subsequent evolution of the galaxy . however , in order to establish its role , we need to understand many properties of the outflow such as the global covering factor of bal region , the column density and velocity field as a factor of the distance to the continuum sources . the absorption line profiles are usually quite stable over time scales of several to ten years , suggesting of smooth outflow and/or saturation of the uv emission lines . similar line strength from ions of very different abundance and strong absorption detected in soft x - rays supports latter interpretations ( brinkmann et al . 1999 ; wang et al . 1999 ; gallagher et al . the broad absorption lines have now probably been detected also in x - rays with much large column densities . if confirmed , this will suggest that the very high velocity outflow is already there at very close to the continuum emission region . efficient acceleration at small scale is required . however , census has yet to be reach on a number of critical issues : ( 1 ) the covering factor of balr is likely a function of fundamental parameters , such as the black hole mass and the accretion rate , which may lead to some difference in the statistical properties of the bal qsos and non - bal qsos ( boroson 2002 ) , but we still need to find concrete evidence for this and their potential relation . ( 2 ) whether the outflow is equatorial or polar is still a matter of controversy . recent vlbi observations of a small number of radio loud bal quasars with equal number of steep and flat radio spectra reveal only compact structure in most case ( jiang d.r . et al . in preparation ) . while based on the radio variability , zhou et al . ( 2006 ) proposed polar outflows in six radio loud quasars . it is still unclear that whether radio loud bal quasars are special . hydrodynamic simulation of accretion disk wind models , however , results in an equatorial outflow . we note including poloid magnetic field in the accretion disk may change the simulation results as for the radio jet model ( blandford & payne 1982 ) ; ( 3 ) whether the outflow carry significant angular momentum , i.e. , whether the massive disk wind serves as the driver of the accretion process . ( 4 ) there is big concern whether certain ultraviolet emission lines such as nv , civ will be significantly affected by resonant scattering process , such that we need to revise our metallicity determination in some objects . our current knowledge about the balr is almost exclusively from either absorption lines or x - ray absorption edge . unfortunately , both types of absorption carries only information of the absorbing gas along the line of sight to the continuum source , and we have to rely on the statistics of a large sample of bal quasars to obtain the average information of the global properties . note such information ( on the global properties ) is contained in the scattered light , i.e. , the polarized flux . broad absorption line qsos ( bal qsos ) are the only highly polarized population among radio quiet qsos ( e.g. , stockman , moore & angel 1984 ) . its optical / uv continuum shows polarization ( e.g. , stockman et al . 1984 ; schmidt & hines 1999 ; hutsem@xmath0kers & lamy 2001 ) , much larger than that of non - bal qsos . the high continuum polarization is believed due to the electron scattering probably in the bal region ( balr , stockman et al . 1984 ; ogle 1997 ; wang , wang , wang 2005 , hereafter paper i ) . in paper i we also show that if the balr exists in all qsos , and covers around 20% of the solid angle , the electron scattering in the balr can successfully explain the observed continuum polarization for both bal qsos and non - bal qsos . observations show that the polarization is even stronger in the bal trough than in the continuum . ogle et al . ( 1999 , hereafter o99 ) presented a spectropolarimetric survey of 36 bal qsos , and found : * the bal troughs are usually more polarized than the continuum , whereas the broad emission lines are less polarized ( also see cohen et al . 1995 ; hines et al . deeper bal troughs tend to have higher polarization degrees . the polarization in the trough can be as high as @xmath120% . * position angle ( pa ) of the polarization in the troughs are quite common , and smaller rotations across the corresponding emission lines were found in some objects . * in the spectra of the polarized flux , the absorption line troughs are usually evident but appear shallower and show various characteristics : the troughs in polarized flux are more blueshifted than that in the total flux spectrum in some objects ; a sub - trough emerges to the red side of the civ , siiv and/or nv absorption trough in the polarized flux in several objects , e.g. , 0105 - 0265 , 0226 - 1024 , 1413 + 1143 @xmath2 1333 + 2840 ; occasionally , a boxy absorption trough , similar to that in the total flux , was also detected ( e.g. , in 2225 - 0534 and 1232 + 1325 ) . * excess polarized flux across the corresponding emission lines is observed in several objects ( see also lamy & hutsem@xmath0kers 2004 ) . two processes were proposed to explain the origin of the polarization in the absorption line troughs . if the balr does not cover or only - partially covers the electron scattering region , the leaked scattered photons will fill the troughs , thus produce high polarization ( hines & wills 1995 ; goodrich & miller 1995 ; ogle 1997 ; o99 ; lamy & hutsem@xmath0kers 2004 ) . on the other hand , lee & blandford ( 1997 , hereafter lb97 ) showed that resonant scattering can produce polarization degree as large as 15% in the troughs for doublet transitions . note lb97 does not calculate the pa rotation for resonant scattering light . since then , our knowledge about the column density , and the geometry of balr has changed considerably from the x - ray observations as well as high resolution uv spectroscopy . in particularly , as showed in paper i , the electron scattering in the balr can produce the continuum polarization . by taking these new information into consideration , we will explore in detail the polarization properties of resonantly scattered light , including the polarization degree , polarized flux and position angle of the polarization for different models using monte carlo method . this paper is organized as follows . the geometries and dynamics of the outflow model and the monte - carlo method will be described in 2 . the results of monte - carlo simulation are given separately for singlet and doublet transitions in 3 and 4 , respectively . in 5 , we will compare our results with the observed polarized spectra of a sample of bal qsos ( o99 ) to put constraints on the geometries and kinematics of the flow . resonantly scattered lines are discussed in 6 .

this material may contribute significantly to the polarization in the absorption lines . in this paper , we present a detailed study of the resonant line scattering process using monte - carlo method to constrain the optical depth , the geometry and the kinematics of bal region ( balr ) . by comparing our results with observed polarized spectra of bal quasars , we find : ( 1 ) resonant scattering can produce polarization up to 9% at the absorption trough for doublet transitions and up to 20% for singlet transitions in radially accelerated flows . to explain the large polarization degree in the civ , nv absorption line troughs detected in a small fraction of bal qsos , a nonmonotonic velocity distribution along the line of sight or / and additional contribution from the electron scattering region is required . ( 2 ) the rotation of the flow can lead to the rotation of the polarization position angle ( pa ) in the line trough .

recent works showed that the absorbing material in broad absorption line ( bal ) quasars is optically thick to major resonant absorption lines . this material may contribute significantly to the polarization in the absorption lines . in this paper , we present a detailed study of the resonant line scattering process using monte - carlo method to constrain the optical depth , the geometry and the kinematics of bal region ( balr ) . by comparing our results with observed polarized spectra of bal quasars , we find : ( 1 ) resonant scattering can produce polarization up to 9% at the absorption trough for doublet transitions and up to 20% for singlet transitions in radially accelerated flows . to explain the large polarization degree in the civ , nv absorption line troughs detected in a small fraction of bal qsos , a nonmonotonic velocity distribution along the line of sight or / and additional contribution from the electron scattering region is required . ( 2 ) the rotation of the flow can lead to the rotation of the polarization position angle ( pa ) in the line trough . large extending angle of balr is required to produce the observed large pa rotation in a few bal qsos . ( 3 ) a large extending angle of balr is required to explain a sub - trough in the polarized flux that was observed in a number of bal qsos . ( 4 ) the resonant - scattering can contribute a significant part of nv emission line in some qsos , and may give rise to anomalous strong nv lines in these quasars . ( 5 ) the polarized flux and pa rotation produced by the resonant scattering in non - bal is uniquely asymmetric , which may be used to test the presence of balr in non - bal qsos .

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polarization provides rich information on the structure and kinematics of balr in qsos , which is complementary to those derived from absorption lines , which only depend on the physical condition and kinematics of gas on the los . to extract this information , we carry out extensive monte - carlo simulations of electron and resonance scattering process in the balrs . both singlet and doublet transitions are considered for radial outflows of two different geometries : equatorial outflows and hollow - conical outflows with and without rotational velocities . in an axisymmetric scatterer model , pa rotation in the absorption trough can be produced only when the outflow carries angular momentum . the pa rotation increases with the angular velocity as well as the subtending angle of the flow . in order to produce a pa rotation @xmath4 10observed in a few bal qsos , subtending angle of the outflow should be larger than 25 . similar requirement is imposed to explain the red sub - trough in the polarized flux observed in some bal qsos . resonant scattering of doublet transition produces much lower polarization at large optical depths ( about 6% for @xmath91 , @xmath80 ) for an accelerating outflow . large ( @xmath410% ) polarization in the absorption trough detected in a few bal qsos may indicate that the optical depth to the resonant scattering is at most moderate , otherwise resonant scattering of @xmath143 transition will erase all polarization . a slowly - accelerating model can produce larger polarization . if the observed high - velocity outflow in x - ray is real , the flow is likely decelerating , which will produce much larger polarization . a large electron scattering region can also produce larger polarization . the jump which appears at the starting velocity of the absorption trough in pa rotation and polarized flux in models with a sesr does not appear in the model with a lesr . this characteristic may be an important indicator to distinguish different electron scattering models . we find that lesr models can explain that the absorption troughs are more blueshifted in polarized flux , relative to that in the total flux , and pa swings in the troughs , @xmath197 relative to continuum , in some objects . we show that the resonantly scattered light will contribute a significant part of nv in some qsos and can give rise to anomalous strong nv lines in these qsos . a correlation between the ew of nv@xmath1471240 with the continuum polarization is expected . we propose that the polarized flux and the pa rotation of the scattering emission can be used to test the presence of balr in non - bal qsos . further observations with large telescopes should allow us to extract the important information about the flow geometry and kinematics . antonucci , r. 1993 , , 31 , 473 arav , n. , becker , r. h. , laurent - muehleisen , s. a. , gregg , m. d. , white , r. l. , brotherton , m. s. , & de kool , m. 1999 , , 524 , 566 blandford , r. , agol , e. , broderick , a. , heyl , j. , koopmans , l. , & lee , h. 2002 , astrophysical spectropolarimetry , 177 blandford , r. d. , & payne , d. g. 1982 , , 199 , 883 brinkmann , w. , wang , t. , matsuoka , m. , & yuan , w. 1999 , , 345 , 43 boroson , t. a. 2002 , , 565 , 78 chandrasekhar s. , 1950 , radiative transfer chartas , g. , brandt , w. n. , gallagher , s. c. , & garmire , g. p. 2002 , , 579 , 169 chartas , g. , brandt , w. n. , & gallagher , s. c. 2003 , , 595 , 85 clavel , j. , schartel , n. , & tomas , l. 2006 , , 446 , 439 cohen , m. h. , ogle , p. m. , tran , h. d. , vermeulen , r. c. , miller , j. s. , goodrich , r. w. , & martel , a. r. 1995 , , 448 , l77 de kool , m. , & begelman , m. c. 1995 , , 455 , 448 dong , x .- b . , zhou , h .- y . , wang , t .- g . , wang , j .- x . , li , c. , & zhou , y .- y . 2005 , , 620 , 629 elvis , m. 2000 , , 545 , 63 everett j.e . , 2002 , submitted to apj ferland g.j . , baldwin j.a . , korista k.t . , hamann f. , carswell r.f . , phillips m. , wilkes b. , williams r.e . , 1996 , apj , 461 , 683 - 697 gallagher , s. c. , brandt , w. n. , chartas , g. , & garmire , g. p.2002 , , 567 , 37 goodrich , r. w. , & miller , j. s. 1995 , , 448 , l73 green , p. j. , aldcroft , t. l. , mathur , s. , wilkes , b. j. , & elvis , m. 2001 , , 558 , 109 hamann f. 1998 , apj , 500 , 798 hamann , f. , & ferland , g. 1992 , , 391 , l53 hamann , f. , & ferland , g. 1993 , , 418 , 11 hamann , f. , korista , k. t. , & morris , s. l. 1993 , , 415 , 541 hines , d. c. , & wills , b. j. 1995 , , 448 , l69 hines , d. , schmidt , g. , smith , p. , & weymann , r. 1995 , bulletin of the american astronomical society , 27 , 1410 hutsem@xmath0kers d. , lamy h. , 2001 , asp conference series konigl , a. , & kartje , j. f. 1994 , , 434 , 446 lamy , h. , & hutsem ' ekers , d. 2004 , , 427 , 107 lee h.w . , blandford r.d . , western l. , 1994 , 267 , 303 - 311 lee h.w . , 1994 , 268,49 - 60 lee h.w . , blandford r.d . , 1997,mnras , 288,19 - 42 martnez - sansigre , a. , rawlings , s. , lacy , m. , fadda , d. , marleau , f. r. , simpson , c. , willott , c. j. , & jarvis , m. j.2005 , , 436 , 666 murray n. , chiang j. grossman s.a . , voit g.m . , 1995 , apj , 451 , 498 - 509 ogle , p. m. 1997 , asp conf . ser . 128 : mass ejection from active galactic nuclei , 128 , 78 ogle p.m. , cohen m.h . , miller j.s . , tran h.d . , goodrich r.m . , martel a.r . , 1999 , 125 , 1 - 34 proga , d. , stone , j. m. , & kallman , t. r. 2000 , , 543 , 686 reichard , t. a. , et al . 2003 , , 126 , 2594 ruiz , j. r. , crenshaw , d. m. , kraemer , s. b. , bower , g. a. , gull , t. r. , hutchings , j. b. , kaiser , m. e. , & weistrop , d. 2001 , , 122 , 2961 schmidt , g. d. & hines , d. c. 1999 , , 512 , 125 stockman , h. s. , moore , r. l. , & angel , j. r. p. 1984 , , 279 , 485 voit , g. m. , weymann , r. j. , & korista , k. t. 1993 , , 413 , 95 wang , h .- y . , wang , t .- , & wang , j .- x . 2005 , , 634 , 149 wang , t. g. , brinkmann , w. , yuan , w. , wang , j. x. , & zhou , y. y. 2000 , , 545 , 77 wang t.g . , wang j.x . , brinkmann w. , matsuoka m. , 1999 , apjl . 519 , l35-l38 weymann r.j . , morris s.l . , foltz c.c . , hewett p.c . , 1991 , apj , 373 , 23 zhou , h. , wang , t. , wang , h. , wang , j. , yuan , w. , & lu , y. 2006 , , 639 , 716 we denote the stokes parameters @xmath72 and @xmath73 of the continuum as @xmath198 and @xmath199 . for simplicity , we choose @xmath200 and @xmath201 , where @xmath202 is the polarized flux of the continuum . if @xmath203 the pa of the continuum polarization ( hereafter @xmath204 ) is 0@xmath8 otherwise @xmath205@xmath10 . we assume that pa of the line scattered photon is pa@xmath169 so the @xmath2062pa@xmath207 . the stokes parameters of the total flux are @xmath208 , @xmath209 ; the total polarized flux @xmath210 reads , @xmath213 + when @xmath214 and @xmath215 , one obtains @xmath212 , i.e , an absorption trough appears in the polarized flux . since the total flux equals to the @xmath216 the feature is not shown in the total flux . on the other hand , if @xmath217 , one yields @xmath218 . in the rest of this appendix we will obtain the relationship between @xmath167 and @xmath198 for different models . now consider an outflow between [ 90@xmath220 , 90@xmath8@xmath9 ] . for light from an incident direction @xmath52 that is scattered into the direction @xmath56 , the density matrix can be written as ( see @xmath60 1 & 2 of paper i ) : in an outflow model , red - shifted photons are escaped from the portion with 90@xmath133 and the blue - shifted ones from the -90@xmath228 . according to @xmath60 a6 , the blue - shifted photons always have @xmath229 . however , the redshifted scattered light may have negative @xmath167 following @xmath60 a7 . the portion of the flow that produces negative @xmath167 increases with @xmath7 . it is small for small @xmath7 and reachs half of backward flow ( 135@xmath230 ) for @xmath231 . consequently , for a small @xmath7 the total @xmath167 of red - shifted scattered photons is larger than 0 . if @xmath198 is also positive , an excess polarized flux across the emission line will be seen ; otherwise , an absorption trough is observed ( fig . 22 ) . for a large @xmath7 , redshifted scattered light has negative @xmath167 , a sub - trough to the red side of primary trough will be observed when @xmath198 is positive .

large extending angle of balr is required to produce the observed large pa rotation in a few bal qsos . ( 3 ) a large extending angle of balr is required to explain a sub - trough in the polarized flux that was observed in a number of bal qsos . ( 4 ) the resonant - scattering can contribute a significant part of nv emission line in some qsos , and may give rise to anomalous strong nv lines in these quasars .

recent works showed that the absorbing material in broad absorption line ( bal ) quasars is optically thick to major resonant absorption lines . this material may contribute significantly to the polarization in the absorption lines . in this paper , we present a detailed study of the resonant line scattering process using monte - carlo method to constrain the optical depth , the geometry and the kinematics of bal region ( balr ) . by comparing our results with observed polarized spectra of bal quasars , we find : ( 1 ) resonant scattering can produce polarization up to 9% at the absorption trough for doublet transitions and up to 20% for singlet transitions in radially accelerated flows . to explain the large polarization degree in the civ , nv absorption line troughs detected in a small fraction of bal qsos , a nonmonotonic velocity distribution along the line of sight or / and additional contribution from the electron scattering region is required . ( 2 ) the rotation of the flow can lead to the rotation of the polarization position angle ( pa ) in the line trough . large extending angle of balr is required to produce the observed large pa rotation in a few bal qsos . ( 3 ) a large extending angle of balr is required to explain a sub - trough in the polarized flux that was observed in a number of bal qsos . ( 4 ) the resonant - scattering can contribute a significant part of nv emission line in some qsos , and may give rise to anomalous strong nv lines in these quasars . ( 5 ) the polarized flux and pa rotation produced by the resonant scattering in non - bal is uniquely asymmetric , which may be used to test the presence of balr in non - bal qsos .

0902.0893

i

transport of inertial particles is involved in several fields of science , e.g. droplets growth in clouds , @xcite , planetary formations , @xcite , or plankton accumulation in the ocean , @xcite . as far as technological applications are concerned , inertial particle dynamics is crucial for solid or liquid fuelled rockets , injection systems of internal combustion engines or for sediments accumulation in pipelines , e.g. @xcite . inertial particles differ from perfectly lagrangian tracers due to inertia which prevents them from following the flow trajectories . the main effect consists of `` preferential accumulation '' , see for instance @xcite . in homogeneous isotropic conditions it amounts to the small - scale clustering discussed in a number of recent papers , @xcite . in presence of inhomogeneity new features emerge leading to the so - called turbophoresis as a preferential accumulation near the boundary in wall turbulence @xcite . under appropriate conditions , particles may achieve extremely large concentrations at the wall with a substantial reduction of mobility . this turbulence - induced transport and the issuing preferential accumulation as been addressed in a number of papers dealing with a variety of configurations , from boundary layers to planar channels and pipes , attacked both from the experimental @xcite and the numerical @xcite side . though a complete understanding of the phenomenon is still lacking , the advection of the particles by the coherent motions in the wall - layer is certainly essential , as discussed by @xcite . in other words the structures responsible for particle accumulation at the wall are the same which sustain turbulence kinetic energy production in the buffer layer , see also @xcite . turbophoresis and small scale clustering are different aspects of the same inertial particle dynamics . both phenomena are induced by non trivial phase relationships due to quasi - coherent vortical structures . the main difference is provided by the characteristic scales , associated with the kolmogorov time unit @xmath1 in one case@xmath2 being kolmogorov length and @xmath3 the kinematic viscosity and with the larger energy producing time scale in the other . inhomogeneity is essential to have spatial segregation . for instance , in the kinetic model presented in @xcite , the spatial transport of particle concentration presents , beside a fick - like gradient type diffusion component , a contribution associated with the spatial variations of turbulence intensity . however anisotropy is probably a key ingredient of the process , see e.g. the preferential direction of the trajectories of particles approaching the wall @xcite . the two features are strongly entangled in wall bounded flows . a special flow exists however the homogeneous shear flow in a confined box which retains most of the anisotropic dynamics of wall bounded flows still preserving , on average , spatial homogeneity . the flow is bound by a computational box of fixed extension and its integral scale grows initially to eventually saturate due to confinement . target of the analysis is the statically steady state with time independent ensemble averages . similar features are found in the the experimental data by @xcite . by using an active grid to generate a flow with integral scale close to the transversal dimension of the apparatus , the authors were able to achieve confinement from the outstart . as a consequence , the integral scale did not increase downstream , see also the discussion in @xcite . our flow shares with the wall - layer streamwise vortices and turbulent kinetic energy production mechanisms . in the numerical experiment , this corresponds to pseudo - cyclic fluctuations associated with the regeneration of streamwise vortical structures . velocity fluctuations are strongly anisotropic at the large scales driven by production while , for smaller separations , the classical energy transfer mechanisms become effective in inducing re - isotropization . this classical issue , see e.g. @xcite , has been recently revisited by more complete diagnostic tools ( e.g. so(3 ) decomposition of turbulent fluctuations ) able to quantify on a scale - by - scale basis the amount of anisotropy in the carrier fluid , as discussed both experimentally @xcite and numerically @xcite ( see @xcite for a review ) . despite anisotropy of the velocity field is now well understood and the carrier fluid shows tendency towards isotropy recovery below the shear scale , @xmath4 with @xmath5 the average turbulent kinetic energy dissipation rate per unit mass and @xmath6 the average shear rate , the behavior of particle distributions is still not fully explored . anisotropic transport of inertial particles has been recently addressed by @xcite , who analyzed numerically the initial transient of the homogeneous shear flow , i.e. before saturation of the integral scale occurs , with the purpose of modeling unconfined conditions . the focus was mainly on the comparison of different particle dynamics models . however , by considering particle configurations in orthogonal planes , the authors also discussed the anisotropy of particle clusters concluding that particles are most concentrated in the streamwise and least concentrated in the cross - stream direction . the same flow was dealt with by @xcite to investigate issues such as turbulence modulation in the two way coupling regime or heat transfer induced by the disperse phase . purpose of the present paper is the quantitative evaluation of the shear induced anisotropy in particles clustering . it is now well known that particles respond to the fluid velocity fluctuations in a certain range of scales which is determined by their stokes time . the relevant parameter is the stokes number , ratio of particle stokes time and flow time scale . in order to work with well defined conditions , one needs a shear flow whose characteristic time and length scales are constant in time . the best candidate , is the statistically steady homogeneous shear flow in a confined box we have described above . in this flow , below the shear scale , the velocity fluctuations tend to recover isotropy . the question is then what happens to particle clusters . do they become isotropic in the smallest scales ? for given velocity field , how is the geometry of the clusters affected by the relaxation time of the particles ? in fact , the main contribution of the present study is the quantitative evidence that particle distributions do not necessarily reduce their anisotropy at small scales , despite the isotropy recovery occurring in the velocity field . rather clusters anisotropy may even grow below the kolmogorov length where the velocity field is smooth and almost isotropic . as a matter of fact , inertia manifest itself in a rather peculiar and unexpected way , and leads , under certain coupling conditions , to singular particle distributions which viscosity can not regularize @xcite . after introducing a suitable observable the angular distribution function its spherical decomposition is used to evaluate the relative importance of its different components . the scaling exponents of the respective singularities show that , under appropriate conditions , anisotropy is a leading order effect which may easily persist down to vanishing separations . the data offer preliminary evidence of the anisotropic geometry of the fractal support of inertial particle distributions under shear flows , thus non - trivially extending results recently achieved for isotropic transport .

recently , clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows . much less is known concerning anisotropic flows . here , by addressing direct numerical simulations ( dns ) of a statistically steady particle - laden homogeneous shear flow , quantitative evaluation is provided by a purposely designed tool , the angular distribution function of particle pairs ( adf ) , which allows to address the anisotropy content of particles aggregates on a scale by scale basis . the data provide evidence that , depending on the stokes relaxation time of the particles , anisotropic clustering may occur even in the range of scales where the carrier phase velocity field is already recovering isotropy . the strength of the singularity in the anisotropic component of the adf quantifies the level of fine scale anisotropy , which may even reach values of more than @xmath0 direction - dependent variation in the probability to find two close - by particles at viscous scale separation .

recently , clustering of inertial particles in turbulence has been thoroughly analyzed for statistically homogeneous isotropic flows . phenomenologically , spatial homogeneity of particles configurations is broken by the advection of a range of eddies determined by the stokes relaxation time of the particles which results in a multi - scale distribution of local concentrations and voids . much less is known concerning anisotropic flows . here , by addressing direct numerical simulations ( dns ) of a statistically steady particle - laden homogeneous shear flow , we provide evidence that the mean shear preferentially orients particle patterns . by imprinting anisotropy on large scales velocity fluctuations , the shear indirectly affects the geometry of the clusters . quantitative evaluation is provided by a purposely designed tool , the angular distribution function of particle pairs ( adf ) , which allows to address the anisotropy content of particles aggregates on a scale by scale basis . the data provide evidence that , depending on the stokes relaxation time of the particles , anisotropic clustering may occur even in the range of scales where the carrier phase velocity field is already recovering isotropy . the strength of the singularity in the anisotropic component of the adf quantifies the level of fine scale anisotropy , which may even reach values of more than @xmath0 direction - dependent variation in the probability to find two close - by particles at viscous scale separation .

1106.4256

r

fig.1(a ) shows the temperature dependence of resistivity for ba@xmath0k@xmath1fe@xmath2as@xmath2 single crystals with doping levels ranging from undoped parent phase to optimally doped compounds . it is clear that the potassium doping makes the system evolve from af ( with a resistivity anomaly ) to superconductive . the sharp drop of resistivity at about 138 k due to the af / structural transition can be observed in the parent phase . with doping holes , the resistivity anomaly is suppressed and shifts to lower temperatures , which is agreeable with the peak in the derivative of the resistivity d@xmath11/dt shown in fig.1(b ) . when the doping level x reaches 0.25 , the resistivity anomaly disappears and a little pit can be observed in d@xmath11/dt where the superconducting transition temperature is 29 k. with further doping , the t@xmath6 reaches a maximum value at 39 k. for the electron - doped fe - based 122 family , the magnetic and structural transition are slightly separated@xcite leading to two close peaks on the d@xmath11/dt vs. t curves . the resistivity anomaly exhibits two kinks which are corresponding to the two peaks in d@xmath11/dt for the underdoped samples . while for hole - doped bafe@xmath2as@xmath2 , some experiments show that the af and structure transition occur at the same temperature in underdoped region @xcite . in our measurements , we observed only one single sharp peak in d@xmath11/dt vs. t curves for underdoped ba@xmath0k@xmath1fe@xmath2as@xmath2 which is agreeable with previous results . here we would like to emphasize several contrasting issues by comparing the resistivity curves in electron doped ba(fe@xmath0co@xmath3)@xmath4as@xmath4 ( co-122)@xcite and hole doped ba@xmath0k@xmath1fe@xmath2as@xmath2 ( k-122 ) samples ( fig.1 ) . firstly , in the co-122 samples , the resistivity at 300 k reduces to half value of undoped sample when the system is optimally doped @xcite , this is actually not the case in the k-122 . one can see from fig.1(a ) that , the resistivity at 300 k drops only about 20 - 30@xmath12 when the doping is getting to the maximum value . what is more interesting is that the resistivity value when the superconductivity sets in is quite close to each other although the t@xmath6 changes from 10 k ( x=0.10 ) to 29 k ( x=0.25 ) . this may suggest the resistivity is mainly dominated by the electron band , which is weakly influenced by the hole doping . the interest triggered by this observation is two fold : the threshold for the occurrence of the superconductivity is governed by the residual resistivity at t@xmath6 , while the t@xmath6 value is determined by the hole concentration , perhaps by how strong the suppression to the antiferromagnetic phase is . it is not clear at this moment what leads to this strange behavior , but clearly it indicates a novel mechanism of the superconductivity . secondly , the resistivity exhibits an up - rising step at the af / structural transition in the electron doped co-122 , while in k-122 , this transition exhibits always as a drop of resistivity at t@xmath13 and it is smeared up gradually with more doping . thirdly , the rrr , namely the ratio between the room temperature resistivity and the residual resistivity ( just above t@xmath6 ) is about 2.4 in co-122,@xcite indicating a strong impurity scattering . but it seems such a strong scattering does not block the superconductivity . based on the picture of pairing through inter - pocket scattering,@xcite the non - magnetic impurities may be detrimental to the supercnductivity if they induce the inter - pocket scattering . in this sense , the impurities here may induce the scattering only with small momentum transfer , for example , intra - pocket scattering . in the optimally hole doped samples , the rrr can get to 14 , indicating a weak impurity scattering . at high temperatures , the @xmath7-t curve shows a bending down feature for the hole doped samples . in the conventional single band metal , the bending down of resistivity was interpreted as the approaching to the ioffe - regel limit , which is corresponding to the case that the mean free path induced by the phonon scattering is comparable to the atomic lattice constant . this seems not the case here , since the electron doped sample co-122 has the same structure and similar phonon spectrum , but the bending down feature of resistivity has not been observed up to 300 k. above mentioned behavior of the resistivity can be qualitatively understood by the two band scenario with asymmetric scattering rate in the hole and the electron pockets . according to the simple two band model , the conductivity can be written as @xmath14 , with @xmath15 the conductivity , @xmath16 the charge carrier density , @xmath17 the relaxation time , @xmath18 the mass of the @xmath19-th band ( @xmath19 = @xmath20 or @xmath21 for the electron and hole band , respectively ) . therefore the resistivity can be described as @xmath22 it is known that the parent phase has identical area of electron and hole fermi surfaces in the non - magnetic phase , therefore we can assume an identical charge carrier densities @xmath23 and @xmath24 for the two bands ( @xmath25 ) . considering m@xmath26@xmath27m@xmath28 as revealed by arpes@xcite and specific heat@xcite , and assuming that @xmath29 , the conductivity is thus dominated by electron band . with the electron doping , the term @xmath30 is getting much larger than @xmath31 which reduces the resistivity further . to the optimally doping at about x = 0.08 , @xmath23 has increased a lot , perhaps doubled , this reduces the resistivity to almost its half . in the case of k-122 , the situation is different . if still adopting the relation of @xmath32 , doping holes will decrease @xmath23 but increase @xmath24 , in this case the resistivity should increase , instead of decrease . actually doping holes will on one hand decrease @xmath23 and increase @xmath24 , but more important is to lower down the @xmath33 and @xmath34 , in this case , the resistivity will be determined by a balance between these quantities and shows a weak doping dependence . a quantitative understanding would require a detailed doping dependence of @xmath16 , @xmath17 , @xmath18 ( @xmath19 = @xmath20 , @xmath21 ) this is out of the scheme of what we can get from a simple resistivity measurement and analysis . some calculations indicate that the conductivity for electrons grows strongly upon electron doping , while the hole conductivity varies weakly compared to that of the electrons@xcite . thus the resistivity of hole - doped ba@xmath0k@xmath1fe@xmath2as@xmath2 at 300 k changes less than that for electron - doped ba(fe@xmath0co@xmath3)@xmath4as@xmath4 . the multi - band effect that one band is strongly coupled and relatively clean , while the other band is weakly coupled and characterized by much stronger impurity scattering will cause anomalous t - dependence of the in - plane resistivity : the curve is convex with the tendency to saturate at high temperature@xcite . ) of ba@xmath0k@xmath1fe@xmath2as@xmath2 . the data sets are offset vertically by 0.25 for clarity . ( b ) the fitting parameter n for six doped superconducting samples ( see text ) . ] k@xmath1fe@xmath2as@xmath2 and ba(fe@xmath0co@xmath3)@xmath4as@xmath4 . no splitting between the structural and afm transitions has been observed in the hole doped samples . the curve of t@xmath6 vs. doping in wide hole doping region ( solid line ) was taken from the ref.@xcite . the data in the electron doped regions were adopted from ref.@xcite . ] in fig.2(a ) we present temperature dependence of the normalized @xmath11 by the room temperature resistivity @xmath7(300k ) . a quick glance at the data can immediately see that the @xmath11-t curve in the low temperature region changes from a non - linear to a linear behavior towards optimal doping . in order to know precisely the evolution of the resistivity with doping , we fit the data in the low temperature region by the equation @xmath35 with three fitting parameters @xmath36 , a and n for each curve . due to the saturation in the resistivity at high temperatures and the anomalies of resistivity induced by the af / structure transition , we fit the data below the af / structure transition ( for x=0.25 and below ) . for the optimally doped sample , the fitting was done with the data between 40 and 120 k. the resulted fitting parameters are presented in table i and the exponent n is shown in fig.2(b ) . the evolving from a power law with exponent n = 2.3 to a linear temperature dependence can be easily observed in fig.2(b ) , which may indicate the crossover from a fermi liquid behavior to non - fermi liquid when the quantum critical point is approached . it was previously pointed out that the exponent n in metals near an afm quantum critical point ( qcp ) may be sensitive to disorder@xcite . while in k-122 the impurity scattering is quite weak , this can be corroborated by the negligible @xmath36 value at the optimal doping . at the optimal doping , the t - linear resistivity in the low temperature region may suggest a quantum critical point . similar behaviors have been observed in sr@xmath0k@xmath1fe@xmath2as@xmath2@xcite , bafe@xmath2as@xmath37p@xmath1 @xcite , ba(fe@xmath0co@xmath3)@xmath4as@xmath4 @xcite etc .. it has been pointed out that the quantum fluctuation becomes very strong when the neel temperature of the afm order becomes zero . it is this strong quantum fluctuation that heavily couple to the itinerant electrons and modifies the transport property . although it was argued that this linear feature may be reconstructed with a residual term and a t@xmath38 term in the optimally doped ba(fe@xmath0co@xmath3)@xmath4as@xmath4 system,@xcite , the systematic evolution shown in our present study can rule out this possibility . for the cuprate superconductors , the antiferromagnetic order of the magnetic moments of the cu@xmath39 is completely suppressed before superconductivity sets in . they do not coexist at any point of the t@xmath6(p ) ( p : doped hole number ) phase diagram ( exception was suggested in the bi-2201 system ) . in contrast , the coexistence of the afm and the superconductivity can be observed in underdoped region of the dome of k-122 @xcite . fig.3 shows the phase diagram of ba@xmath0k@xmath1fe@xmath2as@xmath2 and ba(fe@xmath0co@xmath3)@xmath4as@xmath4 . although there are some reports claiming that magnetically ordered phases and sc state are probably mesoscopically / microscopically separated @xcite , most of the studies on k or co doped samples are in favor for the coexistence of magnetic order and superconductivity and have consistently ruled out the presence of phase separation@xcite . the very small residual specific coefficient @xmath40 in the optimally doped ba@xmath41k@xmath42fe@xmath2as@xmath2 also strongly suggest the absence of macroscopic phase separation , since otherwise one should be able to see a large residual term of specific heat . therefore we argue that the qcp occurs near the optimally doped samples where the afm order vanishes at about zero k. in the specific heat measurements , we also found that the mass enhancement @xmath43 goes up quickly when the optimally doping point is approached.@xcite to confirm the existence of quantum critical point and the coexistence of magnetic order and superconductivity need certainly extra investigations using other local probes . .[tab : test]fit parameters [ cols="^,^,^,^,^,^",options="header " , ] k@xmath1fe@xmath2as@xmath2 ( x = 0 @xmath44 0.37 ) . the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping . the af / structure transition can be found in the underdoping dome ( 0.08 @xmath45 x @xmath45 0.25 ) as a onset of the rising of the hall coefficient r@xmath5 . for the optimal doped sample , r@xmath5 varies less pronounced with the temperature . ( b ) the doping dependence of hall coefficient at different temperatures . ] k@xmath1fe@xmath2as@xmath2 ( x=0@xmath440.37 ) measured at 9 t. inset : magnetoresistivity of the samples ( x=0.2 , 0.25 , 0.37 ) . an anomaly at around 80 - 100 k can be easily observed . ] the hall coefficient r@xmath5 from undoped bafe@xmath2as@xmath2 to optimally doped k-122 are presented in fig.4(a ) and the systematic evolution can be observed . the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping , and it keeps lowering with further doping in low temperature region . for each doping level , the sudden increase of the hall coefficient is corresponding to the af / structure transition which is agreeable with the resistivity anomaly for underdoped k-122 ( x = 0.1@xmath440.25 ) . above the af / structure transition temperature the hall coefficient varies weakly . the general formula for the hall coefficient in the boltzmann approximation reads @xmath46 for fully compensated semimetals within the two - band model , eq.3 reduces to @xmath47 by definition , undoped samples are compensated , that is , n@xmath26 = n@xmath28 = n@xmath48 . the eq . 4 can be written as @xmath49 where @xmath50 ( @xmath51 ) is the mobility . if @xmath52 , then @xmath53 , the transport is dominated by the electron band@xcite . however , with the potassium doping , the hole pocket increases in size instantly and the electron pocket contracts . at the hole doping with an @xmath54 @xmath44 @xmath55 , the hall coefficient changes sign . with further doping , the hole - doped systems have a presence of @xmath56 pocket near ( @xmath57 ) . in addition to ( @xmath58,0 ) scattering between @xmath59 and @xmath60 sheets , new phase space for scattering opens up.@xcite . the asymmetric scattering rate in the hole and the electron pockets play an important role on r@xmath5 . fig.4 shows the doping dependence of hall coefficient at 50 k , 100 k , 150 k , 200 k. in low temperature region , r@xmath5 changes sign and reaches a large value with little potassium doping . with further doping , r@xmath5 decreases gradually . in high temperature region the r@xmath5 varies very little , which is agreeable with the recent calculation@xcite . in the electron doped 122 system , the transport property is dominated by electron . in compensated case , the results can be explained by remarkable different mobilities of hole and electrons@xcite . for hole doped k-122 , the asymmetric scattering rate in the hole and the electron pockets still holds , but the relative ratio between @xmath61 and @xmath62 may change a little bit , namely @xmath62 will get enhanced . this is especially necessary to interpret the dropping down of resistance at high temperatures when the slight holes are doped into the system , as shown in fig.1 . the temperature dependence of magnetoresistivity for nine samples measured at a magnetic field of 9 t are presented in fig.5 . the data shows also a non - monotonic doping dependence and a sudden increase below af / structure transition , which is associated very well with the anomaly found in resistivity and hall effect . in undoped sample , the large magnetoresistivity with a magnitude of about 35% ( at about 9 t ) has been found in low temperature region . with increasing doping , the magnetoresistivity decreases instantly . it remains unclear yet what causes this large magnetoresistance within the af phase . there are two main explanations : ( 1 ) the magnetic field will break down the antiferromagnetic order to some extent and lead to stronger spin fluctuations and thus larger scattering to itinerant electrons ; ( 2 ) a magnetic field will induce a stronger localization leading to an enhanced resistivity . in addition to this strong magnetoresistance in the antiferromagnetic state , an anomalous feature at about 80 to 100 k can be observed even in the optimally doped sample in which the af state dose not exist at all . one can see this in the inset of fig.5 . the magnetoresistance rises up gradually when the temperature is lowered down , but it drops suddenly at about 100 k and reaches almost zero ( for the optimally doped sample ) , then it rises up again in the lower temperature region and smoothly connected to the magnetoresistance induced by the vortex motion in the mixed state . this anomaly at about 100 k may be associated with a possible pseudogap feature due to some unknown reasons . this is consistent with the recent observation in the c - axis resistive measurements where a maximum of @xmath63 is observed.@xcite a high temperature pseudogap was also claimed very recently from the optical conductivity measurements.@xcite further experimental and theoretical investigations are needed to clarify this point .

it is found that the resistivity in the normal state of ba@xmath0k@xmath1fe@xmath2as@xmath2 is insensitive to the potassium doping concentration , which is very different from the electron doped counterpart ba(fe@xmath0co@xmath3)@xmath4as@xmath4 , where the resistivity at 300 k reduces to half value of the undoped one when the system is optimally doped . in stark contrast , the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping , and it keeps lowering with further doping . we interpret this dichotomy due to the asymmetric scattering rate in the hole and the electron pockets with much higher mobility of the latter . the magnetoresistivity shows also a non - monotonic doping dependence indicating an anomalous feature at about 80 k to 100 k , even in the optimally doped sample , which is associated with a possible pseudogap feature . in the low temperature region , it seems that the resistivity has the similar values when superconductivity sets in disregarding the different t@xmath6 values , which indicates a novel mechanism of the superconductivity .

resistivity , hall effect and magnetoresistance have been investigated systematically on single crystals of ba@xmath0k@xmath1fe@xmath2as@xmath2 ranging from undoped to optimally doped regions . a systematic evolution of the quasiparticle scattering has been observed . it is found that the resistivity in the normal state of ba@xmath0k@xmath1fe@xmath2as@xmath2 is insensitive to the potassium doping concentration , which is very different from the electron doped counterpart ba(fe@xmath0co@xmath3)@xmath4as@xmath4 , where the resistivity at 300 k reduces to half value of the undoped one when the system is optimally doped . in stark contrast , the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping , and it keeps lowering with further doping . we interpret this dichotomy due to the asymmetric scattering rate in the hole and the electron pockets with much higher mobility of the latter . the magnetoresistivity shows also a non - monotonic doping dependence indicating an anomalous feature at about 80 k to 100 k , even in the optimally doped sample , which is associated with a possible pseudogap feature . in the low temperature region , it seems that the resistivity has the similar values when superconductivity sets in disregarding the different t@xmath6 values , which indicates a novel mechanism of the superconductivity . a linear feature of resistivity @xmath7 vs. @xmath8 was observed just above @xmath9 for the optimally doped sample , suggesting a quantum criticality .

1106.4256

c

in summary , we investigated resistivity , hall effect and magnetoresistance systematically on single crystals of ba@xmath0k@xmath1fe@xmath2as@xmath2 ranging from undoped to optimally doped samples . the resistivity in the normal state of ba@xmath0k@xmath1fe@xmath2as@xmath2 is insensitive to the potassium doping compared to the electron doped ba(fe@xmath0co@xmath3)@xmath4as@xmath4 samples . the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping , and it keeps lowering with further doping . this contrasting behavior is interpreted as due to the asymmetric scattering between the electron and hole bands with the much larger mobility in the former . an anomalous feature of magnetoresistivity has been observed at about 80 to 100 k and may be associated with a possible pseudogap feature . a linear feature of resistivity @xmath11 vs. @xmath8 was observed just above @xmath9 for the optimally doped sample , which suggests a quantum criticality . acknowledgement : we acknowledge the fruitful discussions with i. i. mazin , m. a. tanatar and p. hirschfeld . this work is supported by the natural science foundation of china , the ministry of science and technology of china ( 973 project no : 2011cba001002 ) , and the ministry of education of china ( 985 project ) . y. kamihara , t. watanabe , m. hirano , and h. hosono , j. am . chem.soc . * 130 * , 3296 ( 2008 ) . i. i. mazin , d. j. singh , m. d. johannes , and m. h. du , phys . rev . lett . * 101 * , 057003 ( 2008 ) . kazuhiko kuroki , seiichiro onari , ryotaro arita , hidetomo usui , yukio tanaka , hiroshi kontani , and hideo aoki , phys . * 101 * , 087004 ( 2008 ) . f. wang , h. zhai , y. ran , a. vishwanath and d. h. lee , phys . rev . lett . * 102 * , 047005 ( 2009 ) . h. ding , p. richard , k. nakayama , k. sugawara , t. arakane , y. sekiba , a. takayama , s. souma , t. sato , t. takahashi , z. wang , x. dai , z. fang , g. f. chen , j. l. luo , and n. l. wang , europhys . lett . * 83 * , 47001 ( 2008 ) . r. t. gordon r. t. gordon , n. ni , c. martin , m. a. tanatar , m. d. vannette , h. kim , g. d. samolyuk , j. schmalian , s. nandi , a. kreyssig , a. i. goldman , j. q. yan , s. l. budko , p. c. canfield , and r. prozorov , phys . * 102 * , 127004 ( 2009 ) . c. ren , z. s. wang , h. q. luo , h. yang , l. shan , and h. h. wen , phys . * 101 * , 257006 ( 2008 ) . b. zeng , g. mu , h. q. luo , t. xiang , i. i. mazin , h. yang , l. shan , c. ren , p. c. dai , and h. h. wen , nature communications * 1 * , 115 ( 2010 ) . j. zhao , q. huang , c. d. cruz , s. l. li , j. w. lynn , y. chen , m. a. green , g. f. chen , g. li , z. li , j. l. luo , n. l. wang , and p. c. dai , nature materials * 7 * , 953 ( 2008 ) . l. fang , h. q. luo , p. cheng , z. s. wang , y. jia , g. mu , b. shen , i. i. mazin , l. shan , c. ren , and h. h. wen , phys . b * 80 * , 140508 ( r ) ( 2009 ) . n. ni , m. e. tillman , j. q. yan , a. kracher , s. t. hannahs , s. l. budko , and p. c. canfield , phys . b * 78 * , 214515 ( 2008 ) . m. rotter , m. pangerl , m. tegel , and d. johrendt , angew . int . ed . * 47 * , 7949 ( 2008 ) . h. chen , y. ren , y. qiu , w. bao , r. h. liu , g. wu , t. wu , y. l. xie , x. f. wang , q. huang , and x. h. chen , europhys . lett . * 85 * , 17 006 ( 2009 ) . j. p. reid , m. a. tanatar , x. g. luo , h. shakeripour , s. ren de cotret , n. doiron - 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resistivity , hall effect and magnetoresistance have been investigated systematically on single crystals of ba@xmath0k@xmath1fe@xmath2as@xmath2 ranging from undoped to optimally doped regions . a systematic evolution of the quasiparticle scattering has been observed . a linear feature of resistivity @xmath7 vs. @xmath8 was observed just above @xmath9 for the optimally doped sample , suggesting a quantum criticality .

resistivity , hall effect and magnetoresistance have been investigated systematically on single crystals of ba@xmath0k@xmath1fe@xmath2as@xmath2 ranging from undoped to optimally doped regions . a systematic evolution of the quasiparticle scattering has been observed . it is found that the resistivity in the normal state of ba@xmath0k@xmath1fe@xmath2as@xmath2 is insensitive to the potassium doping concentration , which is very different from the electron doped counterpart ba(fe@xmath0co@xmath3)@xmath4as@xmath4 , where the resistivity at 300 k reduces to half value of the undoped one when the system is optimally doped . in stark contrast , the hall coefficient r@xmath5 changes suddenly from a negative value in the undoped sample to a positive one with slight k - doping , and it keeps lowering with further doping . we interpret this dichotomy due to the asymmetric scattering rate in the hole and the electron pockets with much higher mobility of the latter . the magnetoresistivity shows also a non - monotonic doping dependence indicating an anomalous feature at about 80 k to 100 k , even in the optimally doped sample , which is associated with a possible pseudogap feature . in the low temperature region , it seems that the resistivity has the similar values when superconductivity sets in disregarding the different t@xmath6 values , which indicates a novel mechanism of the superconductivity . a linear feature of resistivity @xmath7 vs. @xmath8 was observed just above @xmath9 for the optimally doped sample , suggesting a quantum criticality .

0801.0553

i

the ricci flow has been introduced by r. hamilton @xcite with the goal of providing an analytic approach to thurston s geometrization conjecture for three - manifolds @xcite@xmath0 . inspired by the theory of harmonic maps , he considered the geometric evolution equation obtained when one evolves a riemannian metric @xmath1 , on a three - manifold @xmath2 , in the direction of its ricci tensor@xcite @xmath3 , _ i.e. _ @xmath4 in recent years , this geometric flow has gained extreme popularity thanks to the revolutionary breakthroughs of g. perelman @xcite@xmath0 , who , taking the whole subject by storm , has brought to completion hamilton s approach to thurston s conjecture . the prominent themes recurring in hamilton s and perelman s works converge to a proof that the ricci flow , coupled to topological surgery , provides a natural technique for factorizing and uniformizing a three - dimensional riemannian manifold @xmath5 into locally homogeneous geometries . this is a result of vast potential use also in theoretical physics , where the ricci flow often appears in disguise as a natural real - space renormalization group flow . non - linear @xmath6-model theory , describing quantum strings propagating in a background spacetime , affords the standard case study in such a setting @xmath0 . another paradigmatical , perhaps even more direct , application occurs in relativistic cosmology @xcite@xmath0 , ( for a series of recent results see also @xcite and the references cited therein ) . this will be related to the main topic of this talk , and to motivate our interest in it , let us recall that homogeneous and isotropic solutions of einstein s laws of gravity ( the friedman lemaitre robertson walker ( flrw ) spacetimes ) do not account for inhomogeneities in the universe . the question whether they do _ on average _ is an issue @xcite that is the subject of considerable debate especially in the recent literature ( see @xcite and follow up references ; comprehensive lists may be found in @xcite and @xcite ) . in any case , a member of the family of flrw cosmologies ( the so called concordance model that is characterized by a dominating cosmological constant in a spatially flat universe model ) provides a successful _ fitting model _ to a large number of observational data , and the generally held view is that the spatial sections of flrw spacetimes indeed describe the _ physical universe _ on a sufficiently large averaging scale . this raises an interesting problem in mathematical cosmology : devise a way to explicitly construct a constant curvature metric out of a _ scale dependent _ inhomogeneous distribution of matter and spatial curvature . it is in such a framework that one makes the basic observation that the ricci flow ( [ mflow ] ) and its linearization , provide a natural technique@xcite for deforming , and under suitable conditions smoothing , the geometrical part of scale dependent cosmological initial data sets . moreover , by taking advantage of some elementary aspects of perelman s results , this technique also provides a natural and unique way for deforming , along the ricci flow , the matter distribution . the expectation is that in this way we can define a deformation of cosmological initial data sets into a one - parameter family of initial data whose time evolution , along the evolutive part of einstein s equations , describe the ricci flow deformation of a cosmological spacetime .

ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes . this idea has been around since the appearance of the ricci flow on the scene , but it has been difficult to turn it into a sound mathematical procedure . in this expository talk we illustrate , how perelman s recent results in ricci flow theory can considerably improve on such a situation . from a physical point of view

ricci flow deformation of cosmological initial data sets in general relativity is a technique for generating families of initial data sets which potentially would allow to interpolate between distinct spacetimes . this idea has been around since the appearance of the ricci flow on the scene , but it has been difficult to turn it into a sound mathematical procedure . in this expository talk we illustrate , how perelman s recent results in ricci flow theory can considerably improve on such a situation . from a physical point of view this analysis can be related to the issue of finding a constant curvature template spacetime for the inhomogeneous universe , relevant to the interpretation of observational data and , hence , bears relevance to the dark energy and dark matter debates . these techniques provide control on curvature fluctuations ( intrinsic backreaction terms ) in their relation to the averaged matter distribution .

1412.7216

i

several new estimation methods have been recently proposed for the linear regression model with observation error in the design . such problems arise in a variety of applications , see @xcite . in this work we consider the following regression model with observation error in the design : @xmath2 here the random vector @xmath3 and the random @xmath4 matrix @xmath5 are observed , the @xmath4 matrix @xmath6 is unknown , @xmath7 is an @xmath4 random noise matrix , and @xmath8 is a random noise vector . the vector of unknown parameters of interest is @xmath9 which is assumed to belong to a given convex subset @xmath10 of @xmath11 characterizing some prior knowledge about @xmath9 ( potentially @xmath12 ) . similarly to the recent literature on this topic , we consider the setting where the dimension @xmath13 can be much larger than the sample size @xmath14 and the vector @xmath9 is @xmath15-sparse , which means that it has not more than @xmath15 non - zero components . + the need for new estimators under errors in the design arises from the fact that standard estimators ( e.g. lasso and dantzig selector ) might become unstable , see @xcite . to deal with this framework , various assumptions have been considered , leading to different estimators . + a classical assumption in the literature is a uniform boundedness condition on the errors in the design , namely , @xmath16 denotes the @xmath17-norm for @xmath18 . note that this assumption allows for various dependences between the errors in the design . in this setting , the matrix uncertainty selector ( mu selector ) , which is robust to the presence of errors in the design , is proposed in @xcite . the mu selector @xmath19 is defined as a solution of the minimization problem @xmath20 where the parameters @xmath21 and @xmath22 depend on the level of the noises of @xmath7 and @xmath23 respectively . under appropriate choices of these parameters and suitable assumptions on @xmath6 , it was shown in @xcite that with probability close to 1 , @xmath24 different positive constants that do not depend on @xmath9 , @xmath15 , @xmath14 , @xmath13 , @xmath25 . the result ( [ rtmu ] ) implies consistency as the sample size @xmath14 tends to infinity provided that the error in the design goes to zero sufficiently fast to offset @xmath26 , and the number of variables @xmath13 and the sparsity @xmath15 of @xmath27 do not grow too fast relative to the sample size @xmath14 . + an alternative assumption considered in the literature is that the entries of the random matrix @xmath7 are independent with zero mean , the values @xmath28 are finite , and data - driven estimators @xmath29 of @xmath30 are available converging with an appropriate rate . this assumption motivated the idea to compensate the bias of using the observable @xmath31 instead of the unobservable @xmath32 in thanks to the estimates of @xmath30 . this compensated mu selector , introduced in @xcite and denoted as @xmath33 , is defined as a solution of the minimization problem @xmath34 where @xmath35 is the diagonal matrix with entries @xmath36 and @xmath37 and @xmath38 are constants chosen according to the level of the noises and the accuracy of the @xmath39 . + rates of convergence of the compensated mu selector were established in @xcite . importantly , the compensated mu selector can be consistent as the sample size @xmath14 increases even if the error in the design does not vanish . this is in contrast to the case of the mu selector , where the bounds are small only if the bound on the design error @xmath0 is small . in particular , under regularity conditions , when @xmath27 is @xmath15-sparse , it is shown in @xcite that with probability close to 1 @xmath40 has been recently proposed and analyzed in @xcite . the estimator @xmath41 is defined as the first component of any solution of the optimization problem @xmath42 where @xmath43 , @xmath21 and @xmath22 are some positive tuning constants . akin to @xmath33 , this estimator compensates for the bias by using the estimators @xmath36 of @xmath30 . however it exploits a combination of @xmath44 and @xmath45-norm regularization to be more adaptive . it was shown to attain a bound as in ( [ rt13 ] ) and to be computationally feasible since it is cast as a tractable convex optimization problem ( a second order cone programming problem ) . moreover , under mild additional conditions , with probability close to 1 , the estimator ( [ conic ] ) achieves improved bounds of the form @xmath46 converges to @xmath47 in sup - norm with the rate @xmath48 . it is shown in @xcite that the rate of convergence in is minimax optimal in the considered model . + there have been other approaches to the errors - in - variables model , usually exploiting some knowledge about the vector @xmath27 , see @xcite . assuming @xmath49 is known , @xcite proposed an estimator @xmath50 defined as the solution of a non - convex program which can be well approximated by an iterative relaxation procedure . in the case where the entries of the regression matrix @xmath6 are zero - mean subgaussian and @xmath27 is @xmath15-sparse , under appropriate assumptions , it is shown in @xcite that for the error in @xmath45-norm ( @xmath51 ) , @xmath52 depends on @xmath9 , so that there is no guarantee that the estimator attains the optimal bound as in . assuming that the sparsity @xmath15 of @xmath27 is known and the non - zero components of @xmath27 are separated from zero in the way that @xmath53 an orthogonal matching pursuit algorithm to estimate @xmath9 is introduced in @xcite . focusing as in @xcite on the particular case where the entries of the regression matrix @xmath6 are zero - mean subgaussian , it is shown in @xcite that this last estimator satisfies a bound analogous to ( [ 6 ] ) , as well as a consistent support recovery result . + the main purpose of this work is to show that an additional regularization term based on the @xmath1-norm leads to improved rates of convergence in several situations . we propose two new estimators for @xmath27 . the first proposal is applicable under a new combination of the assumptions mentioned above . namely , we assume that the components of the errors in the design are uniformly bounded by @xmath25 as in ( [ wbound ] ) , and that the rows of @xmath7 are independent and with zero mean . however , we will neither assume that a data - driven estimator @xmath54 is available , nor that specific features of @xmath27 are known ( e.g. @xmath15 or @xmath49 ) . the estimator is defined as a solution of a regularized optimization problem which uses simultaneously @xmath44 , @xmath45 , and @xmath1 regularization functions . it can be cast as a convex optimization problem and the solution can be easily computed . we study its rates of convergence in various norms in section [ first ] . one of the conclusions is that for @xmath55 the new estimator has improved rates of convergence compared to the mu selector . furthermore , note that the conic estimator @xmath56 studied in @xcite can be also applied . indeed , our setting can be embedded into that of @xcite with @xmath57 being the identically zero @xmath58 matrix , which means that we have an estimator of each @xmath30 with an error bounded by @xmath59 . comparing the bounds yields that the conic estimator @xmath56 achieves the same rate as our new estimator if @xmath25 is smaller than or of the order @xmath60 . however , there is no bound for @xmath56 available when @xmath61 . + the second estimator we propose applies to the same setting as in @xcite . the idea of taking advantage of an additional @xmath1-norm regularization can be used to improve the conic estimator @xmath56 of @xcite whenever the rate of convergence of the estimator @xmath57 for @xmath30 , @xmath62 , is slower than @xmath48 . this motivates us to propose and analyze a modification of the conic estimator . we derive new rates of convergence that can lead to improvements . however , we acknowledge that in the case considered in @xcite , where the rate of convergence of @xmath57 is @xmath48 , there is no gain in the rates of convergence when using the additional @xmath1-norm regularization . + the paper is organized as follows . section [ sec : assump ] contains the notation , main assumptions and some preliminary lemmas needed to determine threshold constants in the algorithms . the definition and properties of our first estimator are given in section [ first ] whereas those of our second procedure can be found in section [ second ] . section 5 contains simulation results . some auxiliary lemmas are relegated to an appendix .

several new estimation methods have been recently proposed for the linear regression model with observation error in the design . in particular , the literature considered ( 1 ) observation errors in the design uniformly bounded by some @xmath0 , and ( 2 ) zero mean independent observation errors . under the first assumption , the rates of convergence of the proposed estimators depend explicitly on @xmath0 , while the second assumption has been applied when an estimator for the second moment of the observational error is available . this work proposes and studies two new estimators which , compared to other procedures for regression models with errors in the design , exploit an additional @xmath1-norm regularization . as the recent proposals , we allow the number of covariates to be much larger than the sample size . we establish the rates of convergence of the estimators and compare them with the bounds obtained for related estimators in the literature .

several new estimation methods have been recently proposed for the linear regression model with observation error in the design . different assumptions on the data generating process have motivated different estimators and analysis . in particular , the literature considered ( 1 ) observation errors in the design uniformly bounded by some @xmath0 , and ( 2 ) zero mean independent observation errors . under the first assumption , the rates of convergence of the proposed estimators depend explicitly on @xmath0 , while the second assumption has been applied when an estimator for the second moment of the observational error is available . this work proposes and studies two new estimators which , compared to other procedures for regression models with errors in the design , exploit an additional @xmath1-norm regularization . the first estimator is applicable when both ( 1 ) and ( 2 ) hold but does not require an estimator for the second moment of the observational error . the second estimator is applicable under ( 2 ) and requires an estimator for the second moment of the observation error . importantly , we impose no assumption on the accuracy of this pilot estimator , in contrast to the previously known procedures . as the recent proposals , we allow the number of covariates to be much larger than the sample size . we establish the rates of convergence of the estimators and compare them with the bounds obtained for related estimators in the literature . these comparisons show interesting insights on the interplay of the assumptions and the achievable rates of convergence .

1504.01974

i

in a secure two - party computation , two parties or players want to compute a particular function of their inputs keeping the inputs secret from each other . they are only allowed to obtain the output of the function preserving some security notions under certain adversarial model . the secure two - party computation is a special case of ` secure multi - party computation ' ( smc ) . in classical domain , the smc problem has been studied extensively . the security of classical smc comes from some computational hardness assumptions and thus is conditional . on the other hand , in quantum domain the adversary is always assumed to have unbounded power of computation and the security of a protocol comes from the laws of physics . this is why many researchers have tried to exploit the quantum mechanical effect @xcite to solve the problems of smc @xcite . in @xcite , it is pointed out that there are some functions which can not be securely evaluated in quantum domain for two - sided @xcite two party setting . later , ben -or et al . @xcite generalized it by showing an impossibility result for @xmath0 players , when there are @xmath1 or more faulty players . since the work of @xcite in 1997 , in case of two - party quantum computation , some additional assumptions , such as the semi - honest third party etc . , have been introduced to obtain the secure private comparison @xcite . yao s millionaires problem @xcite is one of the examples of the secure two - party computation . yao s millionaires problem @xcite , or more precisely , the ` greater than ' function deals with two millionaires , alice and bob , who are interested in finding who amongst them is richer , without revealing their actual wealth to each other . much effort has been given to solve this problem in quantum domain @xcite , all of which analyzed the security issues against several eavesdropping strategies . jia et al . @xcite dealt the problem with semi - honest party . in @xcite , the millionaires problem is studied considering continuous variable . he @xcite exploited the idea of quantum key distribution to solve the problem . tseng et al . @xcite proposed the use of bell state to solve this problem . their protocol also exploits a third party to assist the players . yang et al . @xcite showed the vulnerability of their protocol if the third party is disloyal . however , none of these works @xcite analyze the security issues considering malicious players . in classical domain the subsequent work by gordon et al . @xcite showed that any function over polynomial - size domains which does not contain an embedded xor " can be converted into the greater than function or more specifically into the millionaires problem . hence , millionaires problem covers all functions without embedded xor . gordon et al . also studied a function which has an embedded xor @xcite , namely , a function that simply checks whether the inputs chosen by two players ( from a specified domain ) are equal or not . exploiting the idea of gordon et al . , we for the first time design two quantum protocols for these two distinct sets of functions and analyze the security issues when players are malicious unlike the existing quantum protocols @xcite . further , we analyze our new quantum protocols considering rational players and this is the first work on secure multi - party quantum computation in rational setting . rational players are neither ` good ' nor ` malicious ' , they are utility maximizing . each rational party wishes to learn the output while allowing as few others as possible to learn the output . thus , each rational party chooses to abort to maximize its utility . this rationality concept comes from game theory . recently , significant effort has been given towards bridging the gap between two apparently unrelated domains , namely , cryptography and game theory @xcite . cryptography deals with the worst case scenario , making the protocols secure against malicious behaviour of a party . however , in game theoretic perspective , a protocol is designed against the rational deviation of a party . very recently , brunner and linden @xcite showed a deep link between quantum physics and game theory . by bringing quantum mechanics into a class of games , known as bayesian games , they showed that players who can use quantum resources , such as entangled quantum particles , can outperform classical players . in quantum domain , the concept of rational players in secret sharing has been first introduced in @xcite . in this paper , we identify that fairness in secure two - party computation in non - rational setting does not imply fairness in rational setting . in rational setting , we modify the protocols to achieve both fairness as well as strict nash equilibrium @xcite . below we summarize our contributions in this work . 1 . for the first time in quantum domain , we identify that for non - simultaneous channel model , there exist some functions which can be computed in two - party setting with complete fairness when one of the parties acts maliciously . we consider two sets of functions . one set consists of the functions without embedded xor , whereas the other set deals with a specific function having an embedded xor . we also consider rational adversaries and modify our protocols accordingly to achieve both fairness and strict nash equilibrium . to our knowledge , ours is the first work on secure multi - party quantum computation in the rational setting . our protocols are secure against both byzantine as well as fail - stop adversaries in both non - rational and rational settings . here we highlight the key differences of our protocols from the existing quantum protocols for secure two and multi - party computation . 1 . lo @xcite showed that , there are certain functions for which two - sided secure two - party quantum computation is impossible if one of them is malicious . ben -or et al . @xcite proved that assuming pairwise quantum channels and classical broadcast channels among the @xmath0 players , a universally composable , statistically secure multi - party quantum computation is possible for less than @xmath1 faulty players . on the other hand , we identify that in non - simultaneous channel model , both the millionaires and the embedded xor problem can be solved in quantum domain with complete fairness when one of the parties is malicious our protocols differ from the existing quantum protocols for private comparison @xcite in the sense that all these protocols analyze the security issues against several eavesdropping strategies . none of those consider malicious players . contrary to this , we analyze the security of our protocols considering malicious behaviour of the players . in our protocols there are no external adversary .

since the negative result of lo ( physical review a , 1997 ) , it has been left open whether there exist some functions that can be securely computed in two - party setting in quantum domain when one of the parties is malicious . in this paper , we for the first time , show that there are some functions for which secure two - party quantum computation is indeed possible for non - simultaneous channel model . we adapt our quantum protocols for both the above types of functions in rational setting to achieve fairness and strict nash equilibrium .

since the negative result of lo ( physical review a , 1997 ) , it has been left open whether there exist some functions that can be securely computed in two - party setting in quantum domain when one of the parties is malicious . in this paper , we for the first time , show that there are some functions for which secure two - party quantum computation is indeed possible for non - simultaneous channel model . this is in sharp contrast with the impossibility result of ben -or et al . ( focs , 2006 ) in broadcast channel model . the functions we study are of two types - one is any function without an embedded xor , and the other one is a particular function containing an embedded xor . contrary to classical solutions , security against adversaries with unbounded power of computation is achieved by the quantum protocols due to entanglement . further , in the context of secure multi - party quantum computation , for the first time we introduce rational parties , each of whom tries to maximize its utility by obtaining the function output alone . we adapt our quantum protocols for both the above types of functions in rational setting to achieve fairness and strict nash equilibrium .

1504.01974

c

in 1997 , lo @xcite showed the impossibility of secure two - party quantum computation of certain functions , when one of the parties is malicious . in this direction , we obtain a positive result for two types of functions . this does not contradict with the generalized impossibility results of @xcite in broadcast channel model , since we show our results in non - simultaneous channel model . further , for the first time , we introduce the idea of secure two - party quantum computation with rational players . when one moves from the non - rational domain to a rational one , the definition for fairness changes . thus , we modify the protocols to achieve fairness in rational setting . in addition , we prove strict nash equilibrium for our proposed protocols in rational setting . we have shown that secure two - party quantum computation is possible for any function without an embedded xor and for a particular function with an embedded xor . thus , it remains an open question whether secure two - party quantum computation is possible for any function with an embedded xor . moreover , generalization of the two - party protocols to @xmath0-party scenario would be an interesting future work , particularly , in the non - simultaneous channel model .

this is in sharp contrast with the impossibility result of ben -or et al . ( focs , 2006 ) in broadcast channel model . the functions we study are of two types - one is any function without an embedded xor , and the other one is a particular function containing an embedded xor . further , in the context of secure multi - party quantum computation , for the first time we introduce rational parties , each of whom tries to maximize its utility by obtaining the function output alone .

since the negative result of lo ( physical review a , 1997 ) , it has been left open whether there exist some functions that can be securely computed in two - party setting in quantum domain when one of the parties is malicious . in this paper , we for the first time , show that there are some functions for which secure two - party quantum computation is indeed possible for non - simultaneous channel model . this is in sharp contrast with the impossibility result of ben -or et al . ( focs , 2006 ) in broadcast channel model . the functions we study are of two types - one is any function without an embedded xor , and the other one is a particular function containing an embedded xor . contrary to classical solutions , security against adversaries with unbounded power of computation is achieved by the quantum protocols due to entanglement . further , in the context of secure multi - party quantum computation , for the first time we introduce rational parties , each of whom tries to maximize its utility by obtaining the function output alone . we adapt our quantum protocols for both the above types of functions in rational setting to achieve fairness and strict nash equilibrium .

1604.08191

i

elections are a general and widely used framework for preference aggregation in human and artificial intelligence applications . an important negative result from social choice theory , the gibbard - satterthwaite theorem @xcite , states that every reasonable election system is manipulable . however , even though every election system is manipulable , it may be computationally infeasible to determine how to manipulate the outcome . bartholdi , tovey , and trick introduced the computational study of the manipulation problem and this began an exciting line of research that explores the computational complexity of different manipulative attacks on elections ( see , e.g. , @xcite ) . the notion of single - peaked preferences introduced by black is the most important restriction on preferences from political science and economics and is naturally an important case to consider computationally . single - peakedness models the preferences of a collection of voters with respect to a given axis ( a total ordering of the candidates ) . each voter in a single - peaked election has a single most - preferred candidate ( peak ) on the axis and the farther candidates are to the left / right from her peak the less preferred they are . single - plateauedness extends this to model when each voter has multiple most - preferred candidates that appear sequentially on the axis , but are otherwise single - peaked @xcite . this standard model of single - peaked preferences has many desirable social - choice properties . when the voters in an election are single - peaked , the majority relation is transitive @xcite and there exist voting rules that are strategy - proof @xcite ( i.e. , a voter can not misrepresent her preferences to achieve a personally better outcome ) . single - peakedness for total orders can also have an effect on the complexity of many different election attack problems when compared to the general case . the complexity of manipulative attacks often decreases when the voters in an election are single - peaked @xcite , and the winner problems for kemeny , dodgson , and young elections are in p when they are @xmath0-complete in general @xcite . most of the abovementioned research on the computational complexity of manipulation of elections , both for the general case and for single - peaked electorates , has been limited to the assumption that voters have tie - free votes . in many real - world scenarios voters have votes with ties , and this is seen in the online repository preflib @xcite that contains several different preference datasets that contain ties . there are also election systems defined for votes with ties , e.g. , the kemeny rule and the schulze rule @xcite . recent work considers the complexity of manipulation for top - order votes ( votes where all of the ties are between candidates ranked last ) @xcite . fitzsimmons and hemaspaandra considered the complexity of manipulation , control , and bribery for more general votes with ties , and also the case of manipulation for a nonstandard model of single - peakedness for top - order votes . menon and larson later examined the complexity of manipulation and bribery for an equivalent ( for top orders ) model of single - peakedness . fitzsimmons and hemaspaandra use the model of possibly single - peaked preferences from lackner where a preference profile of votes with ties is said to be single - peaked with respect to an axis if the votes can be extended to tie - free votes that are single - peaked with respect to the same axis . menon and larson use a similar model for top orders that they state is essentially the model of single - peaked preferences with outside options @xcite . both fitzsimmons and hemaspaandra and menon and larson find that these notions of single - peakedness exhibit anomalous computational behavior where the complexity of manipulation can increase when compared with the case of single - peaked total orders . we are the first to study the computational complexity of manipulation for the standard model of single - peaked preferences for votes with ties , and for single - plateaued preferences for votes with ties . in contrast to the recent related work using other models of single - peakedness with ties , we find that the complexity of weighted manipulation for @xmath1-candidate scoring rules and for @xmath1-candidate copeland@xmath2 elections for all @xmath3 does not increase when compared to the cases of single - peaked total orders , and that the complexity of weighted manipulation does not increase with respect to the general case of elimination veto elections . we also compare the social choice properties of these different models , and state a surprising result on the relation between the societal axis and the complexity of manipulation for single - peaked preferences .

single - peakedness is one of the most important and well - known domain restrictions on preferences . the computational study of single - peaked electorates has largely been restricted to elections with tie - free votes , and recent work that studies the computational complexity of manipulative attacks for single - peaked elections for votes with ties has been restricted to nonstandard models of single - peaked preferences for top orders . we study the computational complexity of manipulation for votes with ties for the standard model of single - peaked preferences and for single - plateaued preferences . we also state a surprising result on the relation between the societal axis and the complexity of manipulation for single - peaked preferences .

single - peakedness is one of the most important and well - known domain restrictions on preferences . the computational study of single - peaked electorates has largely been restricted to elections with tie - free votes , and recent work that studies the computational complexity of manipulative attacks for single - peaked elections for votes with ties has been restricted to nonstandard models of single - peaked preferences for top orders . we study the computational complexity of manipulation for votes with ties for the standard model of single - peaked preferences and for single - plateaued preferences . we show that these models avoid the anomalous complexity behavior exhibited by the other models . we also state a surprising result on the relation between the societal axis and the complexity of manipulation for single - peaked preferences .

1002.0026

i

_ steganography _ is a scientific discipline within the field known as _ data hiding _ , concerned with hiding information into a commonly used media , in such a way that no one apart from the sender and the intended recipient can detect the presence of embedded data . a comprehensive overview of the core principles and the mathematical methods that can be used for data hiding can be found in @xcite . an interesting steganographic method is known as _ matrix encoding _ , introduced by crandall @xcite and analyzed by bierbrauer et al . matrix encoding requires the sender and the recipient to agree in advance on a parity check matrix @xmath2 , and the secret message is then extracted by the recipient as the syndrome ( with respect to @xmath2 ) of the received cover object . this method was made popular by westfeld @xcite , who incorporated a specific implementation using hamming codes in his f5 algorithm , which can embed @xmath3 bits of message in @xmath4 cover symbols by changing , at most , one of them . there are two parameters which help to evaluate the performance of a steganographic method over a cover message of @xmath5 symbols : the _ average distortion _ @xmath6 , where @xmath7 is the expected number of changes over uniformly distributed messages ; and the _ embedding rate _ @xmath8 , which is the amount of bits that can be hidden in a cover message . in general , for the same embedding rate a method is better when the average distortion is smaller . following the terminology used by fridrich et al . @xcite , the pair @xmath9 will be called _ @xmath10-rate_. furthermore , as willems et al . in @xcite , we will also assume that a discrete source produces a sequence @xmath11 , where @xmath5 is the block length , each @xmath12 , and @xmath13 depends on whether the source is a grayscale digital image , or a cd audio , etc . the message @xmath14 we want to hide into a host sequence @xmath15 produces a composite sequence @xmath16 , where @xmath17 and each @xmath18 . the composite sequence @xmath19 is obtained from distorting @xmath15 , and the distortion will be assumed to be a squared - error distortion ( see @xcite ) . in these conditions , if information is only carried by the least significant bit ( lsb ) of each @xmath20 , the appropriate solution comes from using binary hamming codes @xcite , improved using product hamming codes @xcite . for larger magnitude of changes , but limited to @xmath21 , that is , @xmath22 , where @xmath23 , the situation is called @xmath1-steganography " , and the information is carried by the two least significant bits . it is known that the embedding becomes statistically detectable rather quickly with the increasing amplitude of embedding changes . therefore , our interest goes to avoid changes of amplitude greater than one . with this assumption , our steganographic scheme will be compared with the upper bound from @xcite for the embedding rate in @xmath1-steganography " , given by @xmath24 , where @xmath25 is the binary entropy function @xmath26 and @xmath27 is the average distortion . a main purpose of steganography is designing schemes in order to approach this upper bound . in most of the previous papers , @xmath1-steganography " has involved a ternary coding problem . willems et al . @xcite proposed a schemed based on ternary hamming and golay codes , which were proved to be optimal . fridrich and lisonk @xcite proposed a method based on rainbow colouring graphs which , for some values , outperformed the scheme obtained by direct sum of ternary hamming codes with the same average distortion . however , both methods from @xcite and @xcite show a problem when dealing with extreme grayscale values , since they suggest making a change of magnitude greater than one in order to avoid having to apply the change @xmath28 and @xmath29 to a host sequence of value @xmath30 and @xmath31 , respectively . note that the kind of change they propose would obviously introduce larger distortion and therefore make the embedding more statistically detectable . in this paper we also consider the @xmath1-steganography . our new method is based on perfect @xmath0-linear codes which , although they are not linear , they have a representation using a parity check matrix that makes them as efficient as the hamming codes . as we will show , this new method not only performs better than the one obtained by direct sum of ternary hamming codes from @xcite , but it also deals better with the extreme grayscale values , because the magnitude of embedding changes is under no circumstances greater than one . to make this paper self - contained , we review in section [ sec : additivecodes ] a few elementary concepts on perfect @xmath0-linear codes , relevant for our study . the new steganographic method is presented in section [ sec : stegoz2z4 ] , whereas an improvement to better deal with the extreme grayscale values problem is given in section [ sec : anomalies ] . finally , the paper is concluded in section [ sec : conclusions ] .

steganography is an information hiding application which aims to hide secret data imperceptibly into a commonly used media . unfortunately , the theoretical hiding asymptotical capacity of steganographic systems is not attained by algorithms developed so far . in this paper , we describe a novel coding method based on @xmath0-linear codes that conforms to @xmath1-steganography , that is secret data is embedded into a cover message by distorting each symbol by one unit at most .

steganography is an information hiding application which aims to hide secret data imperceptibly into a commonly used media . unfortunately , the theoretical hiding asymptotical capacity of steganographic systems is not attained by algorithms developed so far . in this paper , we describe a novel coding method based on @xmath0-linear codes that conforms to @xmath1-steganography , that is secret data is embedded into a cover message by distorting each symbol by one unit at most . this method solves some problems encountered by the most efficient methods known today , based on ternary hamming codes . finally , the performance of this new technique is compared with that of the mentioned methods and with the well - known theoretical upper bound .

astro-ph0009050

i

simulations of the local group s formation ( klypin et al . 1999 ) predict that an order of magnitude more satellites should be associated with the milky way and m31 than are actually observed . this discrepancy is a significant challenge to hierarchical clustering scenarios . an intriguing suggestion as to the whereabouts of the `` missing '' satellites is provided by the local group infall model of blitz et al . ( 1999 ) , who speculate that a large fraction of the classical ensemble of hvcs are these local group building blocks . the continuing infall of the hvcs onto the disk of the galaxy would then provide the bulk of the fuel necessary to maintain ongoing star formation . hvcs are ubiquitous ( @xmath020% sky covering fraction ) clouds seen in hi emission , whose velocities are incompatible with simple models of galactic rotation . because the majority of their distances are effectively unconstrained , rampant speculation exists as to their exact nature and origin , ranging from solar metallicity galactic fountain gas ( @xmath1kpc and z@xmath0z@xmath2 ) , to magellanic cloud tidal debris ( @xmath3kpc and z@xmath40.25z@xmath2 ) , to the blitz / spergel local group formation remnants ( @xmath5kpc and 0.0@xmath6z@xmath60.1z@xmath2 ) . the fact that each scenario makes specific predictions regarding the distance and metallicity for the `` typical '' hvc means that , in principle , the above models could be distinguished from one another wth appropriate observations . in practice , the definitive observational discriminant has been difficult to obtain .

tantalizing evidence has been presented supporting the suggestion that a large population of extragalactic gas clouds permeates the local group , a population which has been associated with the galactic high - velocity clouds ( hvcs ) . theoretical predictions for the spatial and kinematic distributions , metallicities , distances , and emission properties of blitz / spergel hvcs will be confronted with extant observational data .

tantalizing evidence has been presented supporting the suggestion that a large population of extragalactic gas clouds permeates the local group , a population which has been associated with the galactic high - velocity clouds ( hvcs ) . we comment on both the strengths and weaknesses of this suggestion , informally referred to as the blitz / spergel picture . theoretical predictions for the spatial and kinematic distributions , metallicities , distances , and emission properties of blitz / spergel hvcs will be confronted with extant observational data .

1506.03991

i

spintronics and graphene are exciting , vigorous , and rather new areas of research with a rapid pace of new discoveries . books and a multitude of review articles are available for those that want to learn about one of these fields [ ] . the intersection of both provides fertile soil for an abundance of fascinating physics and its fruits have been partially reaped by previous reviews [ ] . here , we put the cherry on the cake and review specifically spintronics in graphene quantum dots . while classical electronics relies on the charge for information processing , spin - based electronics or _ spintronics _ is the paradigm of an advanced technology where the spin degree of freedom complements or even replaces charge as the carrier of information . the expected benefits of spintronics encompass non - volatile data storage , faster and more energy efficient data processing , increased data density , and many more . in order to fully exploit the potential , efficient generation , transport , transfer , manipulation , and detection of spin polarization is required . all these requirements are closely connected to material properties . therefore , progress in spintronics seems intrinsically connected to the quest for new materials with appropriate characteristics [ ] . c nuclear spin via the hyperfine interaction . ] graphene is a novel material that has undeniably stirred up the solid state community since its isolation more than a decade ago [ ] . it is a monatomically thin , quasi two - dimensional layer of carbon atoms arranged in a honeycomb lattice with two sublattices , a and b. due to its atomic structure , it has the lowest surface mass density of all solids [ ] . at the same time , its in - plane mechanical strength is second to no other material [ ] . the hexagonal structure is the consequence of sp@xmath2-hybridized carbon atoms . the remaining p - orbitals form the @xmath3-bands responsible for transport . electrons move quasi - relativistically with the fermi velocity @xmath4 , where @xmath5 is the vacuum speed of light , and with high mobilities [ ] . spin - orbit couplings are small and nuclear spins are sparse , making it a potentially good host material for spin [ ] . in addition to the real electron spin , the occupation of sublattices a and b can be described by the sublattice pseudospin . moreover , in momentum space , the occupation of the two inequivalent dirac points where valence and conduction bands touch may be denoted by the valley isospin [ ] . electron spin currents can be injected optically in graphene with rashba - type spin - orbit interaction [ ] . this allows to leave away ferromagnetic contacts , thus eliminating a possible source of spin scattering . magnetic behavior has been observed at the edges of graphene [ ] . these and further properties make graphene a very promising material for spintronics . quantum dots ( qds ) , in graphene as well as in other materials , are quasi zero - dimensional regions to which charge carriers can be confined [ ] . with electrostatic gate electrodes that can be used to adjust the confinement potential and with electric contacts for transport , qds allow in principle for full control over the individual electron . in particular , qds provide a controllable playground to investigate the behavior of spins as well as sources of decoherence and methods to increase coherence times [ ] . in general , there are nuclear spins as well as electron spins in a solid . unless explicitly stated otherwise , we always refer to electron spin . in this review , we focus on what we believe to be the most immediate questions related to spintronics with localized electron spins in graphene . however , we point out that there are a several related systems that make use of carbon nanotubes or transition metal dichalcogenides ( tmdcs ) and where the electron spin degree of freedom might be substituted or complemented by a pseudospin or valley isospin [ ] . the review is organized as follows . in the next section , we give an overview over spintronics in quantum dots and motivate the use of graphene . in sec . [ t1sec ] , we discuss various graphene quantum dots and their associated spin relaxation times . closely related to the concept of qds are localized states due to defects in graphene nanoflakes , which we treat in sec . [ gnf ] . in sec . [ nspins ] , we address the influence of nuclear spins on spintronics in graphene . recent experimental achievements and the current status are the topic of sec . finally , we give a summary and perspective in sec . [ cando ] .

thanks to its intrinsic ability to preserve spin coherence , graphene is a prime material for spintronics . in this review article , we summarize recent achievements related to spintronics in graphene quantum dots and motivate this field from a spintronics and a materials science point of view . we discuss spin relaxation in detail . nuclear spins in the host and surrounding material can be considered by several means and the influence of @xmath1c nuclei has been studied in detail .

thanks to its intrinsic ability to preserve spin coherence , graphene is a prime material for spintronics . in this review article , we summarize recent achievements related to spintronics in graphene quantum dots and motivate this field from a spintronics and a materials science point of view . we focus on theory but also discuss recent experiments . the main sources of spin decoherence are interactions with lattice excitations and the hyperfine interaction with present nuclear spins . we explain effective spin - phonon coupling in detail and present a generic power law for the spin relaxation time @xmath0 as a function of the magnetic field . for specific cases , we discuss spin relaxation in detail . the heisenberg exchange interaction is paramount for coherent spin qubit operation and addressed in the context of magnetism in graphene nanoflakes . nuclear spins in the host and surrounding material can be considered by several means and the influence of @xmath1c nuclei has been studied in detail . impressive advances in general spintronics and the fabrication of graphene devices are likely to spark significant advances in spintronics with graphene quantum dots in the near future .

1506.03991

c

we have given an overview of spintronics with electron spin states in graphene quantum dots and nanoflakes . long coherence times can be expected because of weak sources of decoherence , i.e. , small coupling strengths of the spin - orbit and hyperfine interactions , and a marginal abundance of nuclear spins in carbon . we have explained spin relaxation via spin - orbit mediated coupling to acoustic phonons and we have introduced a generic formula for the spin relaxation time @xmath0 for graphene and other systems . valley degeneracy and the lack of a bandgap in bulk graphene pose challenges to spin operations in graphene quantum dots . specific systems where these challenges can be overcome have been reviewed and , if applicable , studies on their spin relaxation times have been discussed . magnetism can be induced in graphene by several means . here , we have focused on magnetism in graphene nanoflakes and _ in - situ _ tunability of antiferromagnetism in symmetric nanoflakes with defects . we have summarized studies on the interaction of electron and nuclear spins and finally , we have pointed out recent experimental achievements relevant for spintronics with graphene quantum dots . we believe that graphene has the potential for a top - notch spintronics material that can outperform established materials like silicon or gaas for specific applications . the observation of the pauli blockade represents a fundamental step towards spintronics with graphene quantum dots . in principle , the necessary architectures exist already but suffer from poor tunability of the source and drain barriers and inefficient spin injection . similarly , the components required for electrostatic confinement of electrons in armchair gnr quantum dots are already available but have not been integrated into one device , yet . with view to the rapid progress of device fabrication , we anticipate significant progress in these fields within the next 2 - 3 years . ultimately , we see spintronics in graphene as a building block for 2d - heterostructured spintronics devices composed of ( functionalized ) graphene and other 2d materials like tmdcs and hbn .

we explain effective spin - phonon coupling in detail and present a generic power law for the spin relaxation time @xmath0 as a function of the magnetic field . for specific cases , impressive advances in general spintronics and the fabrication of graphene devices are likely to spark significant advances in spintronics with graphene quantum dots in the near future .

thanks to its intrinsic ability to preserve spin coherence , graphene is a prime material for spintronics . in this review article , we summarize recent achievements related to spintronics in graphene quantum dots and motivate this field from a spintronics and a materials science point of view . we focus on theory but also discuss recent experiments . the main sources of spin decoherence are interactions with lattice excitations and the hyperfine interaction with present nuclear spins . we explain effective spin - phonon coupling in detail and present a generic power law for the spin relaxation time @xmath0 as a function of the magnetic field . for specific cases , we discuss spin relaxation in detail . the heisenberg exchange interaction is paramount for coherent spin qubit operation and addressed in the context of magnetism in graphene nanoflakes . nuclear spins in the host and surrounding material can be considered by several means and the influence of @xmath1c nuclei has been studied in detail . impressive advances in general spintronics and the fabrication of graphene devices are likely to spark significant advances in spintronics with graphene quantum dots in the near future .

1005.4665

c

the _ chandra _ source catalog is a general purpose virtual x - ray astrophysics facility that provides access to a carefully crafted set of scientifically useful quantities for individual x - ray sources observed by the _ chandra _ x - ray observatory . the first release of the catalog was published to the astronomical community in march 2009 , and includes source properties for 94,676 point and compact x - ray sources detected in a subset of public acis imaging observations from roughly the first eight years of the _ chandra _ mission . this release of the catalog includes sources with observed spatial extents are @xmath0 , and whose flux estimates are at least 3 times their estimated @xmath1 uncertainties . observations that include substantially extended sources are not included in the first release of the catalog . for each x - ray source , the catalog tabulates about 60 distinct measured and derived source properties , generally with associated lower and upper confidence limits , in several energy bands . these properties are generally derived from all of the observations in which a source is detected . however , in the first catalog release , multiple observations are not _ combined _ prior to source detection , so the depth of the catalog is limited by the duration of the longest single exposure of a field . the catalog further tabulates roughly 120 observation - specific properties for each observation of a source , again with associated lower and upper confidence limits , and in several energy bands . tabulated source properties include source position , spatial extent , multi - band aperture fluxes computed in several different ways , x - ray hardness ratios and spectral model fits , and intra- and inter - observation variability measures . in addition to these `` traditional '' catalog elements , for each source detection the catalog includes an extensive set of fits format file - based data products that can be manipulated interactively by the user , including source images , event lists , light curves , and spectra from each observation in which a source is detected . looking towards the future , release 1.1 of the catalog , scheduled for spring 2010 , will include data from public hrc - i imaging observations and newly public acis imaging observations , but will otherwise retain the same limitations as release 1 . in release 2 , we plan to co - add multiple observations of the same field that use the same or similar instrument configurations , and that have similar spacecraft pointings ( within @xmath89 ) prior to source detection , to achieve fainter limiting sensitivities in many fields . we anticipate that new algorithms will allow this release to have a significantly fainter source detection threshold than release 1 . this release should also provide limited improvements in the area of extended source handling ( for example allowing for the inclusion of exposures containing moderately extended emission from galaxy cores up to @xmath518 spatial scale ) , as well as numerous algorithm enhancements that will refine field and source property calculations . the authors would like to thank the _ chandra _ source catalog project review visiting panel , who endorsed the catalog and proposed several key recommendations that have guided the development of the catalog . we would like to acknowledge the support and guidance of the _ chandra _ x - ray center director , harvey tananbaum , and manager , roger brissenden . former _ chandra _ source catalog project team members who have contributed significantly to the definition and development of the catalog include martin elvis , stphane paltani , adam dobrzycki , johnathan slavin , dan harris , peter freeman , and michael wise . we would like to thank taeyoung park for his support enhancing and testing the behr algorithm for use in the catalog processing pipelines . lisa paton and the cxc systems group provided extensive installation and operational support for the catalog production beowulf cluster . the authors would also like to thank the anonymous referee , who performed a very careful and comprehensive review of the first version of the manuscript , and whose suggestions materially improved the content and quality of the paper . the development and operational construction of the catalog made extensive use of the ciao , chips , and sherpa software packages developed by the _ chandra _ x - ray center , and the saoimage ds9 imager developed by the smithsonian astrophysical observatory . support for development of the _ chandra _ source catalog is provided by the national aeronautics and space administration through the _ chandra _ x - ray center , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics and space administration under contract nas 8 - 03060 .

the first release of the csc includes information about 94,676 distinct x - ray sources detected in a subset of public acis imaging observations from roughly the first eight years of the _ chandra _ mission . , the csc provides commonly tabulated quantities , including source position , extent , multi - band fluxes , hardness ratios , and variability statistics , derived from the observations in which the source is detected . in addition to these traditional catalog elements , for each x - ray source the csc includes an extensive set of file - based data products that can be manipulated interactively , including source images , event lists , light curves , and spectra from each observation in which a source is detected .

the _ chandra _ source catalog ( csc ) is a general purpose virtual x - ray astrophysics facility that provides access to a carefully selected set of generally useful quantities for individual x - ray sources , and is designed to satisfy the needs of a broad - based group of scientists , including those who may be less familiar with astronomical data analysis in the x - ray regime . the first release of the csc includes information about 94,676 distinct x - ray sources detected in a subset of public acis imaging observations from roughly the first eight years of the _ chandra _ mission . this release of the catalog includes point and compact sources with observed spatial extents @xmath0 . the catalog ( 1 ) provides access to the best estimates of the x - ray source properties for detected sources , with good scientific fidelity , and directly supports scientific analysis using the individual source data ; ( 2 ) facilitates analysis of a wide range of statistical properties for classes of x - ray sources ; and ( 3 ) provides efficient access to calibrated observational data and ancillary data products for individual x - ray sources , so that users can perform detailed further analysis using existing tools . the catalog includes real x - ray sources detected with flux estimates that are at least 3 times their estimated @xmath1 uncertainties in at least one energy band , while maintaining the number of spurious sources at a level of @xmath2 false source per field for a @xmath3 observation . for each detected source , the csc provides commonly tabulated quantities , including source position , extent , multi - band fluxes , hardness ratios , and variability statistics , derived from the observations in which the source is detected . in addition to these traditional catalog elements , for each x - ray source the csc includes an extensive set of file - based data products that can be manipulated interactively , including source images , event lists , light curves , and spectra from each observation in which a source is detected .

0906.2920

i

in our previous paper @xcite , we proved a conjecture of lisca @xcite , establishing a bijective correspondence between the milnor fibers of the smoothing components of a cyclic quotient singularity and the stein fillings of the corresponding contact lens space , the boundary of the singularity . as a particular case of our results , the milnor fibers corresponding to distinct smoothing components of the reduced miniversal base space of the cyclic quotient singularity are pairwise non - diffeomorphic . here one has to understand the diffeomorphisms _ in a strong sense _ : namely , there are natural identifications of the boundaries of the milnor fibers up to isotopy , and we showed that there are no diffeomorphisms extending those identifications . having in mind the construction of de jong and van straten in @xcite regarding the milnor fibers of sandwiched singularites , it is natural to try to extend the above result for such singularities . one of the main obstructions of this program is that at the present moment the precise description of all the smoothing components of sandwiched singularities ( or / and the classification of all stein fillings of the corresponding contact boundaries ) is out of hope . nevertheless , we will prove a slightly weaker version of the above result . in order to explain it we need some preparation . the class of sandwiched singularities received its name in @xcite from the fact that the corresponding singularities are analytically isomorphic to the germs of surfaces which may be `` sandwiched '' birationally between two smooth surfaces ( see also subsection [ sand ] ) . they form a subclass of the rational surface singularities and their study may be reduced in many respects to the study of plane curve singularities . indeed , de jong and van straten showed that this was the case for their deformation theory as well . namely , one may encode a sandwiched singularity @xmath0 by a _ decorated curve _ @xmath1 , which is a germ of reduced plane curve whose components @xmath2 are decorated by sufficiently high positive integers @xmath3 . one of the main theorems of @xcite states that the deformation properties of a sandwiched singularity reduces to the deformation properties of any such decorated curve which encodes it . in particular , the 1-parameter smoothings of @xmath0 correspond bijectively to the so - called _ picture deformations _ of @xmath1 , which are @xmath4-constant deformations of @xmath5 with generic fibers having only ordinary singularities , accompanied with flat deformations of @xmath6 ( seen as a subscheme of the normalization of @xmath5 ) which generically are reduced and contain the preimage of the singular locus of the generic fiber . the milnor fiber corresponding to a smoothing component of @xmath0 may be reconstructed up to strong diffeomorphism from the embedding in a 4-ball of the generic fiber of a corresponding picture deformation . part of the topological structure of the generic fiber of the deformation of @xmath1 may be encoded in an associated _ incidence matrix _ between the irreducible components of the deformation of @xmath5 and the images of the support of @xmath6 seen as a subscheme of the normalization . this matrix is well - defined up to permutation of columns . as it is proved in @xcite , the validity of lisca s conjecture implies that , _ for cyclic quotient singularities _ , the milnor fibers which correspond to distinct incidence matrices ( up to permutation of columns ) are not strongly diffeomorphic . the aim of this paper is to show that _ the same is true for all sandwiched surface singularities _ ( see theorem [ distinc ] ) . in fact , for any fixed realization of @xmath0 by a decorated curve @xmath1 , we provide a canonical method to reproduce all the incidence matrices ( associated with @xmath1 ) from the milnor fibers . hence , each realization @xmath1 provides a ` test ' to separate the milnor fibers ( in fact , precise criteria to recognize them ) . recall also that de jong and van straten predict ( see ( * ? ? ? * ; * ? ? ? * ( 4.3 ) ) ) that , for any fixed @xmath1 , the set of smoothing components of the deformation space of @xmath0 injects into the set of incidence matrices associated with @xmath1 . in particular , for any class of singularities , when this is indeed the case , we obtain via our result that there is no pair of smoothing components with ( strongly ) diffeomorphic milnor fibers . in order to connect our main result with the set of stein fillings of the contact boundary , we have to face a new aspect of the problem : sandwiched singularities are not necessarily taut ( that is , their analytical structure is not determined by their topology ) . moreover , fixing a topological type , for different analytic types one might have different structure of the miniversal deformation space ( therefore different sets of milnor fibers ) . nevertheless , for a fixed topological type , the induced natural contact structure on the boundary is independent of the analytic realization and is invariant up to isotopy by all orientation - preserving diffeomorphisms ( cf . @xcite ) . therefore , in theorem [ lowbound ] we are able to extend the above recognition criterion of the milnor fibers via incidence matrices by considering all the smoothings associated with the deformations of all the decorated germs of plane curves with a fixed topology . in this way we get a lower bound for the number of stein fillings of the contact boundary of a sandwiched surface singularity , considered up to orientation - preserving diffeomorphisms fixed on the boundary . all the differentiable manifolds we consider are oriented : any letter , say @xmath7 , denoting a manifold denotes in fact an oriented manifold . we denote by @xmath8 the manifold obtained by changing the orientation of @xmath7 , and by @xmath9 its boundary , canonically oriented by the rule that the outward normal _ followed _ by the orientation of @xmath9 gives the orientation of @xmath7 . we work exclusively with homology groups _ with integral coefficients_. if @xmath7 is 4-dimensional , the intersection number in @xmath10 is denoted by @xmath11 . an element of @xmath10 is called _ a @xmath12-class _ if its self - intersection is equal to @xmath13 . if @xmath14 and @xmath15 are two oriented manifolds with boundary , endowed with a fixed isotopy class of orientation - preserving diffeomorphisms @xmath16 , we say that @xmath14 and @xmath15 are _ strongly diffeomorphic _ ( with respect to that class ) if there exists an orientation - preserving diffeomorphism @xmath17 whose restriction to the boundary belongs to the given class .

part of the topology of such a deformation is encoded in the _ incidence matrix _ between the irreducible components of the deformed curve and the points which decorate it , well - defined up to permutations of columns . extending a previous theorem ofours , which treated the case of cyclic quotient singularities , we show that the milnor fibers which correspond to deformations whose incidence matrices are different up to permutations of columns are not diffeomorphic in a strong sense . this gives a lower bound on the number of stein fillings of the contact boundary of a sandwiched singularity .

the _ sandwiched _ surface singularities are those rational surface singularities which dominate birationally smooth surface singularities . de jong and van straten showed that one can reduce the study of the deformations of a sandwiched surface singularity to the study of deformations of a 1-dimensional object , a so - called _ decorated _ plane curve singularity . in particular , the milnor fibers corresponding to their various smoothing components may be reconstructed up to diffeomorphisms from those deformations of associated decorated curves which have only ordinary singularities . part of the topology of such a deformation is encoded in the _ incidence matrix _ between the irreducible components of the deformed curve and the points which decorate it , well - defined up to permutations of columns . extending a previous theorem ofours , which treated the case of cyclic quotient singularities , we show that the milnor fibers which correspond to deformations whose incidence matrices are different up to permutations of columns are not diffeomorphic in a strong sense . this gives a lower bound on the number of stein fillings of the contact boundary of a sandwiched singularity .

0710.1356

i

the fermion hubbard hamiltonian @xcite , originally proposed to describe the physics of transition metal monoxides feo , mno , and coo , has been widely used as a model of cuprate superconductors , whose undoped parent compounds , like la@xmath1cuo@xmath2 , are also antiferromagnetic and insulating . indeed , early quantum monte carlo ( qmc ) simulations of the hubbard hamiltonian suggested that d - wave pairing was the dominant superconducting instability@xcite , a symmetry which was subsequently observed in the cuprates@xcite . however , the sign problem precluded any definitive statement about a phase transition to a d - wave superconducting phase@xcite . over the last several years , qmc studies within dynamical mean field theory and its cluster generalization @xcite are presenting a more compelling case for this transition . the existence of charge inhomogeneities in hartree - fock @xcite and density matrix renormalization group treatments@xcite , along with the experimental observation of such patterns @xcite , offer further indications that significant aspects of the qualitative physics of the cuprates might be contained in the hubbard hamiltonian . nevertheless , there are a number of features of high temperature superconductors which do not completely fit within the framework of the single band hubbard hamiltonian . for example , the cuprate gap is set by the charge transfer energy separating the copper @xmath3 and oxygen @xmath4 orbitals @xcite as opposed to a mott gap between copper @xmath3 states split by the on - site repulsion . considerable evidence for the possible important role of phonon modes in aspects of the physics is available@xcite . hirsch has emphasized the asymmetry in transition temperatures , and other properties , between the electron and hole doped cuprates as a reason to consider more general models , since the particle - hole symmetry of the single band hubbard hamiltonian requires that its behavior be rigorously identical for fillings @xmath5 and @xmath6 . partially motivated by this asymmetry , he introduced @xcite the dynamic hubbard hamiltonian , @xmath7 . \label{hamilton}\end{aligned}\ ] ] here the first term , involving the fermion creation ( destruction ) operators @xmath8 at site @xmath9 with spin @xmath10 , is the tight binding kinetic energy describing the hopping of electrons between near neighbor sites . we consider here a two - dimensional square lattice and chose @xmath11 to set our scale of energy . the on - site interaction energy differs from the usual static hubbard hamiltonian in that its value @xmath12 is modulated by a dynamic field @xmath13 which can take the values @xmath14 . as a consequence the on - site repulsion @xmath12 has bimodal values @xmath15 and @xmath16 . this dynamic field itself has non - trivial quantum fluctuations controlled by the relative values of the longitudinal and transverse frequencies @xmath17 and @xmath18 . here @xmath19 and @xmath13 are pauli matrices@xcite . the variation in @xmath12 , hirsch argued , has its physical origin in the relaxation which occurs with multiple occupation of an atomic orbital . hirsch and collaborators have studied the physics of eq . [ hamilton ] with a variety of methods , including a lang - firsov transformation ( lft)@xcite , exact diagonalization ( ed ) of small clusters@xcite , and world - line quantum monte carlo ( wlqmc ) @xcite in one dimension @xcite . within the lft it is seen that the hopping of electrons is renormalized by the overlap of the states of the dynamic variable on neighboring lattice sites . superconductivity then arises because isolated holes are essentially localized by a small overlap , whereas holes that are on the same or neighboring sites can move around the lattice . furthermore this effect is operative for holes in a nearly filled system , but not electrons in a nearly empty lattice . thus pairing is linked to the presence of holes , and the physics is manifestly not particle - hole symmetric . ed provided quantitative values for the overlaps and confirmed the picture based on the lft on small clusters . ed also allows for the evaluation of the ` binding energy ' , @xmath20 . here @xmath21 is the ground state energy of a cluster with @xmath22 electrons . a negative @xmath23 indicates that it is energetically favorable to put two particles together on a single cluster rather than separate them on two different clusters . on a sufficiently large lattice , two particles would tend to be close spatially rather than widely separated . in fig . [ hirschcheck1 ] we show an evaluation of @xmath23 on a 2x2 lattice . these numbers were obtained independently from , but are identical to , those of ref . . as the coupling @xmath24 to the dynamic field increases , @xmath23 is driven negative , indicating the possibility of binding of particles and hence superconductivity . wlqmc simulations in one dimension confirmed this real space pairing by explicitly showing the preference of the world lines of holes to propagate next to each other and a large gain in kinetic energy when the hole - hole separation becomes small . significantly , these simulations also showed that the kinetic energy disfavors proximity of holes in the holstein model , which also features the tendency of holes to clump together by distorting a local phonon degree of freedom . thus pairing in the dynamic hubbard model is distinguished from that of more traditional electron - phonon models by being driven by the kinetic energy as opposed to a potential energy . in this paper we examine the properties of the dynamic hubbard hamiltonian with determinant quantum monte carlo ( dqmc)@xcite . this approach allows us to work in two dimensions , as opposed to previous ( @xmath25 ) wlqmc studies , and also to examine lattices of an order of magnitude greater number of sites than ed . on the other hand , the ability of dqmc to reach low temperatures is limited by the sign problem@xcite . we find that the extended @xmath0-wave pairing vertex , which is repulsive in the static hubbard model , is attractive in the dynamic model , that is , extended @xmath0-wave superconducting correlations are enhanced by the dynamic fluctuations . however , the pairing susceptibilities are still only rather weakly increasing down to the lowest temperatures accessible to us ( temperature @xmath26 greater than 1/40 the electronic bandwidth ) . we also find , near half - filling , that the antiferromagnetic correlations can be enhanced relative to the static hubbard hamiltonian , particularly for densities _ above _ @xmath27 . the mott gap can also be stabilized . interestingly , the total energy appears to be close to linear in the particle density , as opposed to a clear concave up curvature in the static hubbard model ( with either repulsive or attractive interactions ) . the organization of this paper is as follows : in the next section we present our computational method , dqmc , as it applies to the dynamic hubbard model . we describe several minor adjustments to the dqmc algorithm for the static hubbard model that are needed in order to study the dynamic model . our observables are also defined . in section iii , we present the results from our monte carlo simulations . the topics of antiferromagnetism and the mott transition , pair susceptibilities and superconductivity , and the energy characteristics of the dynamic hubbard model are discussed . the paper closes with conclusions in section iv .

we investigate one such model , introduced by hirsch , using the determinant quantum monte carlo method . our key result is that the extended @xmath0-wave pairing vertex , repulsive in the usual static hubbard model , becomes attractive as the coupling to the fluctuating bose field increases . we also observe a stabilization of antiferromagnetic correlations and the mott gap near half - filling , and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation .

the ` dynamic ' hubbard hamiltonian describes interacting fermions on a lattice whose on - site repulsion is modulated by a coupling to a fluctuating bosonic field . we investigate one such model , introduced by hirsch , using the determinant quantum monte carlo method . our key result is that the extended @xmath0-wave pairing vertex , repulsive in the usual static hubbard model , becomes attractive as the coupling to the fluctuating bose field increases . the sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs . we also observe a stabilization of antiferromagnetic correlations and the mott gap near half - filling , and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation .

0710.1356

c

in this paper we have performed determinant quantum monte carlo simulations of a two dimensional hubbard hamiltonian in which the on - site repulsion is coupled to a fluctuating bosonic field . our studies complement earlier work using the lang - firsov transformation and exact diagonalization and qmc in one dimension . we note a number of interesting features of the model . first , the mott gap at half - filling is stabilized . second , antiferromagnetic correlations are enhanced above half - filling . the extended @xmath0-wave pairing vertex , which is repulsive in the ordinary static hubbard hamiltonian , is made attractive in the dynamic model . the value of @xmath24 for which this attraction manifests is roughly consistent with the value at which the binding energy @xmath23 goes negative on 2x2 clusters . the sign problem prevents simulations at low temperatures to see if an actual pairing instability occurs . we have also observed that as @xmath100 , _ i.e. _ as @xmath105 , @xmath106 becomes linear in @xmath65 signalling possible phase separation into regions of hole - deficient and hole - rich regions when @xmath70 becomes negative for @xmath104 . finally , we note that we have also found , within the hartree - fock framework , that charge inhomogeneities ( stripes ) are supported by this dynamic hubbard model @xcite . kb , fh , and ggb acknowledge financial support from a grant from the cnrs ( france ) pics 18796 , rts from nsf itr 0313390 , and me from the research corporation . we acknowledge very useful help from m. schram and r.waters . a. lanzara , p.v bogdanov , x.j . zhou , s.a kellar , d.l . feng , e.d . lu , t. yoshida , h. eisaki , a. fujimori , k. kishio , j .- shimoyama , t. noda , s. uchida , z.hussain and z .- x . shen , nature * 412 * , 510 ( 2001 ) . actually , j.e hirsch originally proposed a modulation of the on - site repulsion @xmath12 with a coupling to a continuous bosonic mode , @xmath107 . in later papers he argued for the equivalence to a model with a discrete ( ising - like ) degree of freedom . we comment that the attraction exhibited in the @xmath3-wave vertex of the static model is most manifest at half - filling , where the cuprates are antiferromagnetic insulators . this is possibly , however , a consequence of small lattice size since then the pair creation operator @xmath110 which adds two particles to the system , significantly shifts the density .

the ` dynamic ' hubbard hamiltonian describes interacting fermions on a lattice whose on - site repulsion is modulated by a coupling to a fluctuating bosonic field . the sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs .

the ` dynamic ' hubbard hamiltonian describes interacting fermions on a lattice whose on - site repulsion is modulated by a coupling to a fluctuating bosonic field . we investigate one such model , introduced by hirsch , using the determinant quantum monte carlo method . our key result is that the extended @xmath0-wave pairing vertex , repulsive in the usual static hubbard model , becomes attractive as the coupling to the fluctuating bose field increases . the sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs . we also observe a stabilization of antiferromagnetic correlations and the mott gap near half - filling , and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation .

astro-ph9512126

i

when batse observes bursts from different red - shifts at a fixed energy band it detects photons from different energy bands at the source . this spectral dependence complicates the interpretation of the peak - flux and time - dilation distributions . so far several attempts have been made to overcome this problem by modeling the spectral shape of the bursts . we suggest here a different method which is based on the availability of multi channel data in different energy bands . the basic idea beyond our scheme is that we view " all bursts at the same intrinsic energy band independently of their red - shift by by scanning over the different channels until we find the most likely red - shift and using this value to blue - shift " back the observed spectrum to the initial spectrum at the source . now we look at the same energy band at the source for all bursts , avoiding the issue of the spectral shape .

the analysis of the batse s count distribution within cosmological models suffers from observational uncertainties due to the variability of the bursts spectra : when batse observes bursts from different redshifts at a fixed energy band it detects photons from different energy bands at the source . this adds a spectral dependence to the count distribution @xmath0 .

the analysis of the batse s count distribution within cosmological models suffers from observational uncertainties due to the variability of the bursts spectra : when batse observes bursts from different redshifts at a fixed energy band it detects photons from different energy bands at the source . this adds a spectral dependence to the count distribution @xmath0 . similarly variation of the duration as a function of energy @xcite at the source complicates the time dilation analysis . it has even been suggested that these methods lead to inconsistent estimates of the redshift from which the bursts are observed@xcite . clearly it would be best to combine the estimates and to perform a joint analysis of the strength and the duration of the bursts . but for this we have to eliminate first the spectral dependence problem . we describe here a new statistical formalism that performs the required blue shifting " of the count number and the burst duration in a statistical manner . this formalism allows us to perform a combined best fit ( maximal likelihood ) to the count distribution , @xmath0 , and the duration distribution simultaneously . the outcome of this analysis is a single best fit value for the redshift of the observed bursts .

astro-ph9512126

c

the spectrum invariant method is the only way to have a complete usage of all the information available in the multi - spectral channel detectors in situations in which the spectra is being red - shifted differently from burst to burst . it also uses the time - dilation and the peak - luminosity in a way that more than just brings a consistent answer , it uses the whole data to enlarge the statistical confidence of the results . a luminosity distribution influences considerably the confidence the red - shift determination of a single burst origin . however , it has a minor influence when using a large number of bursts . similarly the duration distribution makes it impossible to determine the red - shift of a single burst , however one can determine the parameters of the duration distribution and find whether the red - shift data determined from the time dilation analysis is consistent with the one determined from the peak - flux distribution . fenimore , e. e. , et al , 1995 , apjl , * 448 * , 101l fenimore , e. e. , and bloom , j. s. , 1995 , apj , * 453 * , 25 . norris , j. p. , et al , 1994 , apj . * 424 * , 540 . band , d. l. , 1994 , apjl . wijers , r. a. m. j. , and paczyski , b. , 1994 , apjl , * 437 * , 107l .

similarly variation of the duration as a function of energy @xcite at the source complicates the time dilation analysis . this formalism allows us to perform a combined best fit ( maximal likelihood ) to the count distribution , @xmath0 , and the duration distribution simultaneously .

the analysis of the batse s count distribution within cosmological models suffers from observational uncertainties due to the variability of the bursts spectra : when batse observes bursts from different redshifts at a fixed energy band it detects photons from different energy bands at the source . this adds a spectral dependence to the count distribution @xmath0 . similarly variation of the duration as a function of energy @xcite at the source complicates the time dilation analysis . it has even been suggested that these methods lead to inconsistent estimates of the redshift from which the bursts are observed@xcite . clearly it would be best to combine the estimates and to perform a joint analysis of the strength and the duration of the bursts . but for this we have to eliminate first the spectral dependence problem . we describe here a new statistical formalism that performs the required blue shifting " of the count number and the burst duration in a statistical manner . this formalism allows us to perform a combined best fit ( maximal likelihood ) to the count distribution , @xmath0 , and the duration distribution simultaneously . the outcome of this analysis is a single best fit value for the redshift of the observed bursts .

0910.3081

i

the atlas detector at cern is one of two large general purpose detectors at the large hadron collider ( lhc ) @xcite , a 7 tev on 7 tev proton accelerator . it was designed to have excellent tracking , calorimetry and muon spectroscopy over the entire energy range of the lhc allowing discovery of any new physics in that range . particular discovery potentials include details of the standard model and beyond , such as discovery of the higgs boson , supersymmetry ( susy ) and extra dimensions . more complete discussion of the physics discovery potential of atlas is given in reference @xcite . the atlas detector , under construction for well over a decade , was ready to record collision events on september 10 , 2008 when the lhc started up . single beams were circulated around the accelerator and resulting events were recorded in the detector . as is well known , about one week later , an incident in a superconducting splice between two dipoles resulted in a shutdown of the machine before any beam collisions occurred . this shutdown is still continuing and atlas has used this time to fix minor problems with the detector and commission the subsystems with cosmic ray events . the lhc accelerator is now scheduled to start again in november , 2009 . this paper will describe the current state of each subsystem and present results of these cosmic ray events showing that atlas now fully ready for collision data that is expected later this year .

the atlas detector at the large hadron collider , cern has been under construction for more than a decade . this paper will describe the state of the major subsystems of atlas . these results show that atlas is prepared to make major new physics discoveries as soon as we get colliding beams in late 2009 .

the atlas detector at the large hadron collider , cern has been under construction for more than a decade . it is now largely complete and functional . this paper will describe the state of the major subsystems of atlas . results from the brief single beam running period in 2008 will be shown . in addition , results from a long period of cosmic ray running will be shown . these results show that atlas is prepared to make major new physics discoveries as soon as we get colliding beams in late 2009 .

astro-ph0510744

i

new observational data from the soho and trace spacecraft have revealed a wide array of wave activity in the corona , for example , the discoveries of eit waves @xcite , longitudinal standing waves within coronal loops @xcite , and compressible waves in polar plumes @xcite . @xcite and @xcite give extensive reviews of coronal oscillation observations . these observations underscore the link between wave propagation and magnetic fields . similar observational studies of the connection between wave processes and magnetic fields in the chromosphere are challenging : there are few suitable spectral lines and they form under complex non - lte ( nlte ) conditions . consequently there is no straightforward way to extract information , such as atmospheric temperature and pressure , from these observations . the presence of emission self - reversals in the ca line cores , due to upward - propagating shock - heated plasma , complicates even the simplest doppler shift analysis and obscures the true oscillatory signal . the magnetic flux in the quiet sun is very small ( @xmath1 3 mx @xmath2 in the internetwork , @xcite ) , so useful observations need a high signal - to - noise ratio ( s / n @xmath3 @xmath4 ) , which , when combined with the high time cadence required to resolve the wave propagation , imposes stringent demands on the instrumentation . acoustic waves generated by the turbulent solar convection become non - linear and develop into shocks as they propagate into the low density of the chromosphere @xcite . understanding this complex process is important not only from a fundamental point of view , but also because it has been traditionally thought to be an efficient way to transport energy into the upper atmosphere . in 1948 both biermann and schwarzschild proposed that shock waves heat the chromosphere , but in recent times , this heating mechanism has been challenged . carlsson & stein ( 1995 ) have argued , based on radiation hydrodynamic simulations , as to whether acoustic shocks are capable of heating the non - magnetic chromosphere . and recently fossum & carlsson ( 2005 ) showed , by comparing radiation hydrodynamic simulations and trace observations , that the integrated acoustic wave power , including frequencies up to 50 mhz , is insufficient to heat the non - magnetic chromosphere . even if wave propagation is not the sole answer to the heating problem it is still of interest . atmospheric dynamics depend on wave propagation properties such as wave generation , refraction , reflection , mode coupling and dissipation . because the three mhd waves , i.e. alfvn , slow mhd and fast mhd waves , have quite different properties , a lot of information about the atmospheric conditions are embedded in them . in the mid - chromosphere magnetic fields spread out and fill the space , making the term non - magnetic chromosphere applicable at best only in the low quiet sun chromosphere . the layer where the transition from pressure to magnetic dominated regimes occurs is often referred to as the `` magnetic canopy . '' study of trace observations has shown that there is more oscillatory power below the canopy than above it @xcite and mhd simulations of wave propagation have identified this layer as a place where dramatic changes in wave propagation take place @xcite . waves are also used as a tool in `` coronal seismology '' to probe the physical conditions in the corona . coronal parameters , e.g. magnetic field strengths and transport coefficients , can be determined by combining measurements of the wave properties and oscillations with theoretical models . modeling wave propagation in the solar atmosphere is a daunting task . a realistic model must be three - dimensional ( 3d ) . the treatment of radiation should be non - gray and nlte . the significance of magnetic fields in wave propagation make them an essential part of any comprehensive model . yet another crucial part of any model describing wave propagation in the chromosphere is nonlinear effects such as wave steepening and shocks . because of the complexity of the problem , and the computational power needed to solve it , so far no fully comprehensive model has been developed . instead restricted combinations of the above - mentioned elements have been studied . for example carlsson & stein s ( 1992 , 1994 , 1995 , 1997 , 2002 ) 1d model combines the nonlinear hydrodynamics with full treatment of radiative transfer . the effect of shock dissipation in the chromosphere has been studied also by e.g. @xcite , @xcite , @xcite , and @xcite . @xcite have looked at the nonlinear non - radiative 2d magnetic problem . other numerical simulations on mhd wave propagation include e.g. : @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , @xcite , and @xcite . in this paper we approach the problem from a different perspective . we have combined full treatment of radiative transfer in 1d with magnetohydrodynamics in 2d . the treatment of the interplay between the hydrodynamics and the magnetic field is effected in a suggestive , although not entirely rigorous fashion . a 1d radiation hydrodynamic simulation ( duration of 3690 s ) is employed as the base building block . it is used to kinematically deform a 2d initial magnetic field , @xmath5 , according to the magnetic induction equation , @xmath6 , \label{eqn : induction}\end{aligned}\ ] ] where @xmath7 is prescribed and @xmath8 is derived from the radiation hydrodynamic simulation . by having the plasma-@xmath9 , i.e. the ratio between the gas and magnetic pressures , significantly larger than one , we can justify neglect of the back reaction of the lorentz force on the dynamics . finally we integrate the stokes transfer equation to determine the emergent stokes profiles in i and v for the ca ii infrared ( ir ) triplet lines for each 10 second time step . in this way , all 3 essential ingredients are accounted for in this approach although not fully consistently . the infrared triplet is an excellent diagnostic of chromospheric oscillations in sunspots ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) ) and shows promise to be as useful in the quiet sun . unfortunately , these lines are usually out of the accessible wavelength range for most modern spectro - polarimetric instrumentation . currently the newly commissioned spectro - polarimeter for infrared and optical regions ( spinor , * ? ? ? * ) and the french - italian solar telescope themis operated in the mtr - mode @xcite can routinely provide high - sensitivity observations of these lines . the outline of the paper is as follows . in the second section the numerical simulation and initial conditions are described . then in the third section we show the stokes profiles produced in the simulation and try to explain how they are formed in terms of the atmospheric dynamics . we find interesting time - dependent behavior in the stokes v profiles as shocks propagate through the model atmosphere . disappearing and reappearing stokes v lobes as well as profile asymmetries are closely related to both the local fluid velocity and atmospheric velocity gradients . finally , in the fourth section the results are discussed .

the ca ii infrared triplet around 8540 is a good candidate for observing chromospheric magnetism . the simulation shows interesting time - varying behavior of the stokes @xmath0 profiles as waves propagate through the lines formation regions . disappearing and reappearing lobes in the stokes @xmath0 profiles as well as profile asymmetries are closely related to the atmospheric velocity gradients .

the ca ii infrared triplet around 8540 is a good candidate for observing chromospheric magnetism . we show results from combining a radiation hydrodynamic simulation with a stokes synthesis code . the simulation shows interesting time - varying behavior of the stokes @xmath0 profiles as waves propagate through the lines formation regions . disappearing and reappearing lobes in the stokes @xmath0 profiles as well as profile asymmetries are closely related to the atmospheric velocity gradients .

astro-ph9908001

i

early - type galaxies form the dominant population in the core of all galaxy clusters with few or no exceptions from low redshift to @xmath0 , from poor to rich clusters . the uniformity of the properties of early - type galaxies provide important tools , such as the fundamental plane and the color - magnitude relation ( cmr ) , in the study of galaxy clusters and their evolution . the cmr for early - type galaxies ( e / s0 s ) was first noted by baum ( 1959 ) in that the colors for elliptical galaxies become bluer as they become less luminous . furthermore , e / s0 galaxies are also the reddest normal galaxies at any single given redshift . hence , the e / s0 s form a sequence on the color - magnitude plane which is sometimes called the `` red sequence '' , as illustrated for the cluster abell 2256 using data from lpez - cruz & yee ( 1999a , also see lpez - cruz 1997 ) in figure 1 . the existence of the cmr is in general attributed to a metallicity effect due to the varying ability of spheroids of different masses to retain metals in the presence of supernovae driven winds ( e.g. , see kodama & arimoto 1997 and references therein ) . the dispersion , color , and slope of the red sequence in clusters have been used to study the evolution of cluster galaxies up to a redshift as high as @xmath1 ( e.g. , bower et al . 1992 ; aragn - salamanca et al . 1993 ; stanford et al . 1998 ; and gladders et al . 1998 ) . in this paper , we demonstrate the efficiency of using the color - magnitude relation of clusters as a powerful tool for estimating the redshift of clusters photometrically and detecting clusters from two - filter imaging data .

the color - magnitude relation ( cmr ) of early - type galaxies in clusters provides a powerful tool for finding clusters and determining photometric redshifts for clusters using two - filter imaging data . we demonstrate this using both observed photometric catalogs with redshifts ( from the cnoc2 survey ) and simulations .

the color - magnitude relation ( cmr ) of early - type galaxies in clusters provides a powerful tool for finding clusters and determining photometric redshifts for clusters using two - filter imaging data . we demonstrate the high accuracy of photometric redshifts attainable using the cmr by applying the technique to a sample of 45 abell clusters with known redshifts . furthermore , by using the red sequence of galaxies from the cmr , we have developed an extremely efficient technique for detecting clusters and groups of galaxies . we demonstrate this using both observed photometric catalogs with redshifts ( from the cnoc2 survey ) and simulations .

nucl-th9905011

i

there is an increasing interest in @xmath8-meson physics both experimentally and theoretically . on the experimental side several facilities are now able to produce sufficient @xmath8 s to enable a study to be made of their interactions with other particles . in particular , the photon machines mami@xcite and graal@xcite are supplementing the earlier hadronic machines such as saturne@xcite , celsius@xcite and cosy@xcite . the current theoretical interest stems partly from the early indications that the @xmath16 interaction is attractive and so could possibly lead to @xmath8-nucleus quasi - bound states ( e.g. refs . @xcite , @xcite ) . the theoretical approaches fall into two main categories . in the one , the various processes involving @xmath8-meson interactions are described in terms of microscopic models containing baryon resonances and the exchange of different mesons ( e.g. refs . @xcite , @xcite ) which may be based on a chiral perturbation approach ( e.g.ref . @xcite ) or a quark model ( e.g. ref . @xcite ) . unfortunately , this approach requires a knowledge of the magnitudes and relative phases of many hadron - hadron couplings several of which are very poorly known . in addition , since @xmath8 interactions in the absence of @xmath8-meson beams can only be studied as final state interactions , one has to exploit relationships between the many processes involved . for example , in the present note , the main interest is in the reaction a ) @xmath7 . however , this is dependent on the final state interaction b ) @xmath17 , which in turn depends on the reactions c ) @xmath5 and d ) @xmath4 . similarly , reactions c ) and d ) are related to e ) @xmath6 . therefore , any model that claims to describe reaction a ) must also see its implications in reactions b ) , .. , e ) . this , we believe , is too ambitious a program at present . at this stage it is probably more informative to check the consistency between the data of the above five reactions and be able to relate them in terms of a few phenomenological parameters . when this has been accomplished , it will hopefully be possible to understand these parameters in terms of more microscopic models . with this in mind , in ref . @xcite a @xmath3-matrix model was developed by the authors to describe the reactions a ) , b ) , c ) and d ) in an energy range of about 100 mev each side of the @xmath8 threshold . this model was expressed in the form of two coupled channels for @xmath18-wave @xmath19 and @xmath16 scattering with the effect of the two pion channel ( @xmath20 ) being included only implicitly . the latter was achieved by first introducing the two pion process as a third channel in the @xmath3-matrix and subsequently eliminating that channel as an `` optical potential '' correction to the other two channels . it should be emphasized that this is not an approximation but is done only for convenience , since we do not address cross sections involving explicitly two final state pions . in ref . @xcite the @xmath8-photoproduction cross section was assumed to be proportional to the elastic @xmath16 cross section ( @xmath21 ) . this is in line with the so - called watson approximation @xcite . in this way each of the matrix elements in the two - by - two @xmath22-matrix of ref . @xcite was associated with some specific experimental data @xmath23 with the @xmath0 amplitudes of arndt _ et al . _ @xcite , @xmath24 with the @xmath8-production cross section in the review by nefkens@xcite and @xmath25 with the @xmath8-photoproduction cross section of krusche _ et al._@xcite . in this note we now wish to treat the @xmath2 channel explicitly . an enlargement of the @xmath3-matrix basis then permits a direct estimate of the matrix element @xmath26 , so that @xmath27 , thereby avoiding the earlier assumption that @xmath28 . the @xmath3-matrix would now be a four - by - four matrix with the channels @xmath0 , @xmath1 , @xmath29 and @xmath2 . in principle , 10 different processes , corresponding to each matrix element , could be analysed simultaneously . however , in practice , it is more convenient to elimate some channels by the `` optical potential '' method used already in ref . we , therefore , describe in section 2 the above reactions in terms of three separate @xmath22-matrices . in section 3 , we give the fitting strategy and also the numerical results in terms of the 13 parameters needed to specify the @xmath3-matrices . this section also includes expansions in terms of the @xmath8 momentum for the amplitudes of the @xmath17 and @xmath7 reactions near the @xmath8 threshold . section 4 contains a discussion and some conclusions .

are adjusted to get an optimal fit to @xmath4 , @xmath5 , @xmath6 and @xmath7 data in an energy range of about 100 mev each side of the @xmath8 threshold . expansions are given for the @xmath11 and @xmath12 amplitudes in terms of the @xmath8 momentum .

the coupled @xmath0 , @xmath1 , @xmath2 systems are described by a @xmath3-matrix method . the parameters in this model are adjusted to get an optimal fit to @xmath4 , @xmath5 , @xmath6 and @xmath7 data in an energy range of about 100 mev each side of the @xmath8 threshold . + the coupling of photons to the @xmath9 state is extracted and also an alternative to the current @xmath10 amplitudes suggested . expansions are given for the @xmath11 and @xmath12 amplitudes in terms of the @xmath8 momentum . effects of interference of this state with background potential interactions are discussed and experimental consequences are indicated . epsf 2ex = hip 1999 21 / th + a.m. green@xmath13 , and s. wycech@xmath13 + @xmath14department of physics and helsinki institute of physics , p.o . box 9 , + fin00014 university of helsinki , finland + @xmath15soltan institute for nuclear studies , warsaw , poland pacs numbers : 13.75.-n , 25.80.-e , 25.40.v

nucl-th9905011

c

in this paper the authors have developed a simple @xmath3-matrix parametrization that gives , in an energy range of about 100 mev each side of the @xmath8 threshold , a good fit to @xmath4 , @xmath138 and @xmath7 data . in addition , it has the same trends as the @xmath6 data , which at present is not unique over this energy range . however , this consistent fit should not be considered an end in itself , since it also results in predictions for the @xmath139 @xmath42-wave amplitude . near the @xmath8 threshold this amplitude has been parametrized in the form of the effective range expansion the resultant parameters being given in table [ table3 ] . since this expansion is good over a wide energy range each side of the @xmath8 threshold , it is very useful for discussions concerning the possibility of @xmath8-nucleus quasi - bound states e.g. in ref . @xcite the effective range expansion of ref . @xcite was used to study the production of @xmath8-nuclei , while ref . @xcite uses such an expansion to describe @xmath8-nucleus final state interactions . the indications from table [ table3 ] are that the @xmath140 scattering length is now larger than that extracted in ref . this is even more favourable for the existence of @xmath8-nucleus quasi - bound states and may lead to an early onset of nuclear p - wave states , which are easier to detect in the darmstadt experiment outlined in ref . @xcite . one result of the above fits is the extraction of the photon - nucleon-@xmath141(1535 ) coupling constant @xmath142 as indicated in table 1 , which is equivalent to the partial decay width @xmath143 for @xmath144 . the definition of @xmath143 is not unique , however . below , this question is elucidated on a simple soluble model of the @xmath22 matrix . this model is also used to understand the interference of a resonant interaction described by a singularity in the @xmath3 matrix and potential interactions described by the background parameters @xmath145 . let us , assume a separable @xmath3 matrix model with @xmath146 where , in the notation of eqs . [ ks ] and [ ketagamma ] , @xmath147 . this leads to a separable solution for the @xmath22-matrix @xmath148 } .\ ] ] when the background term @xmath145 vanishes , this model is equivalent to simple breit - wigner multichannel resonances of eigen - width @xmath149 . however , when we relax this restriction a new structure is built upon the resonance . it is determined by the energy dependent term @xmath150,$ ] which generates a zero of the cross section at @xmath151 . now , it is the @xmath152 that sets a new energy scale , which may be independent of the scale given by the width . for a large @xmath145 one finds the resonance to be accompanied by a nearby zero , whereas for small @xmath153 this zero is moved away beyond the resonance width . the resonance shape is thus very different from the lorentian : one reason being the strong energy dependence in @xmath154 and another being the pole - background interference . as discussed above in connection with table [ table2 ] , it is usually natural to define the partial width of a resonance on the basis of eqs . [ sepk ] and [ sept ] as @xmath155 . for the best fits to the data ( sets @xmath156 of table 1 ) this equation produces @xmath157 mev and @xmath158 mev respectively . however , with complicated phenomenological @xmath22 matrices one could define @xmath159 otherwise , e.g. by moulding @xmath22 into the breit - wigner form in the proximity of @xmath160 . thus , at @xmath161 one has @xmath162 . inserting from table [ table2 ] the values of @xmath163 and @xmath164 gives another estimate of @xmath165 . for example , with case @xmath166 , @xmath167 at @xmath168 mev giving @xmath169 and @xmath170 @xmath117 . this results in @xmath171 mev . similarly , @xmath172 at @xmath173 mev giving @xmath174 and @xmath175 @xmath117 . this results in @xmath176 mev . the proximity of these three widths reflects the fact that the realistic situation is fairly close to the separability situation described by eqs . [ sepk ] and [ sept ] . it is found to hold approximately , for all the parameter sets in table 1 . there is another , somewhat unexpected effect of the @xmath150 $ ] interference term in eq . [ sept ] . for @xmath177 one finds that the amplitudes below the resonance are enhanced , and the amplitudes above the resonance are reduced with respect to the pure resonance term . this effect is seen clearly for the @xmath145 and @xmath178 parameter sets , where below the resonance the @xmath179 parameter in the @xmath16 channel is the largest and the real parts of the @xmath16 scattering lengths given in table [ table3 ] are also the largest . on the other hand the @xmath180 production cross section , dominated by the final state @xmath16 interactions , become the smallest above the resonance as seen fig . 4 . one consequence of this effect is that an extension of the @xmath180 cross section measurements to energies above the @xmath9 resonance may by instrumental in fixing more precisely the @xmath16 scattering length . as indicated in the introduction , the real part of this scattering length is crucial in the determination of quasibound states in @xmath8few nucleon systems . on the experimental side there are several groups @xcite,@xcite studying the @xmath7 reaction in or near this interesting energy range . the observation of the cross section near and above @xmath92=1540mev would be of great interest enabling a detailed study to be made of the @xmath9 and possibly leading to a better understanding of the internal structure of this object . at present there is no definite conclusion as to whether or not this resonance structure is due to a pole in the @xmath3-matrix , as advocated here , or arising through coupling to high lying closed channels - see ref . @xcite . in the near future , the authors of ref . @xcite are expected to extract , directly from experiment , separate values for the real and imaginary components of @xmath181 . these will be analogous to the @xmath10 data already available in ref . @xcite and used in the above fits . such a development will then enable the present type of @xmath3-matrix analysis to be even more constrained . one of the authors ( s.w . ) wishes to acknowledge the hospitality of the research institute for theoretical physics , helsinki , where part of this work was carried out . in addition he was partially supported by grant no kbn 2p03b 016 15 . the authors also thank drs . r. arndt and b. krusche for useful correspondence and members of the graal collaboration for useful discussions . this line of research involving @xmath8-mesons is partially supported by the academy of finland . a. m. green and s. wycech , phys . c*55 * , r2167 ( 1997 ) m.l . goldberger and k.m . watson , _ collision theory _ ( wiley , new york london , 1964 ) r.arndt , j.m.ford and l.d.roper , phys.rev . d*32 * , 1085 ( 1985 ) . . the optimised parameters from minuit defining the @xmath3-matrices : there are in column a only 32 @xmath6 data points with @xmath185 mev and error bars all 1.41 , in column b 48 data points with @xmath186 mev and error bars all 1.41 . cases d and c are the same as a and b except that the error bars are reduced to 0.70 . in addition , the first column shows the results from ref . @xcite and the last column the corresponding values from the particle data group @xcite . [ cols="^,^,^,^,^,^,^",options="header " , ] figure 5 . the a ) real and b ) imaginary parts of @xmath26 . the solid curve is the exact value as given by the model . the dotted curve uses expansions of @xmath126 and @xmath127 , whereas the dashed curve uses those for @xmath123 and @xmath187 .

the coupled @xmath0 , @xmath1 , @xmath2 systems are described by a @xmath3-matrix method . the parameters in this model epsf 2ex = hip 1999 21 / th + a.m. green@xmath13 , and s. wycech@xmath13 + @xmath14department of physics and helsinki institute of physics , p.o . box 9 , + fin00014 university of helsinki , finland + @xmath15soltan institute for nuclear studies , warsaw , poland pacs numbers : 13.75.-n , 25.80.-e , 25.40.v

the coupled @xmath0 , @xmath1 , @xmath2 systems are described by a @xmath3-matrix method . the parameters in this model are adjusted to get an optimal fit to @xmath4 , @xmath5 , @xmath6 and @xmath7 data in an energy range of about 100 mev each side of the @xmath8 threshold . + the coupling of photons to the @xmath9 state is extracted and also an alternative to the current @xmath10 amplitudes suggested . expansions are given for the @xmath11 and @xmath12 amplitudes in terms of the @xmath8 momentum . effects of interference of this state with background potential interactions are discussed and experimental consequences are indicated . epsf 2ex = hip 1999 21 / th + a.m. green@xmath13 , and s. wycech@xmath13 + @xmath14department of physics and helsinki institute of physics , p.o . box 9 , + fin00014 university of helsinki , finland + @xmath15soltan institute for nuclear studies , warsaw , poland pacs numbers : 13.75.-n , 25.80.-e , 25.40.v

0907.0294

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the diffuse @xmath0-ray emission , both galactic and extragalactic , is of significant interest for astrophysics , particle physics , and cosmology . the diffuse galactic emission ( dge ) is produced by interactions of crs , mainly protons and electrons , with the interstellar gas ( via @xmath3-production and bremsstrahlung ) and radiation field ( via inverse compton [ ic ] scattering ) . it is a direct probe of cr fluxes in distant locations , and may contain signatures of physics beyond the standard model , such as dark matter annihilation or decay . the dge is a foreground for point - source detection and hence influences the determination of their positions and fluxes . it is also a foreground for the much fainter extragalactic component , which is the sum of contributions from unresolved sources and truly diffuse emission , including any signatures of large scale structure formation , emission produced by ultra - high - energy crs interacting with relic photons , and many other processes ( e.g. , @xcite and references therein ) . therefore , understanding the dge is a necessary first step in all such studies . the excess diffuse emission @xmath1 gev in the egret data @xcite relative to that expected from dge models consistent with the directly measured cr nucleon and electron spectra @xcite led to the proposal that this emission was the long - awaited signature of dark matter annihilation @xcite . more conventional interpretations included variations of cr spectra in the galaxy @xcite , contributions by unresolved point sources @xcite , and instrumental effects @xcite . a model of the dge depends on the cr spectra throughout the galaxy as well as the distribution of the target gas and interstellar radiation field ( isrf ) . starting from the distribution of cr sources and particle injection spectra , the distribution of crs throughout the galaxy is determined taking into account relevant energy losses and gains , then the cr distributions are folded with the target distributions to calculate the dge @xcite . defining the inputs and calculating the models are not trivial tasks and involve analysis of data from a broad range of astronomical and astroparticle instruments @xcite . the _ fermi _ lat was launched on june 11 , 2008 . it is over an order of magnitude more sensitive than its predecessor , egret , with a more stable response due to the lack of consumables . the lat data permit more detailed studies of the dge than have been possible ever before . in this paper , analysis and results for the dge are shown for the galactic mid - latitude range @xmath2 measured by the lat in the first 5 months of the science phase of the mission . this region was chosen for initial study since it maximises the fraction of signal from dge produced within several kpc of the sun and hence uncertainties associated with cr propagation , knowledge of the gas distribution , etc . , should be minimised . at lower galactic latitudes the large - scale dge is dominant while the emission at higher latitudes is more affected by contamination from charged particles misclassified as photons and uncertainties in the model used to estimate the dge . further details of the present analysis are given in @xcite

the diffuse galactic @xmath0-ray emission is produced by cosmic rays ( crs ) interacting with the interstellar gas and radiation field . measurements by the energetic gamma - ray experiment telescope ( egret ) instrument on the _ compton gamma - ray observatory ( cgro ) _ indicated excess @xmath0-ray emission @xmath1 gev relative to diffuse galactic @xmath0-ray emission models consistent with directly measured cr spectra ( the so - called `` egret gev excess '' ) . the excess emission was observed in all directions on the sky , and a variety of explanations have been proposed , including beyond - the - standard - model scenarios like annihilating or decaying dark matter . the large area telescope ( lat ) instrument on the _ fermi _ gamma - ray space telescope has measured the diffuse @xmath0-ray emission with unprecedented sensitivity and resolution . we report on lat measurements of the diffuse @xmath0-ray emission for energies 100 mev to 10 gev and galactic latitudes @xmath2 . the lat spectrum for this region of the sky is well reproduced by the diffuse galactic @xmath0-ray emission models mentioned above and inconsistent with the egret gev excess .

the diffuse galactic @xmath0-ray emission is produced by cosmic rays ( crs ) interacting with the interstellar gas and radiation field . measurements by the energetic gamma - ray experiment telescope ( egret ) instrument on the _ compton gamma - ray observatory ( cgro ) _ indicated excess @xmath0-ray emission @xmath1 gev relative to diffuse galactic @xmath0-ray emission models consistent with directly measured cr spectra ( the so - called `` egret gev excess '' ) . the excess emission was observed in all directions on the sky , and a variety of explanations have been proposed , including beyond - the - standard - model scenarios like annihilating or decaying dark matter . the large area telescope ( lat ) instrument on the _ fermi _ gamma - ray space telescope has measured the diffuse @xmath0-ray emission with unprecedented sensitivity and resolution . we report on lat measurements of the diffuse @xmath0-ray emission for energies 100 mev to 10 gev and galactic latitudes @xmath2 . the lat spectrum for this region of the sky is well reproduced by the diffuse galactic @xmath0-ray emission models mentioned above and inconsistent with the egret gev excess . gamma rays , cosmic rays , fermi gamma - ray space telescope

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up to one percent of the mass of the interstellar cloud surrounding the heliosphere is carried by dust grains that interact with the heliosphere @xcite . the flow of interstellar material past the sun at 26.4 drives large interstellar dust grains into the heliosphere , while small grains are diverted around the heliosphere by the interstellar magnetic field ( ismf ) . the heliospheric trajectories of intermediate sized grains can be complicated and depend on the solar wind magnetic field and thus solar cycle phase . observations of isdgs in the solar system by the ulysses , galileo and cassini spacecraft show that the density of smallest grains are deficient in the inner heliosphere when compared to the nominal mathis et al . `` mrn '' power law size distribution ( e.g. * ? ? ? * ; * ? ? ? for instance , the density of grains of mass @xmath0 g ( @xmath1 ) is reduced in the inner heliosphere by a factor of @xmath2 below the mrn predictions and @xmath3 g ( @xmath4 ) grains are deficient by three orders of magnitude . at the same time large ( @xmath5 ) grains are absent from the mrn distribution , but are abundant in the inflowing isdgs . while several alternative grain size distribution models exist ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , the constraints of staying within the limits of cosmic abundances and explaining the interstellar extinction curve lead in all cases to the presence in the models of small grains that are absent from the observed distribution and a cutoff on the large grain size end that is below that of the observed distribution . the deficiencies of small grains may result from small grains being deflected around the heliosphere because their high charge - to - mass ratios cause them to couple tightly to the ismf . on the other hand , the circumheliospheric interstellar medium ( chism ) may simply be deficient in small grains ( balancing the overabundance of large grains ) . to evaluate which is the case requires calculations of the grain distribution as a function of grain size in the context of realistic heliosphere models . with recent data on the shape of the heliosphere from the crossing of the termination shock ( ts ) by voyagers 1 and 2 @xcite , and on the deflection of inflowing interstellar h@xmath6 relative to he@xmath6 @xcite , such models face tighter constraints than ever before . the inferred asymmetry of the heliosphere can be explained by the orientation of the ismf relative to the direction of the cloud - sun relative motion . the ismf required to fit the heliosphere data , in turn , has direct implications for isdg trajectories . in this paper we present new calculations of grain trajectories and density distributions for small grains that are primarily excluded from the inner heliosphere . small grains experience enhanced charging rates due to the ejection of secondary electrons in the hot @xmath7 k plasma between the termination shock and heliopause @xcite . we calculate grain trajectories in 3-d , based on a self - consistent steady state mhd - kinetic heliosphere model with grain charge calculated at each location along the path according to the plasma conditions and radiation field . ( we note that the recent voyager 2 results @xcite on the lower than expected plasma temperature in the inner heliosheath are not incorporated in the heliosphere model we use . we expect that this could result in somewhat lower dust charging in this region than we calculated , though the detailed effects of charging by thermal particles vs. puis has yet to be fully explored . ) the model of plasma density and magnetic field in the heliosphere at each point of space properly accounts for the asymmetries that result from the angle between the ismf and interstellar gas / dust inflow direction , and ismf and ecliptic plane @xcite . when combined with recent models of grain charging @xcite and a realistic ultraviolet ( uv ) radiation field , the lorentz force at each point in space can be used to calculate the grain trajectory . total 3-d grain densities are then calculated for a sample of interstellar grain sizes based on the total gas - to - dust mass ratio in the chism and isdg models . many previous calculations have been made of grain interactions with the heliosphere ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) but ours is the first to use a realistic heliosphere model , including distortion due to an ismf orientation that is consistent with recent observational data .

the distribution of interstellar dust grains ( isdg ) observed in the solar system depends on the nature of the interstellar medium - solar wind interaction . the charge of the grains couples them to the interstellar magnetic field ( ismf ) resulting in some fraction of grains being excluded from the heliosphere while grains on the larger end of the size distribution , with gyroradii comparable to the size of the heliosphere , penetrate the termination shock . this results in a skewing the size distribution detected in the solar system . we present new calculations of grain trajectories and the resultant grain density distribution for small isdgs propagating through the heliosphere . we make use of detailed heliosphere model results , using three - dimensional ( 3-d ) magnetohydrodynamic / kinetic models designed to match data on the shape of the termination shock and the relative deflection of interstellar and flowing into the heliosphere . we find that the necessary inclination of the ismf relative to the inflow direction results in an asymmetry in the distribution of the larger grains ( 0.1 ) that penetrate the heliopause . smaller grains ( 0.01 ) are completely excluded from the solar system at the heliopause . address = harvard - smithsonian center for astrophysics , 60 garden st . , cambridge , ma 02138 ( usa ) address = dept . astronomy & astrophysics , u. chicago , 5640 s. ellis ave . , chicago , il 60637 ( usa ) address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899 address = dept . of physics and astronomy , 6127 wilder lab , dartmouth college , hanover , nh 03755 address = infrared processing and analysis center , caltech , pasadena , ca 91125 address = u .

the distribution of interstellar dust grains ( isdg ) observed in the solar system depends on the nature of the interstellar medium - solar wind interaction . the charge of the grains couples them to the interstellar magnetic field ( ismf ) resulting in some fraction of grains being excluded from the heliosphere while grains on the larger end of the size distribution , with gyroradii comparable to the size of the heliosphere , penetrate the termination shock . this results in a skewing the size distribution detected in the solar system . we present new calculations of grain trajectories and the resultant grain density distribution for small isdgs propagating through the heliosphere . we make use of detailed heliosphere model results , using three - dimensional ( 3-d ) magnetohydrodynamic / kinetic models designed to match data on the shape of the termination shock and the relative deflection of interstellar and flowing into the heliosphere . we find that the necessary inclination of the ismf relative to the inflow direction results in an asymmetry in the distribution of the larger grains ( 0.1 ) that penetrate the heliopause . smaller grains ( 0.01 ) are completely excluded from the solar system at the heliopause . address = harvard - smithsonian center for astrophysics , 60 garden st . , cambridge , ma 02138 ( usa ) address = dept . astronomy & astrophysics , u. chicago , 5640 s. ellis ave . , chicago , il 60637 ( usa ) address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899 address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899 address = dept . of physics and astronomy , 6127 wilder lab , dartmouth college , hanover , nh 03755 address = infrared processing and analysis center , caltech , pasadena , ca 91125 address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899 address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899 address = u . alabama - huntsville , center for space plasma and aeronomic research , huntsville , al 35899

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implementing relativity in the description of form factors of few - body systems is an important task nowadays . motivated for some part by experiments performed at high @xmath2 at different facilities , especially jlab , this ingredient is required for correctly analyzing the measurements . many approaches have been proposed , ranging from field - theory based to relativistic - quantum mechanics ones @xcite , implying sometimes seemingly founded approximations . a full realistic calculation is difficult and since the calculation of the deuteron form factors by tjon and zuilhof @xcite , there are not so many calculations that have reached the same level of correctness and , simultaneously , of complexity . full calculations can also be performed in other cases @xcite , employing solutions of the bethe - salpeter equation @xcite with a zero - mass boson ( wick - cutkosky model @xcite ) or an infinite one ( feynman triangle diagram ) . they are somewhat academic but turn out to be quite useful as a testing ground of the approximate treatment of relativity in many studies . there are currently many recipes aiming to implement relativity in the description of some system with a reduced amount of effort . they imply for instance minimal relativity factors , @xmath3 , or relativistic energies in place of non - relativistic ones . when considering elastic form factors , that are of main interest here , one also has to deal with boosting appropriately the final state with respect to the initial one . here too , one has looked for simple recipes . in the case of spin - less particles , the first effect one thinks of is the lorentz - contraction . to account for it , it was proposed to make the following replacement in the non - relativistic calculation @xcite @xmath4 ) , \label{11a}\ ] ] where m is the total mass of the system under consideration . this relation , that is still being used @xcite , can be recovered somewhat easily ( it is obtained by a simple change of variable ) . perhaps for this reason , it was believed to represent a realistic way to implement an important feature of relativity ( see some discussion in ref . however , it was realized later on that this prescription leads to constant form factors at high @xmath2 , in disagreement with what is expected from the consideration of the born amplitude . this one underlies predictions of power law behavior of form factors at large @xmath2 ( @xmath5 and @xmath6 for the pion and nucleon form factors in qcd , respectively @xcite , or @xmath6 for the ground state of a system of scalar particles exchanging a scalar boson , as considered in this work @xcite ) . on the other hand , glckle and hamme @xcite ( see also @xcite ) analyzed solutions obtained from some hamiltonian for a similar system . they found support for the lorentz contraction but could not conclude whether the deviations were due to the approximate nature of their hamiltonian . quite recently , another way to implement relativity in the calculation of form factors was proposed by klink @xcite . supposed to be based on the point - form approach , it essentially relies on kinematical boost transformations . it has been applied for calculating form factors of the deuteron @xcite , the nucleon @xcite , a two - body system composed of scalar particles exchanging a zero - mass boson @xcite and a system corresponding to a zero - range interaction @xcite . in the first case , there is no significant improvement with respect to a non - relativistic calculation . in the second case , the agreement is at first sight spectacular , especially at the lowest @xmath2 range considered by the authors . however , one can guess a tendency to an increasing under - prediction of the measurements in the highest range . in the third and fourth cases , there is no experiment but comparison is possible with what can be considered as an `` exact '' calculation as far as relativity is concerned . corrections originating from the field - theory character of the underlying model , such as constituent form factors @xcite , cancel out in the comparison while they should be accounted for in the nucleon case mentioned above . in the last two cases , an important discrepancy shows up , especially in the limit of a zero - mass system or at large @xmath2 , which a relativistic approach should deal with . two features emerge from these form factors when compared to `` exact '' calculations ( as well as non - relativistic ones ) : point - form results evidence an increased charge radius and a rapid fall - off , faster than expected from the born - amplitude . in the present paper , we want to see in particular whether the peculiar features evidenced by recent calculations of form factors are specific to the point - form approach or characterize also other forms of relativistic quantum mechanics , such as the instant- and front - form . in this order , one can start from some mass operator , which enters in the construction of the generators of the poincar group @xcite . however , this does not indicate the connection between the dynamical variables entering this construction and the experimentally physical quantities @xcite . to establish this connection , a physical model has to be considered , while the underlying field - theory could provide an `` exact''calculation of form factors , somewhat playing the role of a measurement . thus , the interaction entering the mass operator should fulfill two different constraints . besides those required to construct the generators of the poincar group , we demand that the interaction allows one to recover the field - theory one in the small coupling limit . this is the least that we can ask . steps of the above program can be found in the literature @xcite ( see also for instance refs . @xcite in a slightly different context ) . for our purpose , we give some of them here , both for comprehensiveness and definiteness . as we want to know how an approach different from the point - form one does in comparison to an `` exact '' calculation , we will specialize in this work on the instant - form approach . while doing so , we give a particular attention to the change of variable which allows one to express the momenta of two particles , let s say @xmath7 and @xmath8 for a two - body system , in terms of the total momentum , @xmath9 , and an internal variable , @xmath10 , which enters the mass operator . this relation , represented by a unitary transformation @xcite , is nothing but the one introduced by bakamjian and thomas @xcite . it is essential for determining how a wave function obtained from some mass operator transforms when the system under consideration is boosted . the condition that the mass spectrum be independent of the momentum of the system is found to provide the standard constraints on the mass operator , from which the bakamjian - thomas construction of the generators of the poincar group immediately follows @xcite . the mass operator so obtained can then be used for the front- or point - form approaches @xcite . when available , we will give results of what can be considered an `` exact '' calculation ( wick - cutkosky model , feynman triangle diagram ) , the corresponding physics being supposed to be accounted for by the different approaches listed above . due to the difficulty to fully account for this physics in the finite - mass boson case ( the bound - state spectrum is not reproduced by the interaction model used to calculate the wave function employed in our study , and current conservation is not necessarily fulfilled ) , we will also present results obtained with a tentatively improved interaction . the comparison of the results will allow one to get some insight into the uncertainty due to the approximate description of the interaction . this aspect is in any case difficult to assess in quantum mechanics approaches which have to account effectively , in one way or another , for the field - theory character of the original model . concerns have been expressed about comparing approaches as different as field - theory and relativistic quantum mechanics , which correspond to problems with an indefinite and a fixed number of particles . we believe that this is what should be done if one wants to check the reliability of some relativistic quantum mechanics approach . when predictions of these approaches are compared to a measurement , they imply the underlying physics , qed , some meson theory or qcd . in all cases , this physics is field - theory based . we could also notice that comparisons similar to the present one have started long ago . coester and ostebee , for instance , noticed some agreement of their instant - form calculation for the deuteron form factor at low @xmath2 @xcite with a field - theory one by gross @xcite . finally , we stress that the two approaches we are using are developed independently . there is no attempt to make some reduction of the bethe - salpeter equation , which is sometimes done . as noticed for instance by lev ( see introduction of ref . @xcite ) , the description of a bound system in relativistic quantum mechanics represents an approximation to the one based on the bethe - salpeter equation but it offers the advantage that it preserves the covariance while the above reduction generally does not . when comparing form factors calculated from different relativistic quantum mechanics approaches , we have in mind that , ultimately , they should coincide , in agreement with the idea that these approaches are equivalent , up to a unitary transformation @xcite . the first step concerns the mass operator , already mentioned , whose solutions can be used in any scheme , only with different transformation properties when going from the variables , @xmath11 , to @xmath12 . the second step concerns the current which consists of a one - body part and , for a two - body system , a two - body one , which is interaction dependent . the contribution of this second part , when added to the former , should ensure the expected equivalence of the various relativistic quantum mechanics approaches . in this work , we will concentrate on the contribution of the single - particle current , most often retained in usual calculations of form factors . as significant differences appear at this level , making it difficult to realize the above unitary equivalence , we will give a particular attention to everything that can cast light on how these differences occur and manifest themselves . concerning the observables , we will consider charge and scalar form factors stemming from the coupling to lorentz - vector and lorentz - scalar probes , respectively . we are still interested in the ground state of a system composed of scalar particles interacting via the exchange of a scalar boson . results , obtained for instant- but also front- , and point - form approaches , will be compared to what could be considered as an `` exact '' calculation . as it is a current practice to compare relativistic calculations to non - relativistic ones , we also include in our study results obtained by applying a galilean boost . the corresponding wave functions are obtained from an effective , theoretically - motivated interaction which does well for the spectrum @xcite and allows for a conserved current . the comparison of the different results for charge and scalar form factors will also evidence other features that are not related to the boost itself but are more or less related to standard exchange currents . these two - body currents , which are required , among other things , to fulfill covariance , will be evoked at many places in the paper but will not be the object of a systematic study . some insight on their contribution will be obtained by looking at the form factors calculated in a frame different from the breit one . as already mentioned , comparison of form factors obtained in the instant form of relativistic quantum mechanics , on which some emphasis is put here , and those obtained in a field - theory framework have already been done in the past @xcite . the system under consideration in the present work will not be as realistic as the one looked at in this earlier work . instead , we consider situations where relativity is expected to play an essential role such as large momentum transfers or strongly bound systems , partly in relation with lorentz - contraction effects . accordingly , we do not make any @xmath13 approximation in dealing with the boost transformation . the plan of the paper is as follows . in the second section , we concentrate on the interaction and its reduction to an invariant mass operator . this interaction allows one to establish some relation with field - theory in the weak coupling limit and is used for the determination of wave functions required for the calculation of form factors . this is done within the instant - form approach while the relation to the work by bakamjian and thomas is emphasized . the third section is devoted to the expression of the form factors we are calculating in different forms of relativistic quantum mechanics . results up to @xmath1 are presented in the fourth section . they concern the scalar and charge form factors of the ground state of the system under consideration . three masses of the exchanged boson , @xmath14 ( wick - cutkosky model ) , @xmath15 and @xmath16 are considered , as well as two masses for the system , @xmath17 , which implies a moderately bound system , and @xmath18 , which is an extreme case that a relativistic approach should in principle be able to deal with . the fifth section contains a discussion and the conclusion .

the effect of different boost expressions is considered for the calculation of the ground - state form factor of a two - body system made of scalar particles interacting via the exchange of a scalar boson . strongly bound systems are considered with masses of the exchanged boson taken as zero , 0.15 times the constituent mass @xmath0 , and infinity . in the first and last cases , a comparison with `` exact '' calculations is made ( wick - cutkosky model and feynman triangle diagram ) . momentum transfers up to @xmath1 are considered . emphasis is put on the contribution of the single - particle current , as usually done .

the effect of different boost expressions is considered for the calculation of the ground - state form factor of a two - body system made of scalar particles interacting via the exchange of a scalar boson . the aim is to provide an uncertainty range on methods employed in implementing these effects as well as an insight on their relevance when an `` exact '' calculation is possible . using a wave function corresponding to a mass operator that has the appropriate properties to construct the generators of the poincar algebra in the framework of relativistic quantum mechanics , form factors are calculated using the boost transformations pertinent to the instant , front and point forms of this approach . moderately and strongly bound systems are considered with masses of the exchanged boson taken as zero , 0.15 times the constituent mass @xmath0 , and infinity . in the first and last cases , a comparison with `` exact '' calculations is made ( wick - cutkosky model and feynman triangle diagram ) . results with a galilean boost are also given . momentum transfers up to @xmath1 are considered . emphasis is put on the contribution of the single - particle current , as usually done . it is found that the present point - form calculations of form factors strongly deviate from all the other ones , requiring large contributions from two - body currents . different implementations of the point - form approach , where the role of these two - body currents would be less important , are sketched . , , relativity , two - body systems , form factors 11.10.qr , 21.45.+v , 13.40.fn

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in this work , we have studied the sensitivity of form factors of a two - body system to various ways of implementing boost effects . the emphasis has been put on the instant form of relativistic quantum mechanics but , as is well known , the corresponding mass operator can be employed for front and point forms of this framework . since we wanted to make some relation with a field - theory model , we proceeded in a way that perhaps differs from other ones . we nevertheless recovered all the ingredients that allowed bakamjian and thomas to construct the generators of the poincar group . the system under consideration consists of two scalar particles interacting by the exchange of another scalar one . only the ground state has been considered . we looked at different values of the exchanged boson mass , @xmath247 . in the first and last cases , results that can be considered as `` exact '' ones are presented . results obtained by applying a galilean boost are also given . dealing with degrees of freedom that have necessarily an effective character , there are uncertainties . the first one has to do with the one- and the two - body parts of the current in relativistic quantum mechanics approaches . in all cases , we required that the same one - body current be recovered in the small coupling limit . beyond , for strongly bound systems , it appeared that the electromagnetic current should incorporate improvements to remove an undesirable feature relative to the ratio of the scalar and charge form factors . this correction , which is part of the developments that should be accounted for in the future , has been done in the same way for the instant- and point - form approaches ( the standard front - form results are unaffected by this change ) . it offers other advantages that let us think that it is a necessary ingredient in the description of the current . another correction has been introduced for the scalar current in the instant form but its role is a minor one . the second uncertainty has to do with the effective interaction when an `` exact '' calculation is available . this concerns the zero - mass case , the infinite mass case being insensitive to the interaction itself once the mass of the system is given . within the above uncertainties , most approaches agree with each other and sometimes produce the same results . in the range of @xmath2 considered here , @xmath248 , the discrepancy between the instant- or front - form results and the `` exact '' ones does not exceed a factor 2 . from earlier studies , it is reasonable to attribute this discrepancy to the interaction model . this one is too simple to account for the full mass spectrum of the `` exact '' calculation . amazingly , a non - relativistic approach , mainly characterized by a galilean boost , is not bad in a regime of large binding energies or large @xmath2 , which is highly relativistic . only the form factors in the point form depart from the other results , confirming what has been obtained elsewhere with different inputs @xcite . two main features should be emphasized : * the form factors at high @xmath2 have most often the wrong power law behavior , missing the expected born amplitude . * the charge or scalar radii tend to infinity when the total mass of the system tends to zero while all the other approaches lead to a finite value . it is noticed that the choice of the form of the single - particle current has little influence on the discrepancy ( a factor 2 at most ) as if minimal ( essentially kinematical ) consistency requirements in the different approaches were fixing this part . the discrepancy therefore points out to the way the boost is incorporated in the wave functions , which is more sensitive to the dynamics . in this respect , one notices that the corresponding expressions entering the form factors involve at many places the product of the momentum transfer , @xmath249 , and a quantity @xmath250 . this last factor , which is larger than one , leads to an enhanced effective momentum transfer , largely explaining the two features emphasized above . it is absent in all the other approaches @xcite . despite uncertainties , there is a cumulative evidence that the form factors in the point form differ from all the other ones when calculated from a single particle current . evidently , this problem can be solved by including two - body currents @xcite . these ones should also be present in the other approaches but it is clear that their role in the point - form calculations is more essential . in this case , one has to correct for orders of magnitude while , in the other ones , one expects contributions of the same size as the single - particle current . in view of such a large discrepancy , one can however wonder whether the implementation of the point - form approach for the calculation of the single - particle current itself is the most convenient one . in this respect , it is reminded that the total momentum operator for a two - body system in the point - form approach may be written as : @xmath251 where @xmath252 represents the interaction part . in the implementation of the point - form used until now , this term assumes a form proportional to the 4-velocity of the system ( @xmath150 in our notations ) . this is the simplest choice one can think of . it is not unique however and one can therefore wonder whether other choices could minimize the problem raised by present results . in the original work by dirac , the point - form approach is described on a hyperbolod , @xmath253 . some studies along these lines have been made @xcite but they did not go quite far , due perhaps to the related nonlinear constraint between the coordinates , @xmath254 and @xmath255 . in practice , recent applications of the point - form approach @xcite rely on employing wave functions issued from a mass operator whose solutions can also be identified with instant - form ones in the center of mass system . these last solutions are characterized by the description of the dynamics on a hyper - plane , @xmath256 , with @xmath257 . as noticed by sokolov @xcite , this point - form approach is not identical to the one proposed by dirac . while the surface , @xmath253 , is invariant under a lorentz transformation , the surface , @xmath256 , is not . it is our opinion that the replacement of the former surface by the latter , which may be roughly appropriate for an isolated system , is not adequate for a process like elastic scattering , which requires two systems with different momenta , @xmath258 and @xmath259 . indeed , when the system at rest described on the hyper - plane , @xmath260 , is kinematically boosted to get initial and final states with four - momenta , @xmath258 and @xmath259 , these ones appear as described ( quantized ) on different surfaces , @xmath261 and @xmath262 , where @xmath263 with @xmath264 . this feature results from the identification of point- and instant - form wave functions in the center of mass . it does not correspond to the usual description of a process which , generally , relies on the same definition of the surface at all steps . as a measure of the difficulties , it is remarked that time has not the same meaning for an observer related to the initial or the final state , preventing one from defining time - ordered diagrams . actually , a large part of the difficulty for implementing relativity in quantum mechanics approaches is precisely to determine how to appropriately boost a system while keeping this constraint . it is also noticed that a system at rest could be described as well on hyper - planes , @xmath25 , with @xmath265 @xcite and there is no compelling argument for choosing the particular hyper - plane , @xmath256 , except perhaps for simplicity . as is well known , changing the hyper - plane implies the dynamics but the problem is not much more complicated than determining the relation between wave functions for different @xmath9 in the instant - form approach , which we presented in sec . 2 . as a complementary remark , we would like to stress that the kinematical boost retained in the point - form approach appears practically as an approximation to the instant - form boost . the latter one , as can be seen in eq . ( [ 20e3 ] ) , also contains an interaction - dependent term whose role is essential for the derivation of an invariant mass operator within the instant - form approach , as well as for reproducing the exact form factors in some cases . examining the transformation , it is noticed that this second term depends on the total momentum , preventing one to split the instant - form boost operation into independent kinematical and dynamical parts . in the point - form approach however , there is the possibility that this was feasible . one could imagine for instance that the wave function in terms of the physical momenta of the constituent particles , @xmath7 and @xmath8 , is related to the center of mass one by a kinematical boost but that the relation of this last one to the solution of the mass operator , given in terms of the total momentum @xmath9 and the internal variable @xmath10 , involves the dynamics . with this respect , it is noticed that the condition for the momenta , @xmath266 , is consistent with the instant form , due to the kinematical character of the momentum , but there is no reason that this holds in other forms where the momentum has , partly or totally , a dynamical character , as can be seen in eq . ( [ 20ba ] ) . the introduction of the dynamics as suggested above would greatly contribute to reduce the qualitative gap between the point - form approach used here , where the boost transformation is insensitive to the dynamics , and the other forms . this would also be more consistent with the existence of a unitary transformation between the different forms @xcite . while some conditions for applying the point - form approach , such as the independence of the interaction on the velocity , have been mentioned in the literature , it sounds that the above aspect relative to the nature of the surface , on which the system is described in practice , has been overlooked . the problem concerns less the construction of the generators of the poincar algebra in terms of the total momentum @xmath9 and the internal variable than the relation of this set of variables to the physical ones . in view of the previous discussion , we believe that some improvement can be introduced , at the expense of making calculations more complicated than they were until now , but not much more than some of the instant - form calculations presented in this work . the idea is to start with states at rest described on two different surfaces , @xmath267 and @xmath268 , in such a way that these ones coincide with a unique one , @xmath25 , after a boost is performed for getting states with the appropriate momenta . providing a better account of the relative boost of initial and final states , this should be sufficient to remove the main differences between the point - form results and the other ones , which appear at small @xmath22 or large @xmath2 when only the contribution of the single - particle current is considered . in the spirit of the point - form approach possibly described on a hyperbolod , one can go a step further and assume that the four vector , @xmath150 , is not a fixed one , like in the instant - form approach , but is allowed to change like any four - vector so that the surface , @xmath25 , is unchanged when a lorentz transformation is made . in this order , the four - vector @xmath150 has to be chosen as a combination of the four vectors entering the process . an immediate choice , which is consistent with the symmetry of the initial and final states for elastic scattering , is : @xmath269 this choice also guarantees that the divergence of the matrix element of the electromagnetic current is zero . however , it does not imply that the current itself is conserved as it should be . this generally requires considering the contribution of two - body currents . the above choice also allows one to recover the prescription made in previous works for an isolated system , since in this case @xmath270 , which is nothing but the four velocity introduced there . it is straightforward to show that a calculation of form factors as described above would provide results identical to those we obtained in the breit frame in instant - form , as presented in tables [ t10]-[t30 ] . as is seen from these tables , this improved implementation of the point - form approach now compares with the other approaches . while starting from the instant - form , the corresponding results can be made covariant via the replacement of the four - vector , @xmath271 , by @xmath150 , as defined in eq . ( [ 50a ] ) , in all steps of the calculation . the identity with the form factors in the instant form only holds in the breit frame , however . in absence of two - body currents restoring the covariance , these form factors in the instant form will generally be different in another frame . this improved implementation of the point - form approach , like recent ones , is an approximation to the one originally proposed by dirac . it has some of its characteristics but it has certainly limitations that have to be explored . the fact that one recovers results obtained by other approaches is an indication that we are on the good track . on the other hand , different relativistic - quantum mechanics approaches should be equivalent up to a unitary transformation . this was hardly conceivable with the earlier implementation of the point - form approach , where initial and final states appeared as described on different hyper - planes . this difficulty is removed with the approach presented above . present results for various forms of relativistic quantum mechanics suggest that , in our model , there is a problem with the implementation of the point - form one . in this last case , either large contributions of two - body currents are required or the present implementation of the point - form approach for calculating the contribution of the single - particle current has to be significantly improved . this conclusion is free of uncertainties due to spin complications or to intrinsic form factors of the constituents , for instance . under these conditions , one may wonder about the agreement with experiment obtained in @xcite of the nucleon form factors . we notice that the main effect encountered there has the same origin as in the present case . it arises for a large part from an effective enhancement of the momentum transfer by a factor @xmath272 , representing the ratio of the kinetic energies to the total mass . if this effect is the result of an incomplete account of interaction effects , as we believe , other explanations for the nucleon form factors have to be found . actually , it is known for a long time that nucleon form factors in the lowest @xmath2 range can be largely accounted for by the vector - meson dominance phenomenology ( see ref . @xcite for an attempt of a microscopic account of this physics ) . at high @xmath2 , there are indications that the fall off of the magnetic nucleon form factors is too fast as compared to the measurements , quite in agreement with our findings for scalar - particle systems . this points to another fault of these results . in comparison to a non - relativistic calculation , a proper account of relativity is expected to enhance the form factors at high @xmath2 : a non - relativistic approach would predict a @xmath221 fall off ( @xmath273 with semi - relativistic kinetic energy ) while the qcd expectation is @xmath6 . the difference is , in first approximation , due to factors @xmath274 that are replaced by @xmath275 in the non - relativistic case @xcite . the point - form results , as presented here and in other works , go in the other direction . it was found that binding energies calculated from the bethe - salpeter equation in ladder approximation could be understood in a quantum - mechanics scheme with a theoretically motivated , effective interaction going beyond the standard instantaneous approximation @xcite . present results show that form factors calculated from solutions of this equation can be reasonably understood within relativistic quantum mechanics ( we assume that the problem for the point - form approach will be solved according to our proposal or equivalent ones ) . these results strongly suggest that the two approaches can lead to the same predictions , a principle which is not universally accepted . taking this principle for granted , many improvements can be considered and tested . they concern the effective interaction and the structure of the current , in particular in relation with its two - body part . a next step could include the introduction of spin , required for the study of realistic systems , or the extension to three - body systems . for the time being , and despite its partly academic character , we believe that the present work can be useful for improving the implementation of relativity in the description of few - body systems , as for the lorentz - contraction or the asymptotic behavior of form factors , for instance . * acknowledgments * the authors are very grateful to s. noguera for stimulating discussions regarding the role of the hyperbolod surface in the point - form approach . we acknowledge v. sauli for providing some results concerning the calculation of form factors in the case of a finite boson mass , using solutions of the bethe - salpeter equation . this work has been supported by the ec - ihp network esop , under contract hprn - ct-2000 - 00130 .

are calculated using the boost transformations pertinent to the instant , front and point forms of this approach . moderately and results with a galilean boost are also given . different implementations of the point - form approach , where the role of these two - body currents would be less important , are sketched . , , relativity , two - body systems , form factors 11.10.qr , 21.45.+v , 13.40.fn

the effect of different boost expressions is considered for the calculation of the ground - state form factor of a two - body system made of scalar particles interacting via the exchange of a scalar boson . the aim is to provide an uncertainty range on methods employed in implementing these effects as well as an insight on their relevance when an `` exact '' calculation is possible . using a wave function corresponding to a mass operator that has the appropriate properties to construct the generators of the poincar algebra in the framework of relativistic quantum mechanics , form factors are calculated using the boost transformations pertinent to the instant , front and point forms of this approach . moderately and strongly bound systems are considered with masses of the exchanged boson taken as zero , 0.15 times the constituent mass @xmath0 , and infinity . in the first and last cases , a comparison with `` exact '' calculations is made ( wick - cutkosky model and feynman triangle diagram ) . results with a galilean boost are also given . momentum transfers up to @xmath1 are considered . emphasis is put on the contribution of the single - particle current , as usually done . it is found that the present point - form calculations of form factors strongly deviate from all the other ones , requiring large contributions from two - body currents . different implementations of the point - form approach , where the role of these two - body currents would be less important , are sketched . , , relativity , two - body systems , form factors 11.10.qr , 21.45.+v , 13.40.fn

1409.2395

r

point group symmetry ) of different sizes . the first intense peak p1 ( clar s @xmath19 band ) is given by doubly degenerate excitations . the lowest energy dipole - forbidden excitations ( d1 and d2 , @xmath20 and @xmath21 bands , according to clar s notation , see also [ table1 ] ) are indicated in the spectra by solid and dashed arrows , respectively . the spectra are obtained by using a lorentzian broadening of 100 mev . ] the optical absorption spectrum of coronene ( [ fig2 ] , top panel ) is characterized by an intense peak in the near - uv region ( p1 , at 4.26 ev , see [ table1 ] ) and by two low energy dark excitations in the visible band ( d1 and d2 at about 3 and 3.5 ev , respectively ) . the lowest energy excited states of hexagonal pahs , corresponding to transitions between the doubly degenerate frontier orbitals ( see [ fig4]a ) and here labeled as d1 , d2 and p1 , are commonly identified as @xmath20 , @xmath22 ( @xmath21 ) and @xmath19 bands , respectively , according to clar s notation ( see e.g. ref . @xcite and references therein ) . these excitations correspond to symmetry forbidden @xmath23 and @xmath24 states ( d1 and d2 in [ fig2 ] ) , and to a higher energy @xmath25 state , characterized by a twofold degeneracy and by a large oscillator strength ( p1 peak ) . within the ci approach , we find that p1 stems from the combined transitions of doubly degenerate frontier orbitals ( highest occupied mo , homo , and lowest unoccupied mo , lumo , see [ table1 ] ) . also d1 and d2 arise from frontier orbital transitions that combine here with opposite sign , hence giving rise to dipole - forbidden transitions . two additional excitations one of them doubly degenerate appear in the spectrum between d2 and p1 : they are symmetry - forbidden and come from combinations of transitions between the four occupied and unoccupied mos closest to the gap . the features of d1 , d2 and p1 can be clearly captured from the transition density plots in [ fig3 ] . the modulation of the positive and negative domains in d1 and d2 provides evidence of the zero dipole moment associated to them , while p1 is characterized by a remarkable polarity . these results are in agreement with the available experimental data @xcite within about 150 mev , as well as with other predictions obtained within different theoretical approaches @xcite . the lowest energy peak is typically identified in experiments as the strongest absorption peak in the uv / vis region . moreover , as a matter of fact , the lowest dipole - forbidden excitations are also detected in experiments @xcite as associated to vibrational modes @xcite or , in general , with structural deviations from the ideal symmetry , generally adopted in theoretical simulations . . c|c|c|c|c|c molecule & excitation & mo transitions ( weight ) & @xmath26 & energy [ ev ] & os + & & h @xmath27 l+1 ( 0.47 ) & -0.683 & & + & & h-1 @xmath27 l ( 0.47 ) & 0.683 & & + & & h @xmath27 l ( 0.49 ) & -0.700 & & + & & h-1 @xmath27 l+1 ( 0.49 ) & -0.700 & & + & & h @xmath27 l ( 0.48 ) & 0.690 & & + & & h-1 @xmath27 l+1 ( 0.48 ) & -0.690 & & + & & h @xmath27 l+1 ( 0.48 ) & 0.690 & & + & & h-1 @xmath27 l ( 0.48 ) & 0.690 & & + & & h @xmath27 l+1 ( 0.44 ) & -0.665 & & + & & h-1 @xmath27 l ( 0.44 ) & 0.665 & & + & & h @xmath27 l ( 0.47 ) & -0.684 & & + & & h-1 @xmath27 l+1 ( 0.47 ) & -0.684 & & + & & h @xmath27 l ( 0.18 ) & 0.428 & & + & & h @xmath27 l+1 ( 0.26 ) & -0.514 & & + & & h-1 @xmath27 l ( 0.26 ) & -0.514 & & + & & h-1 @xmath27 l+1 ( 0.18 ) & -0.428 & & + & & h @xmath27 l+1 ( 0.26 ) & -0.514 & & + & & h @xmath27 l ( 0.18 ) & -0.428 & & + & & h-1 @xmath27 l ( 0.18 ) & -0.428 & & + & & h-1 @xmath27 l+1 ( 0.26 ) & 0.514 & & + & & h @xmath27 l+1(0.42 ) & 0.649 & & + & & h-1@xmath27 l ( 0.42 ) & -0.649 & & + & & h @xmath27 l ( 0.44 ) & 0.666 & & + & & h-1 @xmath27 l+1 ( 0.44 ) & 0.666 & & + & & h @xmath27 l ( 0.41 ) & 0.638 & & + & & h @xmath27 l+1 ( 0.05 ) & 0.228 & & + & & h-1 @xmath27 l ( 0.05 ) & 0.228 & & + & & h-1 @xmath27 l+1 ( 0.41 ) & -0.638 & & + & & h @xmath27 l+1 ( 0.41 ) & -0.638 & & + & & h @xmath27 l ( 0.05 ) & 0.228 & & + & & h-1 @xmath27 l ( 0.41 ) & -0.638 & & + & & h-1 @xmath27 l+1 ( 0.05 ) & -0.228 & & + & & h @xmath27 l+1 ( 0.40 ) & 0.629 & & + & & h-1 @xmath27 l ( 0.40 ) & -0.629 & & + & & h @xmath27 l ( 0.42 ) & 0.646 & & + & & h-1 @xmath27 l+1 ( 0.42 ) & 0.646 & & + & & h @xmath27 l ( 0.40 ) & 0.635 & & + & & h-1 @xmath27 l+1 ( 0.40 ) & -0.635 & & + & & h @xmath27 l+1 ( 0.40 ) & 0.635 & & + & & h-1 @xmath27 l ( 0.40 ) & 0.635 & & + for this series of hexagonal pahs , [ fig2 ] , from the top to the bottom , indicates that the full optical spectrum , including dark excitations , is red - shifted with increasing size , as expected from the higher delocalization of the relevant molecular orbitals , as recently reported for other pah series @xcite . specifically , p1 is brought from the uv to the visible range ( green ) , while the lowest - energy dark excitations move from the visible ( violet ) to the infrared band . as such , p1 undergoes a larger red shift than d1 and d2 , in comparison with the spectrum of coronene . the lowest energy excitation of hbc ( d1 ) , corresponding to the clar s @xmath20 band , is found in our study at 2.84 ev ( [ table1 ] ) . this value is in excellent agreement with recent experimental results of hbc in gas phase @xcite and in rare gas matrix @xcite : these studies assign the lowest energy excitation of hbc , at 2.86 ev and at 2.85 ev , respectively . in ref . @xcite also the position of the @xmath21 band ( d2 , 3.22 ev , see [ table1 ] ) is reported at 3.30 3.35 ev , depending on the embedding gas matrix . also for this excitation our results compare very well with the experiment within an error of 3@xmath28 . the first active peak of hbc ( p1 ) stems from our calculations at 3.82 ev ( [ table1 ] ) , also in very good agreement with the experimental data at about 3.7 ev ( error of 5@xmath28 ) @xcite . as a consequence of the preserved symmetry , the main optical features in all the examined hexagonal pahs remain unchanged throughout the series ( see [ fig2 ] and [ table1 ] ) . this is further confirmed by the resulting transition densities shown in [ fig3 ] . in fact , the mo s contributing to the excitations are the same in all the structures , as their character is maintained by the molecular symmetry . in the low energy spectral region , between d2 and p1 , only one doubly degenerate excitation appears in the spectra of the larger molecules of this set ( hbc , and ) . as discussed for d1 and d2 , also this dark excitation can be activated when coupled to vibrational modes ( see e.g. ref . @xcite for the case of hbc ) . higher energy excitations than p1 fall beyond the spectral range of interest ( visible and near - uv bands ) for coronene and hbc , while this is not the case for and . as shown in [ fig2 ] , higher energy peaks stem from transitions between deeper occupied and higher unoccupied mos , carrying much weaker intensity than p1 . , of the examined optical excitations of hexagonal pahs ( @xmath0 point group symmetry ) . ] proceeding now with the results for the elongated gnfs , the drastic effect on the electronic and optical properties induced by symmetry lowering from @xmath0 to @xmath1 point group is evident already from the comparison between coronene and circumbiphenyl ( see [ fig4 ] ) . the doubly degenerate frontier orbitals of coronene ( both homo and lumo ) are split in circumbiphenyl ( homo and homo-1 , lumo and lumo+1 , [ fig4]a ) : the existence of two inequivalent axes ( @xmath15 and @xmath18 ) in the molecular plane of the @xmath16=4 gnf induces a different parity for homo and homo-1 , as well as for lumo and lumo+1 . in view of this reduced symmetry , the two lowest energy excitations ( t1 and l1 ) are no longer dipole forbidden , as in the case of the @xmath20 and @xmath21 bands in the hexagonal pahs ( [ fig4]b ) . moreover , the main peak p1 of the @xmath0 series ( clar s @xmath19 band ) splits into two distinct absorption lines , l2 and t2 , with 0.1 ev energy separation . these excitations are here labelled according to their polarization , as visualized in the transition density plots in [ fig5 ] : l1 and l2 are polarized along the longitudinal ( @xmath15 ) axis of the flake , while t1 and t2 along the transverse direction ( @xmath18 axis ) . by looking at the composition of the excitations ( [ table2 ] ) , one notices that t1 and t2 stem from the homo @xmath27 lumo+1 and homo-1 @xmath27 lumo transitions , whereas l1 and l2 are due to the homo @xmath27 lumo and homo-1 @xmath27 lumo+1 transitions . however , while in t1 and t2 the weight of the two transitions is almost equivalent , the dominant contribution for l1 ( l2 ) is given by homo @xmath27 lumo ( homo-1 @xmath27 lumo+1 ) . the anisotropy of circumbiphenyl is reflected also in the different oscillator strength of the longitudinally and transversally polarized excitations . the degeneracy of homo and lumo of coronene is broken in the @xmath1 pahs . b ) calculated optical absorption spectra of ribbon - like pahs , with fixed width @xmath17=7 ( about 7.4 ) and variable length parameter ranging form @xmath16=4 to @xmath16=8 . the main optical excitations , polarized either in the longitudinal ( l , @xmath15 axis ) or transverse ( t , @xmath18 axis ) direction are indicated in the spectrum of circumbiphenyl ( @xmath16=4 ) . the dashed - dotted arrows indicate the position of the lowest energy , weak excitation t1 . for comparison , the spectrum of coronene is also shown ( shaded red curve , top , see also [ fig2 ] ) . the spectra are obtained through a lorentzian broadening of 100 mev . ] the relative intensity of the excitations is connected with the anisotropy _ i.e. _ length / width ratio of the @xmath1 pahs . this phenomenon , which was discussed for longer flakes of the same family @xcite , can be definitely clarified here for these short structures . as quantified in [ table2 ] and illustrated in [ fig4]b , going from the @xmath16=4 to the @xmath16=8 ribbon - like pahs , the oscillator strengths increases by almost one order of magnitude , while the intensity of l2 is incremented only by a factor of 1.5 ( see also [ table2 ] ) . a visual picture of this feature is provided by the transition densities in [ fig5 ] , which indicates a similar modulation of l1 and l2 in the @xmath16=8 pah , compared to the stronger dipolar character of l2 for circumbiphenyl . in the case of the l1 excitation , the weight of the homo @xmath27 lumo increases with the length , at the expense of the homo-1 @xmath27 lumo+1 transition : in circumbiphenyl the ratio between these two single - particle transitions is about 1/3 , while it decreases to less than 1/8 in the @xmath16=8 pah . the same occurs for l2 , with a reversed contributions ( [ table2 ] ) . in the limit of very long ribbon - like pahs with @xmath17=7 and length parameter up to @xmath16=20 , corresponding to a length of about 88 , l1 and l2 present an equal oscillator strength @xcite . also here the increasing length of the flakes induces a red shift of the spectra ( see [ fig4]b ) , as observed in hexagonal pahs ( [ fig2 ] ) . on the other hand , since the flake width is held fixed , the excitations with transverse polarization , t1 and t2 , are very similar in all the considered @xmath1 structures : their energy is only slightly modified , and the oscillator strength is preserved along with the relative weight of the dominant mo transitions , so that on longer flakes the direct excitons will be lower than the forbidden ones @xcite . finally , when comparing the energy of the first active excitation for symmetric ( @xmath0 ) and elongated pahs ( @xmath1 ) , one notices that a peak at @xmath292.9 ev is found for both the hexagonal molecule and for the flake ( @xmath16=6 ) , which present a striking ratio of molecular masses with respect to each other . c|c|c|c|c|c molecule & excitation & mo transitions ( weight ) & @xmath26 & energy [ ev ] & os + & & h @xmath27 l+1 ( 0.46 ) & -0.676 & & + & & h-1 @xmath27 l ( 0.44 ) & 0.666 & & + & & h @xmath27 l ( 0.71 ) & 0.842 & & + & & h-1 @xmath27 l+1 ( 0.25 ) & 0.502 & & + & & h @xmath27 l ( 0.26 ) & 0.507 & & + & & h-1 @xmath27 l+1 ( 0.69 ) & -0.834 & & + & & h @xmath27 l+1 ( 0.42 ) & 0.649 & & + & & h-1 @xmath27 l ( 0.43 ) & 0.660 & & + & & h @xmath27 l+1 ( 0.44 ) & 0.663 & & + & & h-1 @xmath27 l ( 0.42 ) & -0.646 & & + & & h @xmath27 l ( 0.78 ) & 0.884 & & + & & h-1 @xmath27 l+1 ( 0.15 ) & 0.387 & & + & & h @xmath27 l ( 0.16 ) & 0.403 & & + & & h-1 @xmath27 l ( 0.76 ) & -0.873 & & + & & h @xmath27 l+1 ( 0.43 ) & 0.654 & & + & & h-1 @xmath27 l ( 0.45 ) & 0.671 & & + & & h @xmath27 l+1 ( 0.41 ) & 0.643 & & + & & h-1 @xmath27 l ( 0.39 ) & 0.627 & & + & l1 & h @xmath27 l ( 0.80 ) & 0.895 & 2.80 & 1.04 + & & h @xmath27 l ( 0.10 ) & 0.323 & & + & & h-1 @xmath27 l ( 0.77 ) & 0.880 & & + & & h @xmath27 l+1 ( 0.41 ) & -0.639 & & + & & h-1 @xmath27 l ( 0.43 ) & 0.658 & & + , of the examined optical excitations of ribbon - like gnfs with @xmath1 point group symmetry . ]

along with broken molecular orbital degeneracies , optical peaks split and dark states are activated in the low - energy part of the spectrum . supported by a systematic analysis of the composition and the character of the optical transitions , our results contribute in shedding light to the mechanisms responsible for spectral modifications in the visible and near uv absorption bands of medium - size pahs . * keywords * : astrochemistry , coronene , configuration interaction , graphene nanoribbons , transition density , zindo polycyclic aromatic hydrocarbons ( pahs ) are the focus of research in significantly diverse fields , ranging from biochemistry @xcite to theoretical chemistry @xcite , from molecular electronics @xcite to astrochemistry @xcite , where pahs are assigned an important role @xcite due to their chemical composition and spectral features @xcite . in this framework , a theoretical identification of the absorption and emission features of these molecules assumes a significant relevance @xcite , since they might drastically vary both upon small structural modifications @xcite and as a consequence of ionization @xcite or dehydrogenation @xcite . in the field of molecular electronics , the interest in medium- and large - sized pahs is intrinsically connected to graphene , as they are viewed as highly stable graphene molecules @xcite . their intriguing and versatile optical properties @xcite , combined with their facile bottom - up synthesis @xcite and their capability to assemble into @xmath2-@xmath2 stacked superstructures @xcite , make them excellent candidates for opto - electronic applications , @xcite where slight structural variations can trigger different properties and functionalities @xcite . in this paper , we perform a theoretical analysis to identify the size- and anisotropy - induced modifications to the spectral features in the visible and near - uv bands of pahs .

the electronic and optical properties of polycyclic aromatic hydrocarbons ( pahs ) present a strong dependence on their size and geometry . we tackle this issue by analyzing the spectral features of two prototypical classes of pahs , belonging to @xmath0 and @xmath1 symmetry point groups and related to coronene as multifunctional seed . while the size variation induces an overall red shift of the spectra and a redistribution of the oscillator strength between the main peaks , a lower molecular symmetry is responsible for the appearance of new optical features . along with broken molecular orbital degeneracies , optical peaks split and dark states are activated in the low - energy part of the spectrum . supported by a systematic analysis of the composition and the character of the optical transitions , our results contribute in shedding light to the mechanisms responsible for spectral modifications in the visible and near uv absorption bands of medium - size pahs . * keywords * : astrochemistry , coronene , configuration interaction , graphene nanoribbons , transition density , zindo polycyclic aromatic hydrocarbons ( pahs ) are the focus of research in significantly diverse fields , ranging from biochemistry @xcite to theoretical chemistry @xcite , from molecular electronics @xcite to astrochemistry @xcite , where pahs are assigned an important role @xcite due to their chemical composition and spectral features @xcite . in this framework , a theoretical identification of the absorption and emission features of these molecules assumes a significant relevance @xcite , since they might drastically vary both upon small structural modifications @xcite and as a consequence of ionization @xcite or dehydrogenation @xcite . in the field of molecular electronics , the interest in medium- and large - sized pahs is intrinsically connected to graphene , as they are viewed as highly stable graphene molecules @xcite . their intriguing and versatile optical properties @xcite , combined with their facile bottom - up synthesis @xcite and their capability to assemble into @xmath2-@xmath2 stacked superstructures @xcite , make them excellent candidates for opto - electronic applications , @xcite where slight structural variations can trigger different properties and functionalities @xcite . in this paper we investigate the effects of size and anisotropy on the optical spectra of pahs , with the aim of providing an useful reference for understanding and predicting their optical response . to tackle this issue , we focus on two prototypical classes of molecules with @xmath0 and @xmath1 point group symmetry , which are related to coronene , viewed as a multifunctional seed . indeed , with its high symmetry and specific electronic structure , coronene is one of the most representative medium - size pahs @xcite . by means of a well - established quantum chemistry approach , we perform a theoretical analysis to identify the size- and anisotropy - induced modifications to the spectral features in the visible and near - uv bands of pahs . the present study aims at showing that the main effect of size increase , moving from coronene to larger hexagonal pahs of fixed symmetry , is an oscillator strength variation of the main excitations and a red shift of the whole spectrum , which brings the strong absorption peaks from the uv to the visible energy region , maintaining overall the character of the excitons . moreover , the additional features produced in the spectra by the anisotropical elongation of coronene in one direction will be investigated ; specific focus will be devoted to the effects of symmetry breaking . finally , it will be clarified that bright excitations in the visible region appear already for the smaller anisotropic molecules , with low mass compared to highly symmetric pahs .

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in conclusion , we have presented a detailed quantum - chemical analysis of the effects of size and anisotropy on the optical properties of two prototypical classes of pahs , with @xmath0 and @xmath1 symmetry . having ruled out spurious effects with the choice of structures with purely armchair edges , the optical properties of these systems appear strongly dependent both on the size and on the anisotropy of the molecule . most importantly , our findings indicate that the energy of the lowest energy active peak depends more crucially on the molecular symmetry , than on the molecular weight , related in this case to the number of c atoms in the structure . in gnfs with @xmath1 symmetry optically active peaks appear in the visible band already in the spectrum of circumbiphenyl ( ) . on the other hand , only hexagonal molecules with a few hundreds of c atoms can absorb a photon in the same spectral region . the results of this work provide significant insights into the interpretation of the experimental spectra of pahs and consequently into the physical mechanisms driving their optical absorption . moreover , they confirm the large tunability of this class of compounds upon size and symmetry variations , regarding the optical properties . in the field of optoelectronics these outcomes represent a valuable indication in view of designing molecular nanodevices . finally , the detailed investigation carried out in the present study on the size and anisotropy effects on the optical spectra of representative classes of pahs can serve as a guide for the astronomical observation of these carbon compounds . specifically , the symmetry analysis of the main excitations in the visible region with respect of the molecular weight is a valuable indication for determining the relative abundance of medium - size aromatic molecules , and hence clarifying the composition of the ism . the authors are grateful to stefano corni and franco gianturco for stimulating discussions . cineca is acknowledged for computational support . part of this research was supported by : the italian ministry of research through the national projects prin - graf ( grant no . 20105zztse ) , firb - flashit ( grant no . rbfr12swoj ) , and the program progetto premiale 2012 " - project abnanotech ; the italian ministry of foreign affairs through the grant no . m. j. c. acknowledges support from fapesp and cnpq ( brazil ) . arfsten , d. p. ; schaeffer , d. j. ; mulveny , d. c. the effects of near ultraviolet radiation on the toxic effects of polycyclic aromatic hydrocarbons in animals and plants : a review . _ ecotox . environ . safe _ * 1996 * , _ 33 _ , 124 clar , e. ; schoental , r. _ polycyclic hydrocarbons _ ; academic press new york , 1964 ; vol . 2 wu , j. ; pisula , w. ; muellen , k. graphenes as potential material for electronics . _ * 2007 * , _ 107 _ , 718747 tielens , a. interstellar polycyclic aromatic hydrocarbon molecules . _ astrophys . _ * 2008 * , _ 46 _ , 289337 leger , a. ; puget , j. identification of the unidentified ir emission features of interstellar dust ? _ astronomy and astrophysics _ * 1984 * , _ 137 _ , l5l8 allamandola , l. ; tielens , a. ; barker , j. polycyclic aromatic hydrocarbons and the unidentified infrared emission bands - auto exhaust along the milky way . _ astrophys . j. _ * 1985 * , _ 290 _ , l25l28 lger , a. ; 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iwasaki , n. absorption spectra of amorphous organic films . lett . _ * 1974 * , _ 24 _ , 2629 orlandi , g. ; zerbetto , f. quantum - chemical analysis of the absorption and emission spectra of coronene . * 1988 * , _ 123 _ , 175185 we recently addressed this issue in the analysis of the optical spectrum of icosahedral . a detailed discussion can be found in ref . an exhaustive and systematic analysis of the size effects on the electronic and optical properties of a representative set of pahs has been recently presented by malloci and coworkers , see ref . kokkin , d. l. ; troy , t. p. ; nakajima , m. ; nauta , k. ; varberg , t. d. ; metha , g. f. ; lucas , n. t. ; schmidt , t. w. the optical spectrum of a large isolated polycyclic aromatic hydrocarbon : hexa - peri - hexabenzocoronene , @xmath30 . _ astrophys . j. lett . _ * 2008 * , _ 681 _ , l49 rouill , g. ; steglich , m. ; huisken , f. ; henning , t. ; mllen , k. uv / visible spectroscopy of matrix - isolated hexa - peri - hexabenzocoronene : interacting electronic states and astrophysical context . _ j. chem . phys . _ * 2009 * , _ 131 _ , 204311 prezzi , d. ; varsano , d. ; ruini , a. ; marini , a. ; molinari , e. optical properties of graphene nanoribbons : the role of many - body effects . b _ * 2008 * , _ 77 _ , 041404(r ) yang , l. ; cohen , m. ; louie , s. excitonic effects in the optical spectra of graphene nanoribbons . _ nano lett . _ * 2007 * , _ 7 _ , 31123115 cocchi , c. ; prezzi , d. ; ruini , a. ; caldas , m. j. ; fasolino , a. ; molinari , e. concavity effects on the optical properties of aromatic hydrocarbons . _ j. phys . chem . c _ * 2013 * , _ 117 _ , 1290912915 malloci , g. ; cappellini , g. ; mulas , g. ; mattoni , a. electronic and pptical properties of families of polycyclic aromatic hydrocarbons : a systematic ( time - dependent ) density functional theory study . * 2011 * , _ 384 _ , 1927

the electronic and optical properties of polycyclic aromatic hydrocarbons ( pahs ) present a strong dependence on their size and geometry . we tackle this issue by analyzing the spectral features of two prototypical classes of pahs , belonging to @xmath0 and @xmath1 symmetry point groups and related to coronene as multifunctional seed . while the size variation induces an overall red shift of the spectra and a redistribution of the oscillator strength between the main peaks , a lower molecular symmetry is responsible for the appearance of new optical features . we investigate the effects of size and anisotropy on the optical spectra of pahs , with the aim of providing an useful reference for understanding and predicting their optical response . to tackle this issue , we focus on two prototypical classes of molecules with @xmath0 and @xmath1 point group symmetry , which are related to coronene , viewed as a multifunctional seed . indeed , with its high symmetry and specific electronic structure , coronene is one of the most representative medium - size pahs @xcite . by means of a well - established quantum chemistry approach the present study aims at showing that the main effect of size increase , moving from coronene to larger hexagonal pahs of fixed symmetry , is an oscillator strength variation of the main excitations and a red shift of the whole spectrum , which brings the strong absorption peaks from the uv to the visible energy region , maintaining overall the character of the excitons . finally , it will be clarified that bright excitations in the visible region appear already for the smaller anisotropic molecules , with low mass compared to highly symmetric pahs .

the electronic and optical properties of polycyclic aromatic hydrocarbons ( pahs ) present a strong dependence on their size and geometry . we tackle this issue by analyzing the spectral features of two prototypical classes of pahs , belonging to @xmath0 and @xmath1 symmetry point groups and related to coronene as multifunctional seed . while the size variation induces an overall red shift of the spectra and a redistribution of the oscillator strength between the main peaks , a lower molecular symmetry is responsible for the appearance of new optical features . along with broken molecular orbital degeneracies , optical peaks split and dark states are activated in the low - energy part of the spectrum . supported by a systematic analysis of the composition and the character of the optical transitions , our results contribute in shedding light to the mechanisms responsible for spectral modifications in the visible and near uv absorption bands of medium - size pahs . * keywords * : astrochemistry , coronene , configuration interaction , graphene nanoribbons , transition density , zindo polycyclic aromatic hydrocarbons ( pahs ) are the focus of research in significantly diverse fields , ranging from biochemistry @xcite to theoretical chemistry @xcite , from molecular electronics @xcite to astrochemistry @xcite , where pahs are assigned an important role @xcite due to their chemical composition and spectral features @xcite . in this framework , a theoretical identification of the absorption and emission features of these molecules assumes a significant relevance @xcite , since they might drastically vary both upon small structural modifications @xcite and as a consequence of ionization @xcite or dehydrogenation @xcite . in the field of molecular electronics , the interest in medium- and large - sized pahs is intrinsically connected to graphene , as they are viewed as highly stable graphene molecules @xcite . their intriguing and versatile optical properties @xcite , combined with their facile bottom - up synthesis @xcite and their capability to assemble into @xmath2-@xmath2 stacked superstructures @xcite , make them excellent candidates for opto - electronic applications , @xcite where slight structural variations can trigger different properties and functionalities @xcite . in this paper we investigate the effects of size and anisotropy on the optical spectra of pahs , with the aim of providing an useful reference for understanding and predicting their optical response . to tackle this issue , we focus on two prototypical classes of molecules with @xmath0 and @xmath1 point group symmetry , which are related to coronene , viewed as a multifunctional seed . indeed , with its high symmetry and specific electronic structure , coronene is one of the most representative medium - size pahs @xcite . by means of a well - established quantum chemistry approach , we perform a theoretical analysis to identify the size- and anisotropy - induced modifications to the spectral features in the visible and near - uv bands of pahs . the present study aims at showing that the main effect of size increase , moving from coronene to larger hexagonal pahs of fixed symmetry , is an oscillator strength variation of the main excitations and a red shift of the whole spectrum , which brings the strong absorption peaks from the uv to the visible energy region , maintaining overall the character of the excitons . moreover , the additional features produced in the spectra by the anisotropical elongation of coronene in one direction will be investigated ; specific focus will be devoted to the effects of symmetry breaking . finally , it will be clarified that bright excitations in the visible region appear already for the smaller anisotropic molecules , with low mass compared to highly symmetric pahs .

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the investigation of the real - time dynamics in quantum - impurity systems ( qiss ) is essential for our understanding of dissipation and decoherence in qubits and electronic transport through nanodevices . such systems consist of a small subsystem comprising a finite number of degrees of freedom , interacting with an infinitely large environment of noninteracting particles . elzerman @xcite have reported the usage of gate - voltage pulses for a single - shot readout of the spin configuration of a single - electron transistor in a finite magnetic field . such a system can be modeled by an anderson impurity model @xcite coupled to a noninteracting metallic host . while the normal single - impurity anderson model ( siam ) has a well - established and rather simple phase diagram @xcite , it can be viewed as a special case ( @xmath1 ) of a more general class of models @xcite whose coupling function @xmath2 to the local impurity contains a pseudogap ; @xmath3 . withoff and fradkin were the first to point out the existence of a critical coupling @xcite using a perturbative renormalization group argument . this system exhibits a wide variety of different phases for @xmath4 . these phases are characterized by different fixed points whose properties and occurrence depend on the bath exponent @xmath5 as well as on particle - hole symmetry or the absence of it . for @xmath6 , there exists @xcite a critical coupling strength @xmath7 governing the transition between a local moment ( lm ) phase for a weak coupling and a strong - coupling ( sc ) phase for a large coupling to the metallic host . in this paper , we analyze the real - time dynamics of different quenches within the lm or the sc phase but also quenches across the quantum critical point ( qcp ) from one to the other phase for the particle - hole symmetric pseudogap anderson impurity model ( pg - siam ) . we employ a recent extension of wilson s numerical renormalization group ( nrg ) @xcite to the nonequilibrium quench dynamics , the time - dependent nrg ( td - nrg ) @xcite . while the quench dynamics in the siam ( @xmath1 ) has been investigated @xcite using the td - nrg , the non - equilibrium dynamics in the pg - siam within and across the qcp has only recently been addressed by a time - dependent gutzwiller ansatz @xcite . using this extension of the well - established variational gutzwiller technique @xcite to nonequilibrium @xcite it has been demonstrated that the pseudogap coupling function can yield nontrivial dynamics as a consequence of the diverse low - energy fixed points of the model @xcite . the pg - siam has been extensively investigated in the context of kondo impurities in unconventional superconductors @xcite or in the context of defects in graphene sheets @xcite . some of the low - energy properties of the fixed points have been worked out in detail @xcite and it has been shown that the universality class of the fixed point changes with the coupling function exponent @xmath5 . one intriguing property of this model is the absence of the kondo screening at low coupling strength @xcite while for a large coupling a sc fixed point is found but with an only partially screened moment for particle - hole symmetric models . the question arises how these orthogonal ground states of the different phases influence the real - time dynamics of a system driven out of equilibrium by a quantum quench . since an effective spin degree of freedom decouples from the impurity in the lm phase , this fixed point ( fp ) property is expected to have a strong influence on the steady - state formation and the thermalization when quenched into the lm phase . we will show , however , that an oversimplified picture does not hold and requires some modification . in all our quenches we find a well - defined steady state at long times . the distance from the thermal equilibrium for the same final hamiltonian serves as a measure for the degree of thermalization . while for quenches within the sc phase , the system thermalizes within the numerical accuracy of the td - nrg @xcite , the deviations from the thermal equilibrium remain negligible even for quenches across the qcp very close to the qcp . the deviation appears to be a continuous function of the distance to the critical coupling . the surprising finding of a well - defined steady state even for quenches across the qcp into the lm phase can be understood in terms of the known fixed point properties of the model . it has been already pointed out in ref . @xcite that the local thermodynamic properties such as double occupancy as well as the fractional local moment on the impurity are continuous across the qcp . in the strong - coupling ( sc ) phase , the kondo temperature @xmath8 governing the excitations around the sc fp vanishes at the qcp and increases with increasing coupling to the pseudogap metallic host . the crossover scale @xmath9 taking the role of @xmath8 in the lm phase characterizes the excitations around the lm fp , decreases with increasing coupling and also vanishes at the qcp . the associated length scales @xmath10 ( @xmath11 ) @xmath12 being the average fermi velocity of the host material can be interpreted as estimate for the spatial extension of the decoupled local moment ( or the kondo singlet in the sc phase . ) only for a very large local coulomb repulsion @xmath13 , the crossover scale @xmath9 becomes large indicating that the local moment is mainly formed closely to or on the impurity . bearing in mind these known equilibrium properties @xcite of the model it becomes apparent that an ansatz for the ground state restricted to a local moment formation on the impurity site only , as used in the gutzwiller approach @xcite , significantly underestimates the critical coupling @xmath7 . then , the local moment formation can only occur in such an approach at much lower coupling @xmath14 or much larger local coulomb repulsion @xmath13 compared to the solution provided by the nrg . this has also a profound consequence for the observed real - time dynamics . due to the extended nature of the decoupled local moment , the local observable still can explore a larger phase space of itinerant states and , therefore , shows signs of thermalization close to the qcp . reducing the size of the local moment by increasing @xmath13 away from the critical @xmath15 will still yield a steady state whose asymptotic properties start to deviate significantly from the thermal expectation values : due to the increase of the nondecaying fraction of the expectation value @xcite the difference between the steady - state and the thermal expectation value increases in the lm phase . this difference , however , will strongly depend on the matrix element of the operator with the decoupling degree of freedom ( dof ) . while for the local double occupancy as a measure for the local correlations we find an increasing deviation between the long - time steady - state value and the thermal expectation value , the energy flow into the hybridization energy seems to be unaffected when crossing over to the localized regime . it is a rather surprising finding that hybridization energy shows thermalization even in the lm phase , although it has been conjectured that the td - nrg might have problems in describing properly the energy flow @xcite . the main objective of this paper is to discuss the real - time dynamics of the pseudogap siam with respect to interaction and hybridization quenches within a given phase and across the quantum critical point . to be more specific , we will introduce the model in sec . [ sec : pg - siam ] and briefly the td - nrg in sec . [ sec : td - nrg ] . we continue with a short overview over the rich phase diagram in sec . [ sec : overview - phases ] a much more comprehensive review can be found in refs . @xcite in order to define the types of quenches that will be investigated in sec . [ sec : results ] , the main part of the paper . for completeness and defining the parameter space , we present the known nrg phase diagram for the symmetric pg - siam and also discuss the differences between the nrg and the equilibrium gutzwiller results in sec . [ sec : equilibriumproperties ] . we start with analyzing our data for interaction quenches , the sudden switching on the local coulomb repulsion . for small @xmath13 and finite hybridization , the system remains in the sc phase . in sec . [ sec : interactionquencheswithin ] , we show that universality can be found for this type of quench with a @xmath13-independent time scale . interaction quenches across the qcp are investigated in sec . [ sec : interactionquenchesover ] . we address the difference between equilibration and thermalization . section [ sec : hybridisationquenches ] is devoted to the two types of hybridization quenches . we augment our td - nrg results with a perturbative analysis details can be found in the appendix and show an excellent agreement between the numerics and the analytics in sec . [ sec : analytic - result ] . we also discuss the energy flow from the reservoir to the impurity after the quench in sec . [ sec : energy - flow ] . we end the paper with a short conclusion .

the energy - dependent scattering of fermions from a localized orbital at an energy - dependent rate @xmath0 gives rise to quantum critical points ( qcps ) in the pseudogap single - impurity anderson model separating a local moment phase with an unscreened spin moment from a strong - coupling phase which slightly deviates from the screened phase of standard kondo problem . using the time - dependent numerical renormalization group ( td - nrg ) approach we show that local dynamic properties always equilibrate towards a steady - state value even for quenches across the qcp but with systematic deviations from the thermal equilibrium depending on the distance to the critical coupling .

the energy - dependent scattering of fermions from a localized orbital at an energy - dependent rate @xmath0 gives rise to quantum critical points ( qcps ) in the pseudogap single - impurity anderson model separating a local moment phase with an unscreened spin moment from a strong - coupling phase which slightly deviates from the screened phase of standard kondo problem . using the time - dependent numerical renormalization group ( td - nrg ) approach we show that local dynamic properties always equilibrate towards a steady - state value even for quenches across the qcp but with systematic deviations from the thermal equilibrium depending on the distance to the critical coupling . local non - equilibrium properties are presented for interaction quenches and hybridization quenches . we augment our numerical data by an analytical calculation that becomes exact at short times and find excellent agreement between the numerics and the analytical theory . for interaction quenches within the screened phase we find a universal function for the time - dependent local double occupancy . we trace back the discrepancy between our results and the data obtained by a time - dependent gutzwiller variational approach to restrictions of the wave - function ansatz in the gutzwiller theory : while the nrg ground states properly account for the formation of an extended spin moment which decouples from the system in the unscreened phase , the gutzwiller ansatz only allows the formation of the spin moment on the local impurity orbital .

1410.1770

c

we have analyzed in detail the impurity dynamics of the pg - siam after local quenches . in sec . [ sec : equilibriumproperties ] we have summarized the known equilibrium properties of the pseudogap model . there we have discussed the limitations of a gutzwiller ansatz @xcite which only allows a decoupling spin moment forming on the impurity site in the lm phase whereas the nrg is able to generate the correct ground state describing a spatially extended spin - moment formation . we have distinguished two quench types : the interaction quench in sec . [ sec : interactionquenches ] and the hybridization quench in sec . [ sec : hybridisationquenches ] . for the former we have found a universal curve for interaction quenches within the sc phase : all dependencies of the coulomb repulsion @xmath97 , the band width @xmath34 , and the bath exponent @xmath5 are included in the scaling function @xmath121 defined by eq . and the crossover time scale @xmath123 approximated by eq . . from the temperature - dependent effective moment @xmath142 in the lm regime we have defined the crossover scale @xmath9 that depends on the distance @xmath364 and vanishes for @xmath15 . since @xmath9 is directly related to the nrg iteration @xmath365 beyond which the lm fp is approached , @xmath366 can be interpreted as a characteristic length scale of the local - moment formation : the larger @xmath9 will be , the more localized the effective spin moment decoupling from the rest of system will be . moreover , we have demonstrated that the difference between the steady - state value @xmath193 and thermodynamic expectation value @xmath367 only depends on @xmath9 independently of varying @xmath97 at fixed @xmath34 or varying @xmath34 for fixed @xmath97 . this spatial dependency of the decoupled moment encoded in the nrg ground state can not be accounted for in the gutzwiller approach @xcite since the wave - function ansatz restricts the moment formation onto the impurity site . in the presented hybridization quenches we always start from a decoupled impurity at @xmath113 and switch on @xmath368 with different coupling strength . for a small hybridization , the system remains in the lm phase while a large hybridization drives the system across the qcp into the sc phase . we have gauged the quality of our numerical results by our analytic second - order perturbation theory , which becomes exact for times @xmath369 , and found excellent agreement between the analytics and the numerics in the applicability range of the perturbation theory . we could show that the short - time dynamics is governed by the time scale @xmath328 which is independent of the coulomb interaction . by comparison of our data with the recent gutzwiller results @xcite we could demonstrate the shortcomings of this variational ansatz that already strongly deviates from the asymptotically exact perturbative result for short - time scales . after illustrating the major difference of the physical content in the ground - state wave function between the approximate gutzwiller approach and the exact nrg ground state , the differences between the equilibrium as well as the nonequilibrium results of both methods become transparent . thermalization was observed within the errors of the td - nrg @xcite for quenches within or into the sc phase . due to the extended nature of the decoupling effective spin in the lm phase , we still found a steady - state value for @xmath89 that , however , increasingly deviates from the thermodynamic expectation value . interestingly , we found a thermalization of the hybridization energy @xmath283 which accounts for the major local energy change after the quench . we also provide a short overview for hybridization quenches for exponents @xmath72 where only a lm fp is found for @xmath26 .

local non - equilibrium properties are presented for interaction quenches and hybridization quenches . we augment our numerical data by an analytical calculation that becomes exact at short times and find excellent agreement between the numerics and the analytical theory . for interaction quenches within the screened phase we find a universal function for the time - dependent local double occupancy .

the energy - dependent scattering of fermions from a localized orbital at an energy - dependent rate @xmath0 gives rise to quantum critical points ( qcps ) in the pseudogap single - impurity anderson model separating a local moment phase with an unscreened spin moment from a strong - coupling phase which slightly deviates from the screened phase of standard kondo problem . using the time - dependent numerical renormalization group ( td - nrg ) approach we show that local dynamic properties always equilibrate towards a steady - state value even for quenches across the qcp but with systematic deviations from the thermal equilibrium depending on the distance to the critical coupling . local non - equilibrium properties are presented for interaction quenches and hybridization quenches . we augment our numerical data by an analytical calculation that becomes exact at short times and find excellent agreement between the numerics and the analytical theory . for interaction quenches within the screened phase we find a universal function for the time - dependent local double occupancy . we trace back the discrepancy between our results and the data obtained by a time - dependent gutzwiller variational approach to restrictions of the wave - function ansatz in the gutzwiller theory : while the nrg ground states properly account for the formation of an extended spin moment which decouples from the system in the unscreened phase , the gutzwiller ansatz only allows the formation of the spin moment on the local impurity orbital .

1206.4543

c

the lack of the observation of additional esr contributions from free carriers is consistent with a full tll state of the electrons even in the bundled metallic tubes with relaxed 1d character . it is also consistent with recent experiments from photo emission where for metallic tubes tll signatures were observed in the spectral function @xcite . the localized spins can be assigned to various defects such as single bonded covalent functionalization or defects on or inside the tubes . the defect concentration is similar to the value of @xmath28/c reported in @xcite from magnetic measurements but considerably higher than values of @xmath29 given in @xcite . the high spin concentration observed here is not surprising since both , purification and separation introduce defects . this is also evidenced from raman scattering which revealed an increase of the d / g ratio by 33% from 0.06 to 0.08 ( 515 nm laser ) for the sc tubes and by 57.5% from 0.13 to 0.21 ( 647 nm laser ) for the m tubes . the defects are in strong interaction with the tubes leading in general to similar behavior for m and sc tubes . however , as far as transition temperatures and spin relaxation are concerned , significant differences are observed . wave functions of the defect spins are in general spread out over a considerable number of hexagonal cells . for example , dft calculations for hydrogen bonded to a small capped ( 3,3 ) swcnt yield a spin distribution over 5 and 8 hexagons in axial and radial direction , respectively @xcite . this provides the possibility of exchange interaction in spite of the large distance between spins . the interaction can be particularly enhanced by the indirect exchange mechanism across the carbon lattice , and , for m tubes , by interaction with free carriers according to the rkky mechanism . in the suggested ferromagnetic state we do not observe the esr response from the magnetically ordered spins , since the easy axes of the magnetic regions are randomly oriented following the random orientation of the nanotubes or bundles of nanotubes . magnetic anisotropy can be traced back to an anisotropic curvature perpendicular and parallel to the tube axis and the concomitant anisotropy in the so coupling . magnetic properties from defects in carbon systems have been reported in several publications @xcite . apparently transversal extension of the tubes or the 3d nature of the bundles is enough to allow ferromagnetic or anti - ferromagnetic interaction but it is not enough to suppress tll nature of the electrons . a decrease of spin susceptibility at low temperatures was recently reported for unseparated swcnts @xcite and speculated to originate from a spin gap opening or from an anti - ferromagnetic ordering of the defect spins as it was suggested for the magnetic behavior of nanohorns @xcite . the low concentration of defect spins in @xcite may be a problem for such interpretation . in contrast , in our case with the much higher spin concentration the temperature dependence of the inverse susceptibility exhibits clear ferromagnetic coupling for sc and m tubes . indications for weak ferromagnetism in small parts of nanotube samples were also reported from magnetization measurements of swcnt with high concentration of defect spins in @xcite . however in this case it was suggested that ferromagnetic ordering occurs in metallic tubes only . in the m tubes the transition temperatures @xmath30 as evaluated from the linear regressions are almost a factor two higher than in the sc tubes . this is suggested to be due to the additional spin - spin interaction mediated by the free carriers . in low dimensional electronic systems the rkky type interaction is very efficient since it extends as @xmath31 where @xmath32 is the distance between two spins and @xmath33 is the dimension of the system @xcite . in swcnt it is particularly interesting since fermi wave vectors can be either zero or @xmath34 where @xmath35 is the nt translation vector @xcite . as a consequence the rkky interaction is not oscillatory , at least not for tubes with @xmath36 . rkky interaction is likewise important for the transition temperatures and for the line widths and was shown in @xcite to decrease with increasing @xmath0 . the increase of the line width with increasing temperature for sc tubes suggests spin - lattice interaction ( sli ) as the relevant process for spin relaxation . sli is usually mediated by either a direct process which is linear in @xmath0 , a raman process which goes with a high power of @xmath0 or an orbach process . since only the latter exhibits saturation with @xmath0 it is natural to invoke it for the description of the experiments . on the other hand , the re - increase of the line width at very low temperatures indicates additional contributions . since it is suggestive that this increase is related to the ferromagnetic phase transition with the statistically distributed transition temperatures a gaussian temperature dependence is appropriate for its description . considering homogeneous and inhomogeneous contributions we describe the line width obtained from the dysonian fits as @xmath37 where @xmath38 is a lorentzian type homogeneous line width following an orbach relaxation @xmath39 and @xmath40 considers the line width from gaussian fluctuations and possible concomitant variations of @xmath41 values . @xmath42 is a temperature independent background line width . this pythagorayan addition of line width components is a commonly used approximation which mimics a folding procedure @xcite . @xmath43 and @xmath21 in the expression for the orbach process are the energetic distance to a higher electronic state for the spin excitation , and a scaling prefactor . @xmath44 , @xmath45 , and @xmath46 are the parameters of the distribution from inhomogeneous fluctuations . as shown in fig.[fig : wfit ] , eq.[eq : orbgauss ] provides a very good representation of the experiments with @xmath21 , @xmath43 , @xmath44 , @xmath45 @xmath46 , and @xmath42 as parameters . for semiconducting samples versus temperature @xmath0 . squares : line width from the experiment , line : fit according to eq.[eq : orbgauss ] ( left ) and explicit representation of the fit components ( right ) . fit parameters were @xmath47 g , @xmath48k for the orbach relaxation and @xmath49 g , @xmath50k , @xmath51k for the gaussian distribution , and @xmath52 g for the background . the insert shows the scheme for the orbach process . ] from the parameter values in the caption of fig.[fig : wfit ] the excitation energy is 3.8 mev ( 45.1k ) . applying the same fitting procedure to the other sample gave very similar values . @xmath43 was in particular found to be 44.5k for the second sample . in the case of a spin - lattice relaxation by an orbach process the excited spin state @xmath53 and the ground state @xmath54 are coupled by a perturbation hamiltonian @xmath55 to an intermediate split off electronic state @xmath56 to which spins are excited before relaxation . a scheme of this process is depicted in fig.[fig : wfit ] . the perturbation is in general phononic or vibronic . in the original work of r. orbach @xcite the extra electronic state came from crystal field splitting . due to the large number of defects in our samples a rather large number of possible excited states can be expected which supports a spin - lattice relaxation by an orbach process . the increase of the line widths for @xmath57k in the sc tubes is the signature of fluctuations when approaching the phase transition . the values from fig.[fig : temp1 ] for @xmath58k are in good agreement with the value of @xmath59k used for the fit in fig.[fig : wfit ] . fluctuations along with structural phase transitions are well known to broaden esr lines . @xcite this broadening often follows a power law of the form @xmath60 with @xmath61 of the order of 1 . the fit depicted in the insert of fig.[fig : msclw ] yields @xmath62 , slightly smaller than expected . this deviation is very likely due to the statistical distribution of @xmath1 with the concomitant flattening of the slope . for the metallic tubes a decrease of line width with increasing temperature is observed . since in our case the defect spins are localized and do not show activated behavior motional narrowing can be ruled out for an explanation . increasing and even diverging line widths for decreasing @xmath0 were also reported for metallic spin systems which undergo a transition to a spin glass @xcite . however , in this case line widths of the order of 100 g are expected . since this is not observed here we are left with an indirect exchange mechanism as responsible for the increase of line with decreasing temperature . in the metallic tubes this mechanism has a strong contribution from the free carrier rkky interaction which increases with decreasing temperature as described above . one may certainly ask why spin lattice interaction e.g. in the form of an orbach process is not active for the metallic tubes . such behavior can indeed not be ruled out . as it would partly compensate the negative temperature coefficient observed for the metallic tubes such relaxation would result in an even stronger decrease of line width with temperature for the metallic tubes . the surprise in the results for the line width concerns not only the different temperature dependence but even more the considerably larger line width for the m tubes as compared to the sc tubes at low temperatures . this , together with the different temperature dependence , leads to a crossover of the line widths with increasing temperature . while the ratio between the excess line width for the m tubes and for the sc tubes is 3.2 at 1.5k on average , it is only 0.6 at 200k . this is suggested to be a consequence of the increasing spin - lattice interaction with increasing @xmath0 and the simultaneous decrease of the line width due to the decreasing rkky interaction .

the signal originates from defect spins but interaction with free electrons leads to a larger line width for m tubes . the latter decreases with increasing @xmath0 whereas it increases with @xmath0 for sc tubes . indirect exchange is suggested to be responsible for the spin - spin interaction , supported by rkky interaction in the case of m tubes . for sc tubes spin - lattice relaxation via an orbach process is suggested to determine the line width .

the esr response from highly metal - semiconductor(m - sc ) separated swcnts for temperatures @xmath0 between 0.39 and 200k is characteristically different for the two systems . the signal originates from defect spins but interaction with free electrons leads to a larger line width for m tubes . the latter decreases with increasing @xmath0 whereas it increases with @xmath0 for sc tubes . the spins undergo a ferromagnetic phase transition below around 10k . indirect exchange is suggested to be responsible for the spin - spin interaction , supported by rkky interaction in the case of m tubes . for sc tubes spin - lattice relaxation via an orbach process is suggested to determine the line width .

1612.09538

i

we are concerned with the existence , uniqueness , and asymptotic behavior of steady transonic flows past a curved wedge , involving transonic shocks , governed by the two - dimensional full euler equations . when a supersonic flow past a straight - sided wedge whose half - angle is less than the detachment angle , a shock is expected to form , which is attached to the wedge vertex . if the upstream steady flow is a uniform supersonic state , we can find the corresponding constant flow downstream along the straight - sided wedge boundary , together with a straight shock separating the two states ( see fig . [ fig - perturbedshock ] ) , by using the shock polar determined by the rankine - hugoniot jump conditions and the entropy condition ( _ cf . [ fig - shockpolaruv ] ) . however , the downstream state is not uniquely solvable . in general , there are two solutions , one of which corresponds to a weaker shock than the other . as normally expected , a physically admissible shock should be stable under small perturbations . therefore , it is important to analyze the stability of these shocks in order to understand underlying physics . the wedge problem described above has a long history at least dating back to the 1930s . prandtl @xcite in 1936 first conjectured that the weaker shock solution is stable , and hence physically admissible . there has been a long debate about whether the stronger shock is stable for decades ; see courant - friedrichs @xcite , section 123 , and von neumann @xcite . see also liu @xcite and serre @xcite . when the downstream flow is supersonic , the corresponding shock is called a supersonic shock , which is a weaker shock . this case has been analyzed for the potential flow equation in @xcite with certain convexity assumption on the wedge and in @xcite for an almost straight - sided wedge . the existence and stability of the steady supersonic shocks for the full euler equations under the bv perturbation of both the upstream flow and the slope of the wedge boundary have been established in chen - zhang - zhu @xcite and chen - li @xcite for lipschitz wedges . for transonic shocks ( _ i.e. _ , the downstream flow is subsonic ) , there are two cases : the transonic shock with the subsonic state corresponding to arc @xmath0 ( which is a weaker shock ) and the one corresponding to arc @xmath1 ( which is a stronger shock ) ( see fig . [ fig - shockpolaruv ] ) . the strong shock case has been studied in chen - fang @xcite for the potential flow . plane , height=257 ] it is well known that the jump of the entropy function across the shock is of cubic order of the shock strength . in general , the strength of transonic shocks is large , so the full euler system is a more accurate model than the potential flow or isentropic euler equations . in fang @xcite , the euler equations are studied with a uniform bernoulli constant for both strong and weak transonic shocks . because the framework is the weighted sobolev space , the asymptotic behavior of the shock slope or subsonic solution was not derived . on the other hand , the asymptotic behavior can be seen more conveniently within the framework of hlder spaces . in yin - zhou @xcite , the hlder norms were used for the estimates of the full euler equations with the assumption on the sharpness of the wedge angle , which means that the subsonic state is near point @xmath2 in the shock polar . in chen - chen - feldman @xcite , the weaker transonic shock , which corresponds to the whole arc @xmath0 , was investigated ; and the existence , uniqueness , stability , and asymptotic behavior of subsonic solutions were obtained . in @xcite , a potential function is used to reduce the four euler equations into one elliptic equation in the subsonic region . the method was first proposed in @xcite and has the advantage of integrating the conservation properties of the euler system into a single elliptic equation . however , working on the potential function further requires its lipschitz estimate , besides the @xmath3estimate , to keep the subsonicity of the flow . there are other related papers about transonic shocks , such as @xcite for transonic flows past three - dimensional wedges and @xcite about transonic flows past a perturbed cone ; see also @xcite for the approaches developed earlier for dealing with transonic shock flows . the purpose of this paper is to analyze both strong and weak transonic shocks and establish the existence , uniqueness , and asymptotic behavior of the subsonic solutions under the perturbation of both the upstream supersonic flows and the wedge boundaries . through rigorous mathematical analysis , we are able to prove the stability of both weak and strong transonic shocks . the strategy is to use the physical variables to make the estimates , instead of the potential function . the advantage of this method is that only the lower regularity ( _ i.e. _ , the @xmath3estimate ) is sufficient to guarantee the subsonicity . furthermore , estimating the physical state function @xmath4 directly ( see equations ) also yields a better asymptotic decay rate : for weaker transonic shocks , the decay rate is only @xmath5 in our earlier paper @xcite ; while , in this paper , we will show that the subsonic solution decays to a limit state at rate , @xmath6 , with @xmath7 depending only on the background states ( see remark [ rem:2.2a ] ) . more precisely , we first use the lagrangian coordinates to straighten the streamlines . the reason for this is that the bernoulli variable and entropy are conserved along the streamlines , and using the streamline as one of the coordinates simplifies the formulation , especially for the asymptotic behavior of the solution . then , as in @xcite , we decompose the euler system into two algebraic equations and two elliptic equations . differentiating the two elliptic equations gives rise to a second - order elliptic equation in divergence form for the flow direction @xmath8 . given @xmath9 in an expected function space for solutions , we can solve for a new variable @xmath10 as the solution of the linear equation for iterations whose coefficients are evaluated on the given function @xmath9 . once we solve for @xmath10 and obtain the desired estimates , the rest variables are then updated . thus , we construct a map @xmath11 , where @xmath12 and @xmath13 are the perturbations from the background subsonic state . the estimates based on our method do not yield the contraction for @xmath14 . therefore , the banach fixed point argument does not work ; instead , we employ the schauder fixed point argument to obtain the existence of the subsonic solution . for the uniqueness , we estimate the difference of two solutions by using the weighted hlder norms with a lower decay rate . one point we want to emphasize here is that the decay pattern is different from that for potential flow . in a potential flow , the decay is with respect to @xmath15 . for example , if @xmath16 converges to @xmath17 at rate @xmath5 , then @xmath18 converges at rate @xmath6 . for the euler equations , because the bernoulli variable and the entropy function are constant along streamlines , the physical variables @xmath19 do not converge to the background state along the streamlines . they converge only across the streamlines away from the wedge . therefore , when the elliptic estimates are performed , the scaling is with respect to the distance from the wedge , rather than @xmath15 . this results in the following decay pattern : in lagrangian coordinates @xmath20 , there exists an asymptotic limit @xmath21 ; @xmath9 converges to @xmath22 at rate @xmath23 , but @xmath24 converges at rate @xmath25 . that is , the extra decay for the derivatives is only along the @xmath26direction . finally , we remark that our analysis of transonic shocks for the euler equations for potential and non - potential flow , started in chen - feldman @xcite to formulate the transonic shock problems as one - phase free boundary problems , is motivated by the previous works on variational one - phase free boundary problems for nonlinear elliptic equations in alt - caffarelli @xcite , alt - caffarelli - friedman @xcite , and the references cited therein . one of the main difficulties in dealing with the transonic shock problems is that the corresponding elliptic one - phase free boundary problems are non - variational in general , so that the complete solution to the free boundary problems requires different approaches and new techniques which are further developed in this paper in the physical realm of the full euler equations for compressible fluids . the rest of the paper is organized in the following sections . in [ sec - setup ] , the wedge problem is formulated as a free boundary problem and the main theorem is stated . in [ sec - lagrange ] , the problem is reformulated in lagrangian coordinates . in [ sec - decompose ] , the euler equations are decomposed into two algebraic equations and a first - order elliptic system of two equations . in [ sec - linearize ] , the linear elliptic system and the boundary conditions for iterations are introduced . in [ sec - keylemma ] , the key estimates of solutions for the linear second - order elliptic equation for iterations are obtained . in [ sec - iteration ] , the iteration map is constructed and the corresponding estimates are obtained , leading to the existence of a weak transonic shock solution . in [ sec - unique ] , the uniqueness of the weaker transonic shock solution is proved . in [ sec - asymptotic ] , the asymptotic behavior and the decay rate of solutions are discussed . in [ sec - th ] , the difference between the weaker and the stronger transonic shocks is revealed in terms of the estimates and the asymptotic behavior of the solution .

the existence , uniqueness , and asymptotic behavior of steady transonic flows past a curved wedge , involving transonic shocks , governed by the two - dimensional full euler equations are established . the stability of both weak and strong transonic shocks under the perturbation of both the upstream supersonic flow and the wedge boundary is proved . the problem is formulated as a one - phase free boundary problem , in which the transonic shock is treated as a free boundary . the full euler equations are decomposed into two algebraic equations and a first - order elliptic system of two equations in lagrangian coordinates . with careful elliptic estimates by using appropriate weighted hlder norms , the iteration map is defined and analyzed , and the existence of its fixed point is established by performing the schauder fixed point argument . the careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full euler equations .

the existence , uniqueness , and asymptotic behavior of steady transonic flows past a curved wedge , involving transonic shocks , governed by the two - dimensional full euler equations are established . the stability of both weak and strong transonic shocks under the perturbation of both the upstream supersonic flow and the wedge boundary is proved . the problem is formulated as a one - phase free boundary problem , in which the transonic shock is treated as a free boundary . the full euler equations are decomposed into two algebraic equations and a first - order elliptic system of two equations in lagrangian coordinates . with careful elliptic estimates by using appropriate weighted hlder norms , the iteration map is defined and analyzed , and the existence of its fixed point is established by performing the schauder fixed point argument . the careful analysis of the asymptotic behavior of the solutions reveals particular characters of the full euler equations .

1105.2209

i

the established evidence that neutrinos oscillate and possess small masses @xcite necessitates physics beyond the standard model ( sm ) , which could manifest itself at the cern large hadron collider ( lhc ) and/or in low energy experiments which search for the lepton flavour violation @xcite . consequently , models of neutrino mass generation which can be probed at present and forthcoming experiments are of great phenomenological interest . neutrinos may obtain mass via the vacuum expectation value ( vev ) of a neutral higgs boson in an isospin triplet representation @xcite . a particularly simple implementation of this mechanism of neutrino mass generation is the `` higgs triplet model '' ( htm ) in which the sm lagrangian is augmented solely by @xmath10 which is a @xmath1 triplet of scalar particles with hypercharge @xmath11 @xcite . in the htm , the majorana neutrino mass matrix @xmath12 ( @xmath13 ) is given by the product of a triplet yukawa coupling matrix @xmath14 and a triplet vev ( @xmath15 ) . consequently , the direct connection between @xmath14 and @xmath12 gives rise to phenomenological predictions for processes which depend on @xmath14 because @xmath16 has been restricted well by neutrino oscillation measurements @xcite . a distinctive signal of the htm would be the observation of doubly charged higgs bosons ( @xmath0 ) whose mass ( @xmath17 ) may be of the order of the electroweak scale . such particles can be produced with sizeable rates at hadron colliders in the processes @xmath4 @xcite and @xmath18 @xcite . the first searches for @xmath0 at a hadron collider were carried out at the fermilab tevatron , assuming the production channel @xmath4 and decay @xmath19 . the mass limits @xmath20 @xcite were derived , with the strongest limits being for @xmath21 @xcite . the branching ratios ( brs ) for @xmath19 depend on @xmath14 and are predicted in the htm in terms of the parameters of the neutrino mass matrix @xcite . detailed quantitative studies of br(@xmath19 ) in the htm have been performed in @xcite with particular emphasis given to their sensitivity to the majorana phases and the absolute neutrino mass i.e. parameters which can not be probed in neutrino oscillation experiments . a study on the relation between br(@xmath19 ) and the neutrinoless double beta decay can be seen in @xcite . simulations of the detection prospects of @xmath0 at the lhc with @xmath22 previously focussed on @xmath4 only @xcite , but recent studies now include the mechanism @xmath18 @xcite . the first search for @xmath0 at the lhc with @xmath23 @xcite has recently been performed for both production mechanisms @xmath4 and @xmath18 , for the decay channels @xmath19 and @xmath24 . in phenomenological studies of the htm , for simplicity it is sometimes assumed that @xmath0 and @xmath25 are degenerate , with a mass @xmath26 which arises from a bilinear term @xmath27 in the scalar potential . in this scenario the only possible decay channels for @xmath0 are @xmath19 and @xmath28 , and the branching ratios are determined by the magnitude of @xmath15 . however , quartic terms in the scalar potential break the degeneracy of @xmath0 and @xmath25 , and induce a mass splitting @xmath29 , which can be of either sign . if @xmath30 then a new decay channel becomes available for @xmath0 , namely @xmath31 . some attention has been given to the decay @xmath31 , and it has been shown that it can be the dominant channel over a wide range of values of @xmath32 and @xmath15 @xcite , even for @xmath33 . another scenario is the case of @xmath34 , which would give rise to a new decay channel for the singly charged scalar , namely @xmath2 . this possibility has been mentioned in the context of the htm in @xcite only . we will perform the first study of the magnitude of its branching ratio , as well as quantify its contribution to the production of @xmath0 at the lhc . has also been briefly mentioned in @xcite in the context of a model with an isospin 3/2 multiplet with hypercharge @xmath35 , which also includes triply charged higgs bosons . ] the decay rate for @xmath2 is easily obtained from the corresponding expression for the decay rate for @xmath31 , and thus one expects that @xmath2 will be sizeable over a wide range of values of @xmath32 and @xmath15 . we point out for the first time that the decay @xmath2 would give rise to an alternative way to produce @xmath0 in pairs ( @xmath36 ) , namely by the production mechanism @xmath18 followed by @xmath37 . production of @xmath36 can give rise to a distinctive signature of four leptons ( @xmath38 ) , and simulations and searches of this channel currently only assume production via the process @xmath4 . our work is organised as follows . in section ii we describe the theoretical structure of the htm . in section iii the decay @xmath2 is introduced . section iv contains our numerical analysis of the magnitude of the cross section for @xmath36 which originates from production via @xmath18 followed by the decay @xmath2 . conclusions are given in section v.

the existence of doubly charged higgs bosons ( @xmath0 ) is a distinctive feature of the higgs triplet model ( htm ) , in which neutrinos obtain tree - level masses from the vacuum expectation value of a neutral scalar in a triplet representation of @xmath1 . , the decays @xmath5 and @xmath6 from production of the neutral triplet scalars @xmath7 and @xmath8 would also provide an additional source of @xmath9 , which can subsequently decay to @xmath0 .

the existence of doubly charged higgs bosons ( @xmath0 ) is a distinctive feature of the higgs triplet model ( htm ) , in which neutrinos obtain tree - level masses from the vacuum expectation value of a neutral scalar in a triplet representation of @xmath1 . we point out that a large branching ratio for the decay of a singly charged higgs boson to a doubly charged higgs boson via @xmath2 is possible in a sizeable parameter space of the htm . from the production mechanism @xmath3 the above decay mode would give rise to pair production of @xmath0 , with a cross section which can be comparable to that of the standard pair - production mechanism @xmath4 . we suggest that the presence of a sizeable branching ratio for @xmath2 could significantly enhance the detection prospects of @xmath0 in the four - lepton channel . moreover , the decays @xmath5 and @xmath6 from production of the neutral triplet scalars @xmath7 and @xmath8 would also provide an additional source of @xmath9 , which can subsequently decay to @xmath0 .

1105.2209

c

doubly charged higgs bosons ( @xmath0 ) , which arise in the higgs triplet model ( htm ) of neutrino mass generation , are being searched for at the tevatron and at the lhc . we showed that @xmath0 can be produced from the decay of a singly charged higgs boson ( @xmath25 ) via @xmath304 , which can have a large branching ratio in a wide region of the parameter space of the htm . from the production mechanism @xmath305 , the above decay would give rise to pair production @xmath36 , with a number of events which can be comparable to that from the conventional mechanism @xmath4 . current simulations and searches for @xmath36 at the tevatron / lhc assume production solely from @xmath4 . the contribution from @xmath18 with decay @xmath304 would be an additional source of pair - produced @xmath0 , which should enhance the detection prospects in this channel ( e.g. four - lepton signatures if the decay mode @xmath19 is dominant ) . we also pointed out that production mechanisms involving the neutral triplet scalars ( @xmath7,@xmath8 ) of the htm can contribute to pair production @xmath36 through the decay chain @xmath306 followed by @xmath304 . we advocate dedicated simulations of @xmath18 with the decay @xmath304 ( and the analogous mechanisms with neutral scalars ) , and a comparison with @xmath4 .

we point out that a large branching ratio for the decay of a singly charged higgs boson to a doubly charged higgs boson via @xmath2 is possible in a sizeable parameter space of the htm . from the production mechanism @xmath3 the above decay mode would give rise to pair production of @xmath0 , with a cross section which can be comparable to that of the standard pair - production mechanism @xmath4 .

the existence of doubly charged higgs bosons ( @xmath0 ) is a distinctive feature of the higgs triplet model ( htm ) , in which neutrinos obtain tree - level masses from the vacuum expectation value of a neutral scalar in a triplet representation of @xmath1 . we point out that a large branching ratio for the decay of a singly charged higgs boson to a doubly charged higgs boson via @xmath2 is possible in a sizeable parameter space of the htm . from the production mechanism @xmath3 the above decay mode would give rise to pair production of @xmath0 , with a cross section which can be comparable to that of the standard pair - production mechanism @xmath4 . we suggest that the presence of a sizeable branching ratio for @xmath2 could significantly enhance the detection prospects of @xmath0 in the four - lepton channel . moreover , the decays @xmath5 and @xmath6 from production of the neutral triplet scalars @xmath7 and @xmath8 would also provide an additional source of @xmath9 , which can subsequently decay to @xmath0 .

1508.05999

i

the discovery of dirac fermions as low - energy quasi - particle excitations in graphene and on the surfaces of topological insulators has drawn significant attention in both fundamental physics research and device applications @xcite . since these dirac - like fermions propagate as massless relativistic particles they behave differently from the conventional charge carriers in metals , semiconductors , and insulators . recently , a new form of massless fermions with lifted degeneracy at the nodal point , from four - fold to two - fold , has been proposed to exist in condensed matter systems through a time reserval or inversion symmetry breaking mechanism . this symmetry breaking operation modifies the quasi - particle s dispersion relation from a dirac to a weyl equation.@xcite many theoretical proposals exist for realizing weyl semimetals that possess interesting physical properties , such as discontinuous fermi arcs and negative magnetoresistance due to the chiral anomaly.@xcite a weyl node with definite chirality is associated with the berry curvature and may be thought of as realizations of magnetic monopoles in momentum space.@xcite recent theoretical works have proposed the realization of the weyl semimetal state in the inversion symmetry breaking taas family.@xcite shortly after the prediction , the first weyl semimetal was experimentally discovered in taas @xcite . the electronic weyl semimetal state in taas was experimentally observed through photoemission spectroscopy@xcite . electrical transport experiments have shown that taas has very high mobility @xcite and , therefore , is consistent with the protected nature of the weyl fermions and reported signatures of the chiral anomaly @xcite . soon after the initial experimental discovery other independent photoemission experimental works have confirmed the weyl semimetal state in taas and , furthermore , the weyl state in other members of the same family , which includes nbas and tap . @xcite provided the inclusion of spin - orbit coupling , these four non - centrosymmetric compounds are proposed to realize weyl fermions without breaking time - reversal symmetry and , consequently , are easily studied under ambient conditions . for example , no external magnetic field or pressure is required for the realization of the weyl semimetal state in this taas family.@xcite conventional semimetals are materials that have a small overlap in energy between the valence and conduction bands . by contrast , a weyl semimetal has valence and conduction bands that touch at a set of discrete points in the bulk brillouin zone , called the weyl nodes . in the presence of additional doping , fermi pockets , or multiple weyl nodes at different energies , a weyl semimetal will naturally contain electron and hole charge carriers , giving rise to a compensated semimetal . this is indeed the case for the taas family of weyl materials as reported in photoemission and transport experiments @xcite the fermi surfaces can originate from the conduction or valence band crossing the fermi energy , the weyl cones , and their combinations . the charge carriers are expected to have small concentrations with a high mobility , at least for the weyl fermions . the interplay between tunable concentrations of multiple charge carriers , high fermi velocities , and the protected nature of the weyl fermion carriers suggests a new avenue for designing novel electronic devices . the weyl semimetals are also good candidates for exploring critical phenomena near the fermi energy , due to their small carrier concentrations and linear band touchings . therefore , it is of interest to explore the electronic structure of these four compounds to better understand their similarities and differences . previous theoretical studies of this family focused on establishing taas as a weyl semimetal and therefore only reported a few key aspects of the electronic structure for that purpose . on the other hand , many systematic details of the band structure , which are crucial for spectroscopy and transport studies , have not been studied . furthermore , a comparative study of the electronic structure of taas with the other members remains lacking . in this study , we perform a comprehensive first - principles calculation to explore the properties of fermi surfaces for the entire family of weyl semimetals , taas , tap , nbas , and nbp , and , thereby , providing the necessary building block for future investigations of weyl semimetals from a theoretical , experimental and application perspective . the paper is organized in the following manner : in section [ sec : computational ] we provide the computational details . in section [ sec : bandstructure ] , electronic band structures and density of states are studied to improve our basic understanding of these four compounds . in section [ sec : fermisurface ] , we discuss the details of the fermi velocities of weyl fermions and fermi surfaces . finally , in section [ sec : discussion ] we present a brief discussion covering the important conclusions reached .

the family of binary compounds including taas , tap , nbas , and nbp was recently discovered as the first realization of weyl semimetals . in order to develop a comprehensive description of the charge carriers in these weyl semimetals , we performed a detailed and systematic electronic band structure calculations which reveal the nature of fermi surfaces and their complex interconnectivity in taas , tap , nbas , and nbp . our work report the first comparative and comprehensive study of fermi surface topology and band structure details of all known members of the weyl semimetal family and provide the necessary building blocks for advancing our understanding of their unique topologically protected low - energy weyl fermion physics .

the family of binary compounds including taas , tap , nbas , and nbp was recently discovered as the first realization of weyl semimetals . in order to develop a comprehensive description of the charge carriers in these weyl semimetals , we performed a detailed and systematic electronic band structure calculations which reveal the nature of fermi surfaces and their complex interconnectivity in taas , tap , nbas , and nbp . our work report the first comparative and comprehensive study of fermi surface topology and band structure details of all known members of the weyl semimetal family and provide the necessary building blocks for advancing our understanding of their unique topologically protected low - energy weyl fermion physics .

1006.2307

i

many relevant properties of complex systems can be described by an appropriate network representation of their elements and interactions @xcite . most of these networks are directed , i. e. there is a directional relationship between two elements defining who influences who in a given order . among the class of directed networks , directed acyclic graphs -henceforth , dags- are an important subset lacking feedback loops . this is specially suitable for the representation of evolutionary , developmental and historical _ processes _ in which the time asymmetry determines a feed - forward ( acyclic ) flow of causal relations . in this context , dags constitute a formal representation of causal relations that display the direct effects of earlier events over latter ones . citation networks are among their most paradigmatic cases @xcite . in these networks nodes are scientific articles and directed links ( or arcs ) stand for bibliographic citations among them . according to a chronological order , directed links are established from former articles to newer ones in a feed - forward manner . in general , time - dependent processes have been formalized as dags . examples of that comprehend article and patent citation networks @xcite , decision jurisprudence processes @xcite and tree genealogies and phylogenies . moreover , other relevant systems such as standard electric circuits @xcite , feed - forward neural @xcite and transmission networks @xcite are also suitably represented as dags . the main objective of this paper is to explore the _ randomness _ -in topological terms- of real systems displaying a directed acyclic structure by the defintion a collection of randomization methods that preserves a fixed number of topological invariants . to this end , the design of null models to highlight the particular features characterizing a system with respect to a neutral or _ random _ scenario @xcite is needed . in this context , the so - called _ configuration model _ @xcite has been probed as a fruitful approximation to provide a null - model scenario of what is expected by _ chance _ in complex networks under the assumptions of sparseness , infinite size and lack of correlations . however , little attention has been paid concerning dags . indeed , a rigorous definition of random dag from its directed degree sequence has been recently proposed @xcite , rising the interest for its study through configuration model approach . borrowing the methodology to build random undirected graphs @xcite , degree sequence is visualized as a set of edge _ stubs_. hence a random dag is constructed by matching stubs according to certain order constraints until they are completely canceled @xcite . without neglecting the important advance it represents for the comprehension of acyclic networks , some problems arise in using this methodology as the null model reference of real nets . firstly , this methodology is dependent on how probable is to construct a graph from a degree sequence , since not all of them produce a graph , i.e. , they are not _ graphical_. additionally , configuration model assumptions are not fulfilled in real systems due to their finite size and the presence of densely connected regions . an alternative approach used in this work is based on iterative processes of edge rewiring over the graph , keeping the _ graphical _ condition during all the process of randomization . this is a relevant issue since the degree sequence , either directed or undirected , imposes a particular space of topological configurations rather limited -as we shall see in this work- for dags . attending to this approach we can estimate where a real graph is placed preserving a graphical ensemble that holds some topological invariants . the two fundamental topological invariants considered in this work for a null model comparison are the degree sequence ( either directed or undirected ) and the component structure . the both types of degree sequences and the degree distribution have been typically chosen as invariant in the random model construction @xcite . however , as is well known in random graph theory , the existence of some graph satisfying a given degree sequence does not guarantee a single connected component containing the whole set of nodes , except at high connectivities . therefore sparse networks representing connected systems are expected to be fragmented during a randomization process . this may be an undesirable effect when studying historical processes since it breaks the flow of causality . besides this problem , there are also real systems that display more than a single connected component . those disconnected components do not interact among them and , arguably , can be considered to be independent systems in terms of causality . it is worth to note that preservation of connected component in graph randomization processes has recently raised the interest of network community @xcite . according to the above considerations , in order to produce comparable ensembles for the evaluation of the randomness of a real dag , we propose a collection of four randomization methods for dags that ensure the topological invariants mentioned above . these randomization techniques were applied to two extreme -in terms of degree - degree relations- network models : an erds rnyi dag and a highly ordered graph called _ snake_-dag . our methodology was then applied to three real dags : a citation network , a phd - student advisor network and the cell lineage in the development of _ caebnorhabditis elegans _ worm . the paper is organized as follows : section ii offers the basic concepts related to dags . section iii explicitly defines the set of four randomization algorithms according to different topological invariants . section iv describes and characterizes the randomness indicators and apply the randomization processes to the systems under study : two toy models -which enable us to validate the performance of the algorithms- and three real systems . section v discusses the relevance of the obtained results .

the feed - forward relationship naturally observed in time - dependent processes and in a diverse number of real systems -such as some food - webs and electronic and neural wiring- can be described in terms of so - called directed acyclic graphs ( dags ) . an important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs , thereby quantifying the _ randomness _ of the real systems with respect to suitable null models . this approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so - called _ a highly ordered dag , called _ snake_-graph and a erdos - rnyi dag were used to validate the performance of the algorithms . finally , three real case studies , namely , the _ c. elegans _ cell lineage network , a phd student - advisor network and the milgram s citation network were analyzed using each randomization method . conversely , if the direction of the links is conserved throughout the randomization process , disorder indicators are close to the obtained from the null - model ensemble , although some deviations are observed .

the feed - forward relationship naturally observed in time - dependent processes and in a diverse number of real systems -such as some food - webs and electronic and neural wiring- can be described in terms of so - called directed acyclic graphs ( dags ) . an important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs , thereby quantifying the _ randomness _ of the real systems with respect to suitable null models . this approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so - called _ configuration model_. in this paper we analyze four methods of dag randomization as defined by the desired combination of topological invariants ( directed and undirected degree sequence and component distributions ) aimed to be preserved . a highly ordered dag , called _ snake_-graph and a erdos - rnyi dag were used to validate the performance of the algorithms . finally , three real case studies , namely , the _ c. elegans _ cell lineage network , a phd student - advisor network and the milgram s citation network were analyzed using each randomization method . results show how the interpretation of degree - degree relations in dags respect to their randomized ensembles depend on the topological invariants imposed . in general , real dags provide disordered values , lower than the expected by chance when the directedness of the links is not preserved in the randomization process . conversely , if the direction of the links is conserved throughout the randomization process , disorder indicators are close to the obtained from the null - model ensemble , although some deviations are observed .

1201.6265

i

the determination of the nuclear mass composition of uhecr ( ultra high energy cosmic rays ) is fundamental to unveil the origin of the most energetic particles known in nature . uhecr are detected by means of the extensive air showers created in the earth s atmosphere , which are composed by a cascade of hadrons and electromagnetic ( em ) particles . the depth at which the em shower reaches its maximum , @xmath0 , strongly correlates with the depth where the primary firstly interacted . the @xmath0-distribution carries information about the primary particle and the physical processes in the cascade . the hadronic cascade is composed mostly by pions , of which the charged pions might decay in flight into a muon and a neutrino . due to their long lifetime and low cross section , muons can leave the core of the hadronic cascade traveling kilometers away and be detected . electrons spread out in time and space because of coulomb scattering , whereas muons practically travel following straight lines . the time structure of the shower disc encodes the history of the shower , allowing us to recover information about the longitudinal evolution by analyzing the time distribution of the particles arriving at ground level . the pierre auger observatory , located on the high plateau of the pampa amarilla , is the largest cosmic ray observatory ever built . its hybrid design allows to collect the shower particles by a surface detector ( sd ) and to observe the longitudinal development of the em profile by collecting the uv light with a fluorescence detector ( fd ) . the sd spans 1600 cherenkov detectors in a 1.5 km triangular grid over 3000 km@xmath1 , whereas the fd is composed by 24 telescopes distributed over 4 sites overlooking the array . the baseline design is being complemented with enhancements both on the sd and fd , and new detection techniques @xcite . in this paper we present the latest @xmath2 and rms-@xmath0 results as a function of energy , and the @xmath0-distributions for the highest and lowest energy bins . we also present the evolution with energy of sd observables extracted from the time distributions of the signal which are sensitive to the longitudinal evolution of the shower . we compare our results with the predictions of hadronic interaction models @xcite .

the fluorescence detector of the pierre auger observatory measures the atmospheric depth , @xmath0 , where the longitudinal profile of the high energy air showers reaches its maximum . this is sensitive to the nuclear mass composition of the cosmic rays . due to its hybrid design , the pierre auger observatory also provides independent experimental observables obtained from the surface detector for the study of the nuclear mass composition . we present @xmath0-distributions and an update of the average and rms values in different energy bins and compare them to the predictions for different nuclear masses of the primary particles and hadronic interaction models . we also present the results of the composition - sensitive parameters derived from the ground level component .

the fluorescence detector of the pierre auger observatory measures the atmospheric depth , @xmath0 , where the longitudinal profile of the high energy air showers reaches its maximum . this is sensitive to the nuclear mass composition of the cosmic rays . due to its hybrid design , the pierre auger observatory also provides independent experimental observables obtained from the surface detector for the study of the nuclear mass composition . we present @xmath0-distributions and an update of the average and rms values in different energy bins and compare them to the predictions for different nuclear masses of the primary particles and hadronic interaction models . we also present the results of the composition - sensitive parameters derived from the ground level component .

1306.5084

i

some even - even nuclei are energetically forbidden to decay via single @xmath12 emission , while the decay via emission of two electrons and two neutrinos is energetically allowed . the experimentally observed neutrino accompanied double beta ( @xmath13 ) decay is a second order weak process with half lives of the order of 10@xmath14 yr @xcite . the decay process without neutrino emission , neutrinoless double beta ( @xmath0 ) decay , is of fundamental relevance as its observation would imply lepton number violation indicating physics beyond the standard model of particle physics . the gerda experiment @xcite is designed to search for @xmath0 decay in the isotope @xmath1ge . this process is identified by a monoenergetic line in the energy sum spectrum of the two electrons at 2039 kev @xcite , the @xmath2-value of the decay . the two precursor experiments , the heidelberg moscow ( hdm ) and the international germanium experiment ( igex ) , have set limits on the half live @xmath15 of @xmath0 decay @xmath15@xmath161.9@xmath17 yr @xcite and @xmath15@xmath161.6@xmath17 yr @xcite ( 90% c.l . ) , respectively . a subgroup of the hdm experiment claims to have observed @xmath0 decay with a central value of the half life of @xmath15=1.19@xmath17 yr @xcite . this result was later refined using pulse shape discrimination ( psd ) @xcite yielding a half life of @xmath15=2.23@xmath17 yr . several inconsistencies in the latter analysis have been pointed out in ref . @xcite . the design of the gerda apparatus for the search of @xmath0 decay follows the suggestion to operate high purity germanium ( hpge ) detectors directly in a cryogenic liquid that serves as cooling medium and simultaneously as ultra - pure shielding against external radiation @xcite . gerda aims in its phase i to test the hdm claim of a signal and , in case of no confirmation , improve this limit by an order of magnitude in phase ii of the experiment . prerequisites for rare - event studies are @xmath18 extremely low backgrounds , usually expressed in terms of a background index ( bi ) measured in cts/(kev@xmath3kg@xmath3yr ) , and @xmath19 large masses and long measuring times , expressed as exposure . reducing the background and establishing a radio - pure environment is an experimental challenge . proper analysis methods must be applied to guarantee an unbiased analysis . the gerda collaboration has blinded a region of @xmath2@xmath2020 kev during the data taking period @xcite . during this time , analysis methods and background models have been developed and tested . the latter is described in this paper together with other parameters demonstrating the data quality . the raw data are converted into energy spectra . if the energies of individual events fall within a range @xmath2@xmath2120 kev , these events are stored during the blinding mode in the backup files only . they are not converted to the data file that is available for analysis . this blinding window is schematically represented in fig . [ fig : windows ] by the yellow area , including the red range . after fixing the calibration parameters and the background model , the blinding window was partially opened except the peak range at @xmath2 , indicated in red in fig . [ fig : windows ] . the blue range covers the energies from 100 kev to 7.5 mev . the data from this energy range were available for analysis all the time . the observable @xmath11 lines can be used to identify background sources . a range between 1930 kev and 2190 kev was then used to determine the bi . the energy regions around significant @xmath11 lines are excluded in the latter , as shown schematically in fig [ fig : windows ] . representation of energy spectra for definition of the energy windows used in the blind analysis . ] data were taken until until may 2013 . these data provide the exposure for phase i. the data used in this analysis of the background are a subset containing data taken until march 2013 . the extraction of the background model is described in detail in this paper . in the process , the necessary parameters are defined for the upcoming @xmath0 analysis . an important feature is the stable performance of the germanium detectors enriched in @xmath1ge ; this is demonstrated for the complete data taking period ( sec . [ sec : exp ] ) . the data with exposure is used to interpolate the background within @xmath22 . the expectation for the bi is given in this paper before unblinding the data in the energy range @xmath22 , the region of highest physics interest . the paper is organized as follows : after presenting the experimental details , particularly on the detectors used in phase i of the gerda experiment , coaxial and bege type ( sec . [ sec : exp ] ) , the spectra and the identified background sources will be discussed ( sec . [ sec : spectradata ] and [ sec : back ] ) . these are the basic ingredients for the background decomposition for the coaxial detectors ( sec . [ sec : modeling ] ) and for the bege detectors ( sec . [ sec : begemodel ] ) . the models work well for both types of detectors . after cross checks of the background model ( sec . [ sec : cross - checks ] ) the paper concludes with the prediction for the background at @xmath2 and the prospective sensitivity of gerda phase i ( sec . [ sec : extrapol ] ) .

the germanium detector array ( ) experiment at the gran sasso underground laboratory ( lngs ) of infn is searching for neutrinoless double beta ( @xmath0 ) decay of @xmath1ge . the signature of the signal is a monoenergetic peak at 2039 kev , the @xmath2 value of the decay . to avoid bias in the signal search the main parameters needed for the @xmath0 analysis are described . has been used to test if the predictions of the background model are consistent .

the germanium detector array ( ) experiment at the gran sasso underground laboratory ( lngs ) of infn is searching for neutrinoless double beta ( @xmath0 ) decay of @xmath1ge . the signature of the signal is a monoenergetic peak at 2039 kev , the @xmath2 value of the decay . to avoid bias in the signal search , the present analysis does not consider all those events , that fall in a 40 kev wide region centered around @xmath2 . the main parameters needed for the @xmath0 analysis are described . a background model was developed to describe the observed energy spectrum . the model contains several contributions , that are expected on the basis of material screening or that are established by the observation of characteristic structures in the energy spectrum . the model predicts a flat energy spectrum for the blinding window around @xmath2 with a background index ranging from 17.6 to 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . a part of the data not considered before has been used to test if the predictions of the background model are consistent . the observed number of events in this energy region is consistent with the background model . the background at @xmath2 is dominated by close sources , mainly due to @xmath5k , @xmath6bi , @xmath7th , @xmath8co and @xmath9 emitting isotopes from the @xmath10ra decay chain . the individual fractions depend on the assumed locations of the contaminants . it is shown , that after removal of the known @xmath11 peaks , the energy spectrum can be fitted in an energy range of 200 kev around @xmath2 with a constant background . this gives a background index consistent with the full model and uncertainties of the same size . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

1306.5084

i

the background model developed has some predictive power that can be checked with the available data . this section describes cross checks performed on the background model . from the best fit models the resulting half life @xmath57 for @xmath13 decay can be extracted . @xmath57 is calculated using the relation @xmath58 where @xmath59 is the best fit number of @xmath13 decays derived from the individual model . the efficiency @xmath60 is given by the weighted detection efficiency of @xmath13 decays in the fit range , @xmath61 , @xmath62 table [ tab:2vbb_half_lives ] gives the half lives extracted from the different background models . all results are consistent with the earlier @xmath13 analysis @xcite within the uncertainties . note , that a three times larger exposure was available for this analysis as compared to the analysis in ref . @xcite while systematic uncertainties are not considered . lrl model & [ kg@xmath3yr ] & @xmath57@xmath63yr + ' '' '' _ gold - coax _ minimum & 15.40 & 1.92@xmath64 + ' '' '' _ gold - coax _ maximum & 15.40 & 1.92@xmath65 + ' '' '' _ gold - nat _ minimum & 3.13 & 1.74@xmath66 + ' '' '' _ sum - bege _ & 1.80 & 1.96@xmath67 + ' '' '' analysis in ref . @xcite & 5.04 & 1.84@xmath68 + at energies below 600 kev the energy spectrum is dominated by @xmath69ar with an activity of @xmath70=[1.01@xmath210.02(stat ) @xmath210.08(syst ) ] bq / kg @xcite homogeneously distributed in lar . this part of the spectrum has not been included into the background fit to avoid uncertainties due to the n@xmath32 dead layer thickness and the theoretical shape of the beta decay spectrum . a strong @xmath11 line at 352 kev is , however , expected from decays of @xmath6bi in the vicinity of the detectors . the intensity of this line depends strongly on the distance of the @xmath6bi contamination from the detectors . hence , this cross check can give a hint on how realistic the assumed distribution of the @xmath6bi contamination is . the minimum ( maximum ) model predicts 20.1@xmath71 ( 17.5@xmath72 ) counts/(kg@xmath3yr ) in the peak while a fit of a gaussian plus a linear background to the data gives 20.4@xmath73 counts/(kg@xmath3yr ) for the _ gold - coax _ data set . [ fig:352kev ] shows the energy spectrum of the _ gold - coax _ data set in the energy region between 310 and 440 kev . the gaussian plus linear background fit to the data as well as the minimum model prediction without the @xmath69ar contribution dominating the spectrum in this energy region is shown . for the _ gold - nat _ data set the minimum model prediction of ( 22.1@xmath74 counts/(kg@xmath3yr ) is also consistent with the observed ( 25.6 @xmath75 6.2 ) counts/(kg@xmath3yr ) . this cross check makes it possible to distinguish between the locations of @xmath6bi contaminations if it is assumed that the decays of @xmath6bi and @xmath6pb happen at the same location . it excludes the results for @xmath6pb contamination in or on the radon shroud as the best fit maximum model for the _ gold - nat _ data set predicts . this model predicts only ( 4.6@xmath76 counts/ ( kg@xmath3yr ) . this cross check confirms the indication from the background model that close sources are responsible for most of the @xmath6bi background contribution . energy spectrum of the _ gold - coax _ data set ( filled histogram ) and the minimum model prediction ( red histogram ) . the data and the model spectrum are fitted with a gaussian plus linear background ( dashed lines ) . ] r|r|ccc|ccciso- & energy & & + tope & ' '' '' [ kev ] & + & ' '' '' & global & global & fit to & global & global & fit to + & & analysis & analysis & data & analysis & analysis & data + & & ( min . fit ) & ( max . fit ) & & ( min . fit ) & ( max . fit ) & + @xmath39k & 1460.8 & 11.9 [ 10.6,13.6 ] & 11.8 [ 10.6,13.6 ] & 13.6[12.5,15.0 ] & 19.4 [ 16.7,23.0 ] & 19.8 [ 16.7,23.1 ] & 18.3 [ 15.7,21.4 ] + @xmath5k & 1524.7 & 61.2 [ 59.3,63.8 ] & 61.4 [ 48.5 , 66.2 ] & 60.3[58.1 , 62.5 ] & 75.0 [ 70.2 , 82.4 ] & 75.6 [ 49.1 , 78.3 ] & 73.8 [ 69.1 , 80.1 ] + @xmath8co & 1173.2 & 2.5 [ 1.6 , 3.7 ] & 1.6 [ 0.6 , 2.9 ] & 4.2 [ 2.8 , 5.6 ] & 2.0 [ 0.1 , 4.6 ] & 1.9 [ 0.1 , 3.2 ] & @xmath403.8 + & 1332.3 & 2.3 [ 1.4 , 3.4 ] & 1.5 [ 0.5 , 2.6 ] & @xmath401.6 & 1.9 [ 0.1 , 4.4 ] & 1.7 [ 0.1 , 2.8 ] & 3.3 [ 1.6 , 5.2 ] + @xmath7ac & 911.2 & 3.8 [ 2.2 , 5.8 ] & 3.4 [ 1.0 , 3.6 ] & 3.9 [ 2.2 , 5.6 ] & 6.1 [ 3.9 , 8.6 ] & 5.4 [ 0.5 , 9.8 ] & 4.9 [ 2.7 , 7.3 ] + & 969.0 & 2.7 [ 1.5 , 4.1 ] & 2.8 [ 0.8 , 2.8 ] & 3.5 [ 1.8 , 5.0 ] & 4.4 [ 2.8 , 6.2 ] & 3.9 [ 0.4 , 7.1 ] & 4.8 [ 2.6 , 7.4 ] + @xmath77tl & 583.2 & 2.9 [ 2.5 , 3.5 ] & 1.3 [ 0.3 , 2.0 ] & 3.9 [ 1.8 , 5.7 ] & 3.0 [ 1.8 , 4.7 ] & @xmath400.9 & 2.5 [ 0.4 , 4.6 ] + & 2614.5 & 1.4 [ 1.2 , 1.7 ] & 1.0 [ 0.2 , 1.5 ] & 1.2 [ 0.9 , 1.5 ] & 1.5 [ 0.9 , 2.4 ] & 1.5 [ 0.0 , 6.7 ] & 1.4 [ 0.6 , 2.3 ] + @xmath6pb & 351.9 & 20.1 [ 17.9,22.7 ] & 17.5 [ 4.2,24.5 ] & 20.4 [ 16.2,24.8 ] & 22.1 [ 17.7,27.3 ] & 4.6 [ 3.1,6.0 ] & 25.6 [ 18.1,34.1 ] + @xmath6bi & 609.3 & 11.2 [ 10.0 , 12.6 ] & 8.0 [ 2.0 , 11.2 ] & 10.0 [ 8.0 , 12.3 ] & 11.2 [ 9.0 , 13.8 ] & 6.5 [ 4.6 , 8.6 ] & 7.6 [ 4.8 , 11.0 ] + & 1120.3 & 2.6 [ 2.3 , 2.9 ] & 1.8 [ 0.4 , 2.5 ] & @xmath403.1 & 2.6 [ 2.1 , 3.2 ] & 3.0 [ 2.1 , 3.9 ] & 4.0 [ 1.8 , 6.3 ] + & 1729.6 & 1.0 [ 0.9 , 1.1 ] & 1.0 [ 0.2 , 1.4 ] & 0.5 [ 0.2 , 0.9 ] & 1.3 [ 1.0 , 1.6 ] & 0.8 [ 0.5 , 1.1 ] & 0.9 [ 0.3 , 1 . ] + & 1764.5 & 3.6 [ 3.2 , 4.1 ] & 2.7 [ 0.7 , 3.8 ] & 3.1 [ 2.6 , 3.7 ] & 4.1 [ 3.3 , 5.1 ] & 3.7 [ 2.5 , 4.9 ] & 3.5 [ 2.4 , 5.0 ] + & 1847.4 & 0.6 [ 0.5 , 0.7 ] & 0.6 [ 0.1 , 0.8 ] & 0.6 [ 0.3 , 1.0 ] & 0.7 [ 0.6 , 0.9 ] & 0.5 [ 0.3 , 0.6 ] & 1.2 [ 0.5 , 2.1 ] + & 2204.2 & 1.0 [ 0.9 , 1.1 ] & 0.8 [ 0.2 , 1.1 ] & 0.8 [ 0.5 , 1.2 ] & 1.2 [ 1.0 , 1.5 ] & 1.3 [ 0.9 , 1.7 ] & 0.8 [ 0.2,1.6 ] + & 2447.9 & 0.3 [ 0.27 , 0.34 ] & 0.2 [ 0.05 , 0.3 ] & 0.2 [ 0.1 , 0.4 ] & 0.3 [ 0.2 , 0.4 ] & 0.4 [ 0.3 , 0.5 ] & @xmath401.8 + as the fit has been performed with a binning larger than the energy resolution of the detectors , the information from the line intensities is not maximized in the fitting procedure . hence , it is instructive to cross check the line intensities obtained from fitting the peaks with a gaussian plus linear background in the different data sets with the expectation from the models . table [ tab : backgroundlines ] compares the @xmath11-line intensities from the minimum and maximum models to those obtained from a fine binned analysis , i.e. a fit to data . note , that for some of the @xmath11 peaks no fit could be performed due to limited number of events in the peak region or the low intensity of the @xmath11 line compared to the other background contributions . in those cases the number of counts in the @xmath213@xmath78 energy range around the peak positions were used . the background has been estimated according to the continuum seen in the @xmath215@xmath78 side bands at lower and higher energies around the peak . a narrower side band is used when there is a second line close to the peak . the intensities of the @xmath11 lines are obtained by marginalizing the posterior probability distribution of the signal rate . the uncertainties on the predicted rate by the global models are due to the fit uncertainty on the parameters of the model components that give contribution to the @xmath11-ray line . the statistical uncertainties due to the simulated number of events is on the order of 0.1% , i.e. negligible compared to the fit uncertainty . there is excellent agreement between the numbers from the global analysis and those from the fine - binned analysis . to check for stability , the fits were performed using different binnings . as the energy resolution of the detectors is around 4.5 kev at @xmath2 and the calibration at higher energies e@xmath165 mev , relevant for the @xmath9 model is precise to about 10 kev , the lowest binning chosen was 10 kev . also a 50 kev binning was performed . the activities of different components derived from the fits with different binnings do not vary outside the uncertainties given for the 30 kev binning fits . additionally it was checked whether the overall goodness of fit and the predicted bi and individual contributions in the region of interest changes if biases are introduced to the fits by single strong assumptions on individual background components . minimum model fits for the _ gold - coax _ and _ gold - nat _ data sets were performed with the following individual modifications : @xmath7th and @xmath7ac are only in or on the radon shroud ; no @xmath6bi is present on the p@xmath56 surface ; @xmath5k is only on the p@xmath56 surface ; @xmath5k is present on the p@xmath56 surface ; @xmath8co is only inside the crystal , @xmath8co is only inside the detector assembly . except for the unrealistic assumption that all @xmath5k comes from p@xmath56 surface contaminations all fits describe the measured spectrum reasonably well . the prediction for the bi at the region of interest varies by 10% between the different models for the _ gold - coax _ data set and by 15% for the _ gold - nat _ data set . the predictions for the activities of the individual components of the different models are consistent within the 68% uncertainty range quoted in table [ tab : fits_results_golden ] . an important contribution to the background model are surface events from @xmath10ra daughters . these include the decays of @xmath6bi and @xmath6po . @xmath6po has a half life of only 164.4 @xmath29s . hence , a number of events is expected where a low energy event from the @xmath6bi decay is followed by a high energy @xmath9 event from the @xmath6po decay in the same detector , a bipo tag . the data reduction includes cuts that remove pile up events . as the half life of @xmath6po is of the order of the decay time of the preamplifier signal , the analysis is not tailored to reconstruct typical bipo events . hence it is difficult to quantify precisely the efficiency for this tag . nevertheless , for the purpose of a qualitative statement an order of magnitude guess is made : an efficiency of 50% is assumed for the bipo recognition efficiency . using the number for the _ gold - coax _ data set obtained by the marginalized probability density function of the fit the number of detected @xmath79po surface events is 13.5 being reduced to approximately seven events from @xmath6bi decays on the surface that can lead to energy deposition in the detector active volume ( the decrease being due to the decay nucleus recoiling away from the surface ) . with an efficiency of the order of 50% to detect the bipo tag only roughly 3 to 4 bipo events are expected . in the _ gold - coax _ data set in total 5 events have been found ( 2 in ang 2 , 2 in ang 3 and 1 in rg 1 ) that satisfy the criteria for a bipo tag . a mono - parametric pulse shape analysis technique for the identification of surface interactions on the p@xmath32 electrode of coaxial detectors has been recently developed and applied on phase i data @xcite . the method is based on a cut on the rise time of the charge pulses computed between 5% and 50% of the maximum amplitude . the cut level is calibrated on experimental data using the pure sample of high - energy @xmath9-induced events . the analysis has been extended to the entire _ gold - coax _ data set . fixing the cut to accept 95% of the events occurring in the proximity of the @xmath80 electrode , in the energy region of interest 43% of the events survive the cut . part of the events surviving the cut is expected to be due to @xmath11 interactions in the proximity of the @xmath80 surface . applying the corrections described in ref . @xcite , the total amount of @xmath9 and @xmath12 induced events on the p@xmath32 electrode is estimated to be between 15% and 35% of the number of events in the energy region of interest . this result is consistent with the number of decays on the p@xmath32 surface predicted by the minimal model ( 20.5@xmath212.7)% , given by the @xmath9 emitting isotopes plus @xmath6bi . it is slightly lower compared to the maximal background model that requires 50% considering @xmath9 , @xmath6bi and @xmath5k on the p@xmath32 surface . as a large fraction of the contaminations are , according to the background model(s ) , located inside the detector array ( i.e. in the detector assembly , or in lar close to the surfaces of the detectors ) , a significant number of events are expected to have coincident hits in two detectors . the efficiency to detect coincident events is expected to be increased with respect to single @xmath11 emitters for decays of isotopes with emission of multiple @xmath11 rays such as @xmath5k , @xmath8co , @xmath6bi and @xmath77tl . coincident spectra are , thus , sensitive to differences in source locations . a sum coincidence spectrum was produced for the _ gold - coax _ data set by summing the energies of all detectors in an event and filling the corresponding bin of the histogram . also a single coincidence spectrum was produced by filling the corresponding bin of the histogram for each individual detector separately . the same procedure as for the minimum fit model ( see sec . [ sec : modeling ] ) was applied to get best fit coincidence models for the single and sum spectra . the results for the activities obtained from the minimum model best fit to the sum spectrum ( except for @xmath8co , where the single spectrum was used ) are summarized in table [ tab : fits_results_golden ] . the obtained activities from coincident and single detector spectra are consistent with each other . note , that the simulations were not tuned for the coincidence analysis . the background source distribution was simplified in the simulation , while small changes in source location , especially within the detector array , can have significant effects on the coincidence efficiencies . the fact that the @xmath5k activity derived from the coincidence fit is slightly higher than for the minimum and maximum models of the _ gold - coax _ and _ gold - nat _ data sets may be a hint that the distribution of @xmath5k in lar is not homogeneous . the consistency between the derived activities from coincident and single detector spectra support the result of the background model that the spectrum around @xmath2 is dominated by contaminants close to the detectors .

the model contains several contributions , that are expected on the basis of material screening or that are established by the observation of characteristic structures in the energy spectrum . the individual fractions depend on the assumed locations of the contaminants . this gives a background index consistent with the full model and uncertainties of the same size . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

the germanium detector array ( ) experiment at the gran sasso underground laboratory ( lngs ) of infn is searching for neutrinoless double beta ( @xmath0 ) decay of @xmath1ge . the signature of the signal is a monoenergetic peak at 2039 kev , the @xmath2 value of the decay . to avoid bias in the signal search , the present analysis does not consider all those events , that fall in a 40 kev wide region centered around @xmath2 . the main parameters needed for the @xmath0 analysis are described . a background model was developed to describe the observed energy spectrum . the model contains several contributions , that are expected on the basis of material screening or that are established by the observation of characteristic structures in the energy spectrum . the model predicts a flat energy spectrum for the blinding window around @xmath2 with a background index ranging from 17.6 to 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . a part of the data not considered before has been used to test if the predictions of the background model are consistent . the observed number of events in this energy region is consistent with the background model . the background at @xmath2 is dominated by close sources , mainly due to @xmath5k , @xmath6bi , @xmath7th , @xmath8co and @xmath9 emitting isotopes from the @xmath10ra decay chain . the individual fractions depend on the assumed locations of the contaminants . it is shown , that after removal of the known @xmath11 peaks , the energy spectrum can be fitted in an energy range of 200 kev around @xmath2 with a constant background . this gives a background index consistent with the full model and uncertainties of the same size . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

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ll|rcrc|rc|rc|c & & & & & exp . from + component & location & & & & & screening + & & + ' '' '' total & & 18.5 & [ 17.6,19.3]&21.9 & [ 20.7,23.8 ] & 29.6 & [ 27.1,32.7 ] & 38.1 & [ 32.2,43.3 ] & + ' '' '' @xmath5k & lar homogeneous & 3.0 & [ 2.9,3.1 ] & 2.6 & [ 2.0,2.8 ] & 2.9 & [ 2.7,3.2 ] & 2.0 & [ 1.8,2.3 ] & + @xmath5k & p@xmath32 surface & & & 4.6 & [ 1.2,7.4 ] & & & & & + @xmath5k & n@xmath32 surface & & & 0.2 & [ 0.1,0.4 ] & & & 20.8 & [ 6.8,23.7 ] & + @xmath8co & det . assembly & 1.4 & [ 0.9,2.1 ] & 0.9 & [ 0.3,1.4 ] & 1.1 & [ 0.0,2.5 ] & & @xmath404.7 & + @xmath8co & germanium & 0.6 & @xmath160.1 @xmath26 ) & 0.6 & @xmath160.1 @xmath26 ) & 9.2 & [ 4.5,12.9 ] & 1.0 & [ 0.3,1.0 ] & + @xmath31ge & germanium & & & & & & & & 1.5 ( @xmath406.7 ) & + @xmath6bi & det . assembly & 5.2 & [ 4.7,5.9 ] & 2.2 & [ 0.5,3.1 ] & 4.9 & [ 3.9,6.1 ] & 5.1 & [ 3.1,6.9 ] & @xmath412.8 + @xmath6bi & lar close to p@xmath32 & & & 3.1 & @xmath404.7 & & & & & @xmath400.7 + @xmath6bi & p@xmath32 surface & 1.4 & [ 1.0,1.8 ] @xmath26 ) & 1.3 & [ 0.9,1.8 ] @xmath26 ) & 3.7 & [ 2.7,4.8 ] @xmath26 ) & 0.7 & [ 0.1,1.3 ] @xmath26 ) & + @xmath6bi & radon shroud & & & 0.7 & @xmath403.5 & & & & & + @xmath7th & det . assembly & 4.5 & [ 3.9,5.4 ] & 1.6 & [ 0.4,2.5 ] & 4.0 & [ 2.5,6.3 ] & 4.2 & [ 1.8,8.4 ] & @xmath400.3 + @xmath7th & radon shroud * ) & & & 1.7 & @xmath402.9 & & & & & @xmath411.0 + @xmath9 model & p@xmath32 surface and & 2.4&[2.4,2.5 ] & 2.4 & [ 2.3,2.5 ] & 3.8 & [ 3.5,4.2 ] & 1.5 & [ 1.2,1.8 ] & + & lar close to p@xmath32 & & & & & & & & & + @xmath26 ) prior : discussed in sec . [ sec : modeling ] + @xmath81 ) representing all distant sources including the heat exchanger , the wall of the steel cryostat and the calibration source at the bottom of the tank . the background models obtained by global fits in the 570 - 7500 kev region allow to predict the individual background contributions and the total background at @xmath2 . table [ tab : background_components ] lists the predictions for the bi from different contributions in a 10 kev window for coaxial detectors and in a 8 kev window for bege detectors around @xmath2 for different data sets . the results obtained from the best fit parameters are quoted together with the smallest 68% interval of the marginalized distributions of the parameters . if the maximum of the marginalized distribution is at zero a 90% upper limit is given . for the case of an internal @xmath8co contamination a 90% lower limit is given , because a higher contamination gives a better fit , however , is constrained by prior knowledge of above ground exposure to cosmic rays . according to the models the main contributions to the background at @xmath2 are due to the @xmath9-emitting isotopes in the @xmath10ra decay chain , @xmath5k , @xmath8co , @xmath6bi and @xmath7th . the fraction with which each component contributes depends on the assumed source location . tab . [ tab : background_components ] also lists the bis expected from the screening measurements as reported in tab . [ tab : thorium ] . the bis due to the individual identified components do not match well with the bis derived from the background model , indicating that the unidentified close - by @xmath6bi and @xmath7th contributions have to be present . [ fig:0nbb_region ] shows the best fit minimum and maximum models and the individual contributions together with the observed spectrum around @xmath2 for the _ gold - coax _ data set . the spectral shapes of the best fit models are constant around @xmath2 . no peaks are predicted in the blinded regions . this indicates that the bi at @xmath2 can be estimated by interpolating the results of a fit to the observed number of events outside the signal search window . the window to be used for this estimation is chosen as sum of the 19302019 kev , 20592099 kev , 21092114 kev and 21242190 kev intervals for a total width of 200 kev . the bi evaluation window excludes the central 40 kev window around @xmath2 and the regions within @xmath215 kev from the @xmath11 lines expected from the background model namely , single escape peak from @xmath77tl at 2104 kev and the @xmath6bi @xmath11 line at 2119 kev . the resulting background indices from the interpolation are listed in table [ tab : extrapolated_bi ] for different data sets together with the prediction of the background models for comparison . the lower panels of the plots in fig . [ fig:0nbb_region ] demonstrate that the background model can be described by a constant in the bi evaluation windows . the difference in the resulting bi is less than 1% if a linear instead of a constant distribution is assumed . the statistical uncertainty for the approximation of the bi by an interpolation is of the same size as the systematic uncertainty expected by the model . lccc & _ gold - coax _ & _ gold - nat _ & _ sum - bege _ + ' '' '' & + & + interpolation & 17.5 [ 15.1,20.1]&30.4 [ 23.7,38.4 ] & 36.1 [ 26.4,49.3 ] + minimum & 18.5 [ 17.6,19.3]&29.6 [ 27.1,32.7 ] & 38.1 [ 32.2,43.3 ] + maximum & 21.9 [ 20.7,23.8]&37.1 [ 32.2,39.2 ] & + ' '' '' & + & 30 kev & 40 kev & 32 kev + data & 13 & 5 & 2 + minimum & 8.6 [ 8.2,9.1 ] & 3.5 [ 3.2,3.8 ] & 2.2 [ 1.9,2.5 ] + maximum & 10.3 [ 9.7,11.1 ] & 4.2 [ 3.8,4.6 ] & + the global fits were performed by excluding the central 40 kev region around @xmath2 which was completely blinded until may 2013 . thereafter , a 30 kev ( 32 kev ) window was opened for analysis by keeping the central 10 kev ( 8 kev ) window still blinded for the enriched coaxial ( bege ) detectors . the natural detector gtf 112 was completely unblinded . the first step of unblinding gives the possibility to compare the model predictions to the observed number of events in those regions as a consistency check for the model . table [ tab : extrapolated_bi ] also lists the predicted and observed number of events in these energy regions for different data sets . in total 13 events were observed in the unblinded 30 kev window of the _ gold - coax _ data set . the predictions in this window were 8.6 events from minimum and 10.3 events from maximum model . the probability to observe 13 events or more given the predictions are 10% and 24% , respectively . in the _ gold - nat _ data set 5 events were found in the 40 kev unblinded window , resulting in a 27% probability for the minimum model prediction of 3.5 events and a 41% probability for the maximum model prediction of 4.2 events . for the _ sum - bege _ data set there is a perfect agreement between the observed two events and the expectation of 2.2 events from the model . if the additional events seen in the 30 kev unblinded window are included to the interpolation the expected bi at @xmath2 increases to 19@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) for the _ gold - coax _ data set . given , for the _ gold - coax _ data set , the background prediction of the minimum model of 18.5@xmath310@xmath49 cts/(kev@xmath3kg@xmath3yr ) and the known 17.90 kg@xmath3yr exposure at the end of phase i , the sensitivity for the @xmath0 decay half life @xmath15 was calculated . the value of the exposure - averaged total efficiency ( see eq . [ equ : efficiency ] ) for the _ gold - coax _ data set is @xmath820.688 . from the energy spectrum an upper limit on the @xmath0 signal strength @xmath83 at specified probability or confidence level can be derived and converted to a half life limit @xmath84 using @xmath85 in order to estimate the limit setting sensitivity without pulse shape analysis , 10@xmath86 mc realizations of gerda were generated assuming no @xmath0 signal . for each realization , the number of events was allowed to fluctuate according to a poisson distribution with expectation given by the number of predicted background events . the expected lower limit for @xmath15 was estimated by using both , bayesian and frequentist analyses . in both analyses the signal and background strengths were free parameters . for the frequentist analysis , the @xmath0 decay rates were estimated from a profile likelihood fit to the unbinned energy spectrum of each realization . the 90% c.l . lower limit @xmath15 @xmath161.9@xmath310@xmath87 yr ( 90% c.l . ) corresponds to the median of the 90% quantile of the profile likelihood . in the bayesian analysis , the 90% probability lower limit for @xmath15 was calculated as the median of the 90% quantiles of the posterior marginalized probabilities p@xmath88 , where @xmath89 is the hypothesis that both background and @xmath0 events contribute to the spectrum . the result is @xmath15 @xmath161.7@xmath310@xmath87 yr ( 90% c.l . ) . the difference in the numerical values from the bayesian and frequentist analysis ( which have conceptually a different meaning ) is mainly due to the behavior of the two approaches in the cases when the number of observed counts is smaller than the background expectation . the sensitivity is expected to be about 10% better than calculated from the _ gold - coax _ data set only , because of the extra exposure available in the _ silver - coax _ and _ sum - bege _ data sets . also the sensitivity might further increase by applying pulse shape discrimination techniques to the _ gold - coax _ , _ silver - coax _ and _ sum - bege _ data sets @xcite .

, the present analysis does not consider all those events , that fall in a 40 kev wide region centered around @xmath2 . the model predicts a flat energy spectrum for the blinding window around @xmath2 with a background index ranging from 17.6 to 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . a part of the data not considered before the observed number of events in this energy region is consistent with the background model . the background at @xmath2 is dominated by close sources , mainly due to @xmath5k , @xmath6bi , @xmath7th , @xmath8co and @xmath9 emitting isotopes from the @xmath10ra decay chain .

the germanium detector array ( ) experiment at the gran sasso underground laboratory ( lngs ) of infn is searching for neutrinoless double beta ( @xmath0 ) decay of @xmath1ge . the signature of the signal is a monoenergetic peak at 2039 kev , the @xmath2 value of the decay . to avoid bias in the signal search , the present analysis does not consider all those events , that fall in a 40 kev wide region centered around @xmath2 . the main parameters needed for the @xmath0 analysis are described . a background model was developed to describe the observed energy spectrum . the model contains several contributions , that are expected on the basis of material screening or that are established by the observation of characteristic structures in the energy spectrum . the model predicts a flat energy spectrum for the blinding window around @xmath2 with a background index ranging from 17.6 to 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . a part of the data not considered before has been used to test if the predictions of the background model are consistent . the observed number of events in this energy region is consistent with the background model . the background at @xmath2 is dominated by close sources , mainly due to @xmath5k , @xmath6bi , @xmath7th , @xmath8co and @xmath9 emitting isotopes from the @xmath10ra decay chain . the individual fractions depend on the assumed locations of the contaminants . it is shown , that after removal of the known @xmath11 peaks , the energy spectrum can be fitted in an energy range of 200 kev around @xmath2 with a constant background . this gives a background index consistent with the full model and uncertainties of the same size . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

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the background measured by the experiment has been presented in an energy range between 100 and 7500 kev . it has been demonstrated that stable low background data taking with the innovative technique of operating bare hpge detectors in a cryogenic liquid is possible over a time period of about 1.5 yr . more than 20 kg@xmath3yr of data have been acquired by the experiment with six enriched coaxial detectors of a total mass of 14.6 kg and with four enriched bege detectors of a total mass of 3.0 kg . a background model has been developed with the @xmath22=40 kev blinded that allows to predict the bi in this energy range . the predictions of the models have been tested for consistency on a 30 kev ( 32 kev ) range for the coaxial ( bege ) detectors , while the central @xmath22=10 kev region of interest and @xmath22=8 kev region for the bege detectors around @xmath2 was still blinded . the model describes the background in an energy range from 570 to 7500 kev well . the only significant background contributions in originate from decays of @xmath5k in the lar bath , from @xmath6bi in the detector assembly , from residual @xmath37rn dissolved in lar , from @xmath7th and @xmath8co in the detector assembly , and from surface @xmath9 particles . the largest contributions come from contaminants located close to the detectors . several cross checks confirm the validity of the background model . the 68% credibility intervals of the bi expected due to the minimum and maximum models at @xmath2 of @xmath1ge span the range between 17.6 and 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . this range includes the systematic uncertainty due to different source location assumptions . predictions for the number of events in the blinded region around @xmath2 have been made . it could be shown that the expected background is flat in a region of @xmath41 200 kev around @xmath2 and that no significant peak like structures are expected in the blinded energy region . the background model and an interpolation of a fit to data from a 200 kev energy window into the blinded energy window give compatible results . the bi interpolated into the region of interest are + ( 1.75@xmath90)@xmath3@xmath47 cts/(kev@xmath3kg@xmath3yr ) for the coaxial detectors and ( 3.6@xmath91)@xmath3@xmath47 cts/(kev@xmath3kg@xmath3yr ) for the bege detectors . the statistical uncertainty on the bi prediction from interpolation is of the same size as the systematic uncertainty from the choice of the background model . the bi obtained from interpolation of the spectrum in a 200 kev window around @xmath2 will be used in the @xmath0 analysis of the phase i data . given the expected background rate without pulse shape discrimination and assuming no signal , the sensitivity for the _ gold - coax _ data set is @xmath92 yr ( 90% c.l . ) using a profile likelihood fit and @xmath93 yr ( 90% c.i . ) using a bayesian analysis .

a background model was developed to describe the observed energy spectrum . it is shown , that after removal of the known @xmath11 peaks , the energy spectrum can be fitted in an energy range of 200 kev around @xmath2 with a constant background .

the germanium detector array ( ) experiment at the gran sasso underground laboratory ( lngs ) of infn is searching for neutrinoless double beta ( @xmath0 ) decay of @xmath1ge . the signature of the signal is a monoenergetic peak at 2039 kev , the @xmath2 value of the decay . to avoid bias in the signal search , the present analysis does not consider all those events , that fall in a 40 kev wide region centered around @xmath2 . the main parameters needed for the @xmath0 analysis are described . a background model was developed to describe the observed energy spectrum . the model contains several contributions , that are expected on the basis of material screening or that are established by the observation of characteristic structures in the energy spectrum . the model predicts a flat energy spectrum for the blinding window around @xmath2 with a background index ranging from 17.6 to 23.8@xmath3@xmath4 cts/(kev@xmath3kg@xmath3yr ) . a part of the data not considered before has been used to test if the predictions of the background model are consistent . the observed number of events in this energy region is consistent with the background model . the background at @xmath2 is dominated by close sources , mainly due to @xmath5k , @xmath6bi , @xmath7th , @xmath8co and @xmath9 emitting isotopes from the @xmath10ra decay chain . the individual fractions depend on the assumed locations of the contaminants . it is shown , that after removal of the known @xmath11 peaks , the energy spectrum can be fitted in an energy range of 200 kev around @xmath2 with a constant background . this gives a background index consistent with the full model and uncertainties of the same size . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

0707.3256

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solar filaments are large regions of dense cool plasma suspended in the hot corona @xcite . they are well observed in h@xmath0 , either in absorption against the disk or in emission at the limb . for historical reasons in the latter case they are usually termed `` prominences '' . coronal magnetic fields are key to the existence of filaments @xcite , as they both support the filament mass against gravity and help to insulate it from the surrounding corona . since the earliest magnetograph observations @xcite it has been known that filaments form above polarity inversion lines ( pils ) in the photosphere , which divide regions of positive and negative magnetic flux . in the filament itself , the dominant magnetic field component is found to be along the filament s long axis @xcite . the filament may be classified as having either dextral or sinistral chirality ( handedness ) according to the direction of this dominant axial field @xcite . viewing the filament from the positive polarity side of the pil , a right - pointing field is dextral and a left - pointing field is sinistral . this is illustrated in figure [ fig : chirality ] . the property of filament chirality is notable because it follows a hemispheric pattern , whereby dextral filaments dominate in the northern hemisphere and sinistral in the southern hemisphere . the pattern was initially observed in polar crown prominences by , who noted that the field direction was opposite to that expected from differential rotation . it was later observed by with hanle - effect measurements , and then confirmed by and using h@xmath0 observations . the latter paper found that 80% 85% of quiescent filaments ( which form between the remnants of decaying active regions ) followed the rule . a feature of the hemispheric pattern is that it remains the same when the sun s polar field reverses , approximately every 11 years . suggested that the hemispheric pattern could be produced by a combination of supergranular motions , differential rotation , and magnetic reconnection @xcite , without recourse to unobservable subsurface phenomena as in some earlier theories @xcite . this suggests that the pattern for quiescent filaments could be a natural result of the observed evolution of bipolar active regions , and their interaction as they are transported poleward . a series of papers , beginning with , have used coupled numerical modelling of the surface and coronal magnetic fields to investigate this idea . having reached the conclusion that emerging active - region helicity does play an important role @xcite , gave a convincing explanation for the hemispheric filament pattern . however , this was a parameter study which considered only a pair of model magnetic bipoles in a localised region of the solar corona . in this study we aim to extend the model to the global corona , and to simulate the real sun for a period of 6 months , allowing us to compare the local direction of the simulated magnetic field with the chirality of a large number of observed filaments during the period . a distinction must be made between two approaches that have been used to model the coronal magnetic field based on photospheric flux transport . in the first approach the photospheric flux transport simulations are carried out independently from the coronal field modelling ( _ e.g. _ ; ; ) . here the flux transport simulations are used at discrete intervals , perhaps every 27 days , to supply the lower boundary condition for the extrapolation of a potential magnetic field in the coronal volume . the potential field is analysed at that time instant and then discarded , a new potential field being constructed after the next 27 days . in this approach , which has been successful in the past , there is evidently no direct coupling between the flux transport model evolving the photospheric field , and the extrapolated coronal fields . this precludes any memory in the coronal field of previous field line connectivity . in contrast , more recent flux transport models have coupled the photospheric and coronal magnetic fields , and include the models of and , developed to investigate the hemispheric pattern of filaments . the technique described in the latter paper has been used with small modifications in a series of papers (; , @xcite , @xcite ) , and is used again in this study . as carried out in , the radial magnetic field component in the photosphere is taken as the initial boundary condition , and an initial potential coronal field extrapolated from it . both the photospheric and coronal fields are then evolved together , allowing the build - up of magnetic energy and helicity in the coronal volume as a result of the photospheric motions . applied the model to 10 filaments forming above an observed activity complex . in these simulations , the emergence of new flux was not included , so the photospheric field became less accurate over time . for this reason the photospheric fields were reset to the observed field after every 27 days of evolution . at this point , the sheared coronal field had to be discarded and a new potential field constructed . although a significant advance on previous models with a purely potential coronal field , the build - up of magnetic energy and shear was limited to rather short periods of time compared to that on the real sun . despite the loss of accuracy in the surface field , the authors tried running the simulation for several months without resetting , and found in fact that the chirality results were slightly improved . we have now modified the model , enabling us to simulate coronal magnetic fields for much longer periods of time without having to reset the photospheric or coronal fields every 27 days . key to our new technique is the insertion of individual active regions throughout the simulation , based on the observed photospheric field . the new surface flux transport model is described and illustrated in this paper , simulating the real sun over a particular 6-month period in 1999 . a sample of 255 filaments have been observed in h@xmath0 images from big bear solar observatory ( bbso ) , over the same period . the chiralities of these filaments have been determined where possible , as described in this paper . in a follow - up paper the full 3d coronal field evolution will be computed , coupled to the new surface simulation . the resulting magnetic skew will be compared with the chirality of filaments at the locations where they were observed . the structure of this paper is as follows . section [ sec : filaments ] describes the filament data , and the observed chiralities . the numerical model for surface flux transport is outlined in section [ sec : model ] , while section [ sec : flux ] describes in detail the method for including newly - emerging active regions . example surface simulation results are given in section [ sec : results ] , and a concluding summary in section [ sec : conclusions ] .

our technique differs significantly from those of other authors , where the coronal field is either assumed to be purely potential , or has to be reset back to potential every 27 days in order that the photospheric field remain accurate . in our case we ensure accuracy by the insertion of newly - emerging bipolar active regions , based on observed photospheric synoptic magnetograms . the large - scale surface field is shown to remain accurate over the 6-month period , without any resetting .

the hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona . in recent work mackay and van ballegooijen have shown how , for a pair of interacting magnetic bipoles , the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere . this study aims to test this earlier result through a direct comparison between theory and observations , using newly - developed simulations of the actual surface and 3d coronal magnetic fields over a 6-month period , on a global scale . in this paper we consider two key components of the study ; firstly the observations of filament chirality for the sample of 255 filaments , and secondly our new simulations of the large - scale surface magnetic field . based on a flux - transport model , these will be used as the lower boundary condition for the future 3d coronal simulations . our technique differs significantly from those of other authors , where the coronal field is either assumed to be purely potential , or has to be reset back to potential every 27 days in order that the photospheric field remain accurate . in our case we ensure accuracy by the insertion of newly - emerging bipolar active regions , based on observed photospheric synoptic magnetograms . the large - scale surface field is shown to remain accurate over the 6-month period , without any resetting . this new technique will enable future simulations to consider the long - term build - up and transport of helicity and shear in the coronal magnetic field , over many months or years .

1207.4796

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the excursion set theory initially introduced by bond et al . @xcite provides a self - consistent mathematical framework to infer the properties of the halo mass distribution from the statistics of the initial density field . the formalism generalizes the original press - schechter idea @xcite by formulating the halo mass counting problem as one of stochastic calculus . the starting point is the realization that at any location in space the linear matter density fluctuation field performs a random walk as function of a filtering scale @xmath0 . in average , this scale naturally defines a mass scale @xmath1 , where @xmath2 is the mean matter density and @xmath3 the enclosed spatial volume . by counting the number of trajectories which first - cross a collapse threshold it is then possible to compute the fraction of mass elements in halos @xmath4 and consequently derive the halo mass function @xmath5 . the requirement of first - crossing is key to solving the so called `` cloud - in - cloud '' problem affecting the original press - schechter result . in fact , the first - crossing condition guarantees that in the small scale limit ( @xmath6 ) and independently of the properties of the random walks the fraction of mass into collapsed objects always tends to unity . the excursion set is analytically solvable in the case of uncorrelated ( markov ) random walks for which the evaluation of the first - crossing distribution is reduced to solving a standard diffusion problem . however , uncorrelated random walks are generated by a special filtering of the linear density field which corresponds to a non - physical halo mass definition . in contrast any filtering which specifies a physically meaningful mass generates correlated random walks for which @xmath4 can be inferred only through a numerical computation . this has represented a major limitation since monte carlo simulations are computationally expensive and moreover do not provide the same level of physical insight of analytic solutions . the seminal work by maggiore & riotto @xcite has made a major step forward in this direction . using the path - integral formulation of the excursion set theory the authors have shown that the first - crossing distribution of correlated random walks can be computed as a perturbative expansion about the markovian solution . using this methodology it has been possible to derive analytical formulae for the halo mass function under different halo collapse model assumptions as well as gaussian and non - gaussian ( ng ) initial conditions @xcite . in a series of papers @xcite we have used this formalism to evaluate the imprint of the non - spherical collapse of halos on the mass function . to this end we have introduced an effective stochastic diffusive drifting barrier ( ddb ) model which parametrizes the main features of the ellipsoidal collapse of halos . accounting for such effects can reproduce the halo mass function from n - body simulations with remarkable accuracy both for gaussian and non - gaussian initial conditions . here , we extend the work presented @xcite to derive a more accurate expression of the contribution to the halo mass function of the primordial bispectrum expanded in the large scale limit to next - to - leading order and compute the leading order contribution of the primordial trispectrum . the paper is organized as follows . in section [ seci ] we review the path - integral formulation of the excursion set and its application to gaussian and non - gaussian initial conditions in the case of the ddb model . in section [ secii ] we evaluate a lower limit on the interval validity of the bispectrum expansion at next - to - leading order . in section [ seciii ] and [ seciv ] compute the bispectrum and trispectrum contribution to the mass function respectively . finally , we present our conclusion in section [ secv ] .

we also found an excellent agreement with n - body simulation results . here , we perform a more accurate computation which accounts for the interval validity of the bispectrum expansion to next - to - leading order and extend the calculation to the case of a non - vanishing primordial trispectrum .

the high - mass end of the halo mass function is a sensitive probe of primordial non - gaussianity ( ng ) . in a recent study @xcite we have computed the ng halo mass function in the context of the excursion set theory and shown that the primordial ng imprint is coupled to that induced by the non - linear collapse of dark matter halos . we also found an excellent agreement with n - body simulation results . here , we perform a more accurate computation which accounts for the interval validity of the bispectrum expansion to next - to - leading order and extend the calculation to the case of a non - vanishing primordial trispectrum .

1303.3350

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in a series of recent papers we describe observations and interpretations of far infrared emission from dust in early - type galaxies , emphasizing emission from dust that is in thermal contact with hot gas virialized in galactic or group potential wells ( temi , brighenti & mathews 2005 ; 2007a , b ; 2008 ; 2009a , b = tbm05 ; tbm07,a , b ; tbm08 ; tbm09a , b ) . we propose that interstellar dust is ejected and stripped from asymptotic giant branch ( agb ) stars as they orbit through the hot interstellar gas ( @xmath0k ) . interstellar dust is heated both by diffuse galactic starlight and by impacts of thermal electrons . the loss of thermal energy by electron - grain impacts can cool gas near black holes in the galactic cores , possibly stimulating energetic feedback events ( mathews & brighenti 2003 ) . dust both influences and is influenced by agn events . in addition , mid infrared circumstellar emission observed in elliptical galaxies is emitted by hotter dust associated with outflows from mass - losing agb stars . when mid ( 24@xmath1 m ) and far ( 70@xmath1 m ) infrared luminosities from galaxies of all types are compared and normalized by the @xmath2-band luminosity , @xmath3 and @xmath4 , galaxies of all hubble types occupy a remarkably well - defined banana - shaped correlation . remarkably , the galactic hubble sequence is ordered along the correlation from early to late morphologies ( tbm09b ) . for spiral and irregular galaxies this color - color correlation results from increasing specific star formation toward later type galaxies . evidently , dust heated to a range of temperatures by young stars emits mid and far infrared radiation in nearly the same proportion , independently of the specific star formation rate . by contrast , early - type elliptical galaxies , in which star formation is small or absent , are contiguous with the earliest spiral galaxies in the color - color plot and occupy an extended region of decreasing @xmath5 with nearly constant @xmath6 . in general , mid and far infrared emission from dust grains in early - type galaxies does not indicate the star formation rate . here we discuss an improved , sharper version of the banana color - color plot for normal galaxies in which galaxies with concentrated mid infrared emission ( probably mostly agns ) are removed . in addition , we propose possible explanations for the cosmic scatter among elliptical galaxies in the infrared color - color plot .

the hubble morphological sequence from early to late galaxies corresponds to an increasing rate of specific star formation . the hubble sequence also follows a banana - shaped correlation between 24 and 70 micron luminosities , both normalized with the k - band luminosity . normally regarded as passive , elliptical galaxies are the most active galaxies in the ir color - color correlation .

the hubble morphological sequence from early to late galaxies corresponds to an increasing rate of specific star formation . the hubble sequence also follows a banana - shaped correlation between 24 and 70 micron luminosities , both normalized with the k - band luminosity . we show that this correlation is significantly tightened if galaxies with central agn emission are removed , but the cosmic scatter of elliptical galaxies in both 24 and 70 micron luminosities remains significant along the correlation . we find that the 24 micron variation among ellipticals correlates with stellar metallicity , reflecting emission from hot dust in winds from asymptotic giant branch stars of varying metallicity . infrared surface brightness variations in elliptical galaxies indicate that the k - 24 color profile is u - shaped for reasons that are unclear . in some elliptical galaxies cold interstellar dust emitting at 70 and 160 microns may arise from recent gas - rich mergers . however , we argue that most of the large range of 70 micron luminosity in elliptical galaxies is due to dust transported from galactic cores by feedback events in ( currently ir - quiet ) active galactic nuclei . cooler dusty gas naturally accumulates in the cores of elliptical galaxies due to dust - cooled local stellar mass loss and may accrete onto the central black hole , releasing energy . agn - heated gas can transport dust in cores 5 - 10 kpc out into the hot gas atmospheres where it radiates extended 70 micron emission but is eventually destroyed by sputtering . this , and some modest star formation , defines a cycle of dust creation and destruction . elliptical galaxies evidently undergo large transient excursions in the banana plot in times comparable to the sputtering time or agn duty cycle , 10 myrs . normally regarded as passive , elliptical galaxies are the most active galaxies in the ir color - color correlation .

1303.3350

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the banana - shaped infrared color - color correlation for normal galaxies a plot of @xmath71 vs. @xmath72 ( bottom panel of figure 1 ) approximately follows the morphological progression along hubble types . as @xmath72 and @xmath71 increase with the specific star - forming rate , the dominant hubble type becomes progressively later : sa , sab @xmath12 sb , scd @xmath12 irr . by contrast , most e galaxies lie near the bottom of the banana in a contiguous region of restricted @xmath72 and decreasing @xmath71 . some gas - rich e galaxies lie along the star - forming locus of late type galaxies and s0 galaxies are found throughout the banana . our concern here is to understand the variation of @xmath72 and @xmath71 among normal elliptical galaxies in the banana plot . we show that the banana - shaped correlation , first discussed by tbm09 , becomes much tighter when galaxies with agn emission are removed . dust grains can be significantly heated by agn radiation and emit strongly at 24@xmath1 m within several arcseconds of the galactic centers . these galaxies , having hard , highly concentrated infrared emission , can be identified by the presence of airy diffraction rings at 24@xmath1 m . agn galaxies of all types with airy rings lie above the infrared banana correlation . to achieve this , centrally illuminated dust would need to move along a trajectory @xmath73 that is steeper than the star formation trajectory along the upper banana , @xmath14 . because of this slope difference , we suggest that the concentrated source of central ir radiation is due to agn rather than small starburst regions unresolved at 24@xmath1 m . an increasing specific star formation rate from early spiral to irregular galaxies with @xmath74 apparently explains the progressive transition toward later galactic hubble types upward along the banana . the bottom part of the infrared banana is populated by elliptical galaxies with a relatively small but significant scatter in 24@xmath1 m emission , @xmath75 , and a much larger scatter in 70@xmath1 m emission , @xmath76 in units of ( erg s@xmath40)/@xmath77 . we find that the scatter in @xmath78 among elliptical galaxies correlates with their stellar metallicity , @xmath79^{0.7}$ ] . emission from hotter dust at 24@xmath1 m is likely to originate in circumstellar regions near agb stars where dust is thought to be produced . the correlation of 24@xmath1 m emission with metallicity is probably due to the simple expectation that outflows from metal - rich agb stars produce more dust per gram of gas ejected . but the surface brightness variation in 24@xmath1 m emission from elliptical galaxies , while largely mimicking the de vaucouleurs profile , contains unexpected color variations when compared with the @xmath2-band . when plotted against galactic radius normalized by the @xmath2-band effective radius @xmath30 , the mean @xmath24 color for a sample of well - observed elliptical galaxies first decreases in a power - law fashion , then undergoes a broad minimum followed by a rise at large radius @xmath30 . the initial decrease is consistent with decreasing stellar metallicity with radius similar to that found at optical wavelengths , @xmath34/\delta \log r \approx -0.3 $ ] . the origin of the flattening and possible rise in @xmath24 beyond @xmath80 is uncertain . if hot dust in agb winds is thermally heated , increasing @xmath24 with decreasing stellar metallicity may be related to increasing effective temperature of agb stars with decreasing metallicity . alternatively , lower velocity ( radiation pressure - driven ) outflows from metal poor agb stars might have larger 24@xmath1 m emissivity . the intrinsic scatter of elliptical galaxies in the banana - shaped infrared correlation at longer wavelengths , 70@xmath1 m and 160@xmath1 m , is much larger . recent gas - rich mergers may be a source of cold dust for some elliptical galaxies . however , for most ellipticals we propose that this scatter is due to transient hydrodynamic flows of cold dust from galactic cores far out into the surrounding hot galactic interstellar gas following agn feedback events . the variation of @xmath5 is uncorrelated with x - ray luminosity @xmath81 of the galactic / group baryonic halo . the @xmath4 ratios of some group - centered e galaxies like ngc 4472 and 1399 are in good agreement with a steady state model in which dust created by agb stars is locally destroyed by sputtering at each radius in the galactic atmospheres . other ellipticals such as ngc 4636 and 5044 have much larger @xmath8 luminosities from excess cold dust that can not be produced by local stars . lacking convincing evidence of recent gas - rich mergers in these otherwise normal elliptical galaxies , we propose that agn outbursts cause excess dust to be hydrodynamically transported out to 5 - 10 kpc into the hot virialized gaseous atmospheres . spatially extended 70@xmath1 m emission has been confirmed in relatively nearby elliptical galaxies ( tbm07a , b ) . evidently , values of @xmath4 for elliptical galaxies along the bottom of the banana plot are transient and may vary on @xmath50 yr timescales , depending on the grain sputtering time and the agn duty cycle . the outward relocation of variable masses of cold dust from the central reservoir , observed at different phases of the outflow , may explain why galaxies of similar @xmath9 have @xmath8 luminosities that vary over two orders of magnitude . however , the continuity of the banana plot from e galaxies to early spirals ( where @xmath3 and @xmath4 are due to star formation ) requires that the enhanced 70@xmath1 m emission from extended excess cold dust in e galaxies must not exceed @xmath4 as produced by dust in star - forming galaxies of later types . to explain this unlikely coincidence , we speculate that star formation naturally begins in the cores of elliptical galaxies as the mass of accumulated cold gas and dust approaches some star - forming threshold . this conjecture follows from the expected secular accumulation of dust - cooled gas from agb stellar mass loss in the central @xmath67kpc of elliptical galaxies ( mathews & brighenti 2003 ) . .2 cm this work is based on observations made with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology , under nasa contract 1407 . studies of the evolution of hot gas in elliptical galaxies at uc santa cruz are supported by an nsf grant for which we are very grateful . support for this work was provided by nasa adp grant . aknowledges financial support from prin miur 2010 - 2011 , prot . 2010ly5n2 t . we acknowledge the usage of the hyperleda database ( http://leda.univ-lyon1.fr ) and the nasa / ipac extragalactic database ( ned ) . lccccc ngc 0315 & -4 & 58.9 & 11.71 & 42.68 & 42.77 + ngc 0814 & -1.8 & 20.7 & 9.508 & 42.65 & 42.82 + ngc 0526 & -2.0 & 78.7 & & 43.44 & 43.02 + ngc 1266 & -2.1 & 30.1 & 10.51 & 43.07 & 43.77 + ngc 1386 & -0.8 & 16.5 & 10.56 & 42.69 & 42.98 + ngc 1377 & -2.1 & 22.2 & 10.15 & 43.13 & 43.2 + ngc 2110 & -3.0 & 31.3 & 11.08 & 42.97 & 43.4 + ngc 2325 & -4.7 & 31.9 & 11.2 & 41.62 & 41.3 + ngc 3226 & -4.8 & 23.5 & 10.66 & 41.35 & 41.97 + ngc 3265 & -4.8 & 21.3 & 9.83 & 42.3 & 42.8 + ngc 4261 & -4.8 & 31.6 & 11.44 & 41.88 & 41.81 + ngc 5077 & -4.8 & 32.4 & 11.08 & 41.72 & 41.85 + ngc 6776 & -4.1 & 70.4 & 11.43 & 42.08 & 42.5 + ngc 5273 & -1.9 & 16.5 & 10.32 & 41.53 & 41.96 + ic 5063 & -0.9 & 45.3 & 11.16 & 43.82 & 43.67 + e103 - 035 & -0.3 & 54.2 & 10.68 & 43.87 & 43.43 + eso428 - 014 & -1.7 & 21.3 & 10.5 & 42.99 & 43.04 rccccccrcccc 221 & -4.7 & 9.13 & 39.22 & 37.93 & 0.00@xmath820.05 & -0.08@xmath82 0.05 & 4.9@xmath821.3 & 0.81 & 27.0 & 0.11 & 2.72 + 315 & -4.0 & 11.71 & 42.68 & 42.77 & 0.32@xmath820.06 & 0.17@xmath820.06 & 6.9@xmath821.9 & 58.88 & 22.2 & 6.36 & 0.96 + 507 & -3.3 & 11.68 & 42.02 & & 0.18@xmath820.06 & 0.28@xmath820.13 & 3.5@xmath822.7 & 67.19 & 24.0 & 7.84 & 1.36 + 584 & -4.6 & 11.18 & 41.48 & 41.18 & 0.48@xmath820.03 & 0.26@xmath820.07 & 3.4@xmath821.1 & 23.76 & 23.3 & 2.69 & 1.62 + 636 & -4.8 & 10.67 & 40.73 & & 0.34@xmath820.07 & 0.10@xmath820.05&6.8@xmath821.4 & 22.28 & 15.3 & 1.66 & 1.39 + 720 & -4.8 & 11.14 & 41.42 & 40.69 & 0.44@xmath820.15 & 1.13@xmath820.42 & 1.1@xmath820.8 & 22.29 & 25.2 & 2.73 & 1.57 + 821 & -4.8 & 10.95 & 41.06 & & 0.22@xmath820.03 & 0.12@xmath820.05 & 7.1@xmath821.2 & 24.09 & 21.9 & 2.56 & 1.07 + 1374 & -4.3 & 10.68 & 40.73 & & 0.13@xmath820.07 & & 9.5@xmath822.6 & 19.77 & 15.4 & 1.48 & 1.25 + 1399 & -4.5 & 11.40 & 41.49 & 40.50 & 0.29@xmath820.06 & & 11.5@xmath822.4 & 19.40 & 32.9 & 3.10 & 2.83 + 1404 & -4.7 & 11.20 & 41.45 & 40.80 & 0.25@xmath820.05 & & 9.0@xmath822.5 & 19.40 & 18.7 & 1.76 & 3.57 + 1427 & -4.0 & 10.66 & 40.90 & 40.89 & -0.07@xmath820.03 & & 12.2@xmath821.6 & 23.55 & 21.5 & 2.46 & 1.45 + 1700 & -4.7 & 11.27 & 41.51 & 41.35 & 0.50@xmath820.03 & 0.32@xmath820.05 & 2.8@xmath820.5 & 38.04 & 14.9 & 2.76 & 1.57 + 2300 & -3.4 & 11.18 & 41.36 & & 0.36@xmath820.04 & 0.14@xmath820.04 & 10.1@xmath822.0 & 27.67 & 22.3 & 2.99 & 1.54 + 2778 & -4.7 & 10.26 & 40.37 & & 0.29@xmath820.07 & -0.04@xmath820.06 & 14.9@xmath823.5 & 22.91 & 10.5 & 1.17 & 1.67 + 3377 & -4.8 & 10.47 & 40.50 & 40.74 & 0.19@xmath820.06 & -0.12@xmath820.04 & 5.9@xmath821.2 & 11.22 & 25.4 & 1.39 & 0.76 + 3379 & -4.8 & 10.89 & 41.03 & 40.56 & 0.21@xmath820.04 & 0.00@xmath820.04 & 13.2@xmath822.4 & 10.57 & 28.5 & 1.46 & 1.09 + 3608 & -4.8 & 10.83 & 41.00 & 41.27 & 0.26@xmath820.04 & 0.07@xmath820.07 & 9.0@xmath822.5 & 22.91 & 16.2 & 1.80 & 1.44 + 4261 & -4.8 & 11.44 & 41.88 & 41.81 & 0.18@xmath820.04 & -0.01@xmath820.03 & 21.0@xmath821.7 & 31.62 & 24.2 & 3.72 & 1.17 + 4374 & -4.2 & 11.39 & 41.45 & 42.03 & 0.12@xmath820.03 & -0.01@xmath820.05&14.4@xmath822.8 & 18.37 & 33.5 & 2.99 & 1.12 + 4472 & -4.8 & 11.65 & 41.71 & 40.96 & 0.25@xmath820.05 & 0.18@xmath820.06 & 8.4@xmath822.7 & 17.06 & 56.1 & 4.65 & 0.89 + 4478 & -4.8 & 10.52 & 40.74 & & 0.29@xmath820.10 & -0.01@xmath820.04 & 10.3@xmath821.7 & 18.11 & 11.8 & 1.04 & 1.35 + 4489 & -4.8 & 10.10 & 40.11 & & 0.14@xmath820.06 & -0.15@xmath820.04 & 4.6@xmath820.5 & 17.86 & 14.1 & 1.22 & 1.13 + 4552 & -4.6 & 11.03 & 41.26 & 41.06 & 0.27@xmath820.04 & 0.10@xmath820.04 & 13.1@xmath822.7 & 15.34 & 22.8 & 1.70 & 1.65 + 4649 & -4.6 & 11.52 & 41.58 & 40.86 & 0.27@xmath820.04 & 0.05@xmath820.04 & 18.3@xmath822.8 & 17.06 & 42.1 & 3.49 & 0.46 + 4697 & -4.8 & 11.22 & 41.26 & 41.92 & 0.06@xmath820.05 & -0.29@xmath820.04 & 15.6@xmath822.5 & 16.22 & 39.5 & 3.11 & 0.65 + 5813 & -4.8 & 11.40 & 41.37 & 41.51 & -0.04@xmath820.03 & -0.20@xmath820.06 & 24.3@xmath822.0 & 32.21 & 36.2 & 5.66 & 0.95 + 5831 & -4.8 & 10.84 & 41.10 & & 0.54@xmath820.04 & 0.18@xmath820.06 & 4.2@xmath821.0 & 27.16 & 19.4 & 2.56 & 0.75 + 5846 & -4.7 & 11.36 & 41.43 & 41.53 & 0.14@xmath820.05 & -0.13@xmath820.04 & 23.1@xmath822.7 & 24.89 & 32.7 & 3.96 & 2.47 + 6703 & -2.8 & 11.06 & 41.34 & 41.36 & 0.30@xmath820.06 & 0.03@xmath820.06 & 7.9@xmath822.1 & 32.06 & 20.1 & 3.13 & 1.16 + 7619 & -4.7 & 11.58 & 41.62 & & 0.20@xmath820.03 & 0.07@xmath820.04&15.1@xmath822.2 & 52.97 & 16.4 & 4.22 & 1.64 + 7626 & -4.8 & 11.34 & 41.44 & 41.17 & 0.16@xmath820.04 & -0.06@xmath820.02 & 18.2@xmath822.0 & 39.99 & 20.7 & 4.02 & 1.13 + 7785 & -4.8 & 11.46 & 41.58 & 41.45 & 0.20@xmath820.04 & -0.01@xmath820.04 & 15.0@xmath822.3 & 55.46 & 17.2 & 4.64 & 0.84 + vs. @xmath4 for sings galaxies showing progression of hubble types . central panel : ir color - color plot showing galaxies in the tbm09b sample with x indicating sings galaxies . green squares indicate tbm09b ( agn or starburst ) galaxies with centrally concentrated 24@xmath1 m emission . bottom panel : same as central panel without galaxies having centrally concentrated 24@xmath1 m emission . ] m images of ngc 1398 and 315 showing airy diffraction rings and ngc 4472 with diffraction - free image . the colors and contours are qualitative only , intended to illustrate non - axisymmetric features in the diffraction pattern . lower panel : azimuthally averaged radial diffraction fluxes at 24@xmath1 m for the three galaxies imaged above : ngc 1386 ( black dotted line ) ; ngc 0315 ( blue dashed line ) ; ngc 4472 ( light blue long dash - triple dotted line ) . for comparison we plot the point response function of the spitzer telescope at 24@xmath1 m ( green solid line ) . all fluxes are normalized to 100 ( in arbitrary units ) at one arcsecond . , title="fig:",width=374 ] 2.7 in ) at the bottom of the banana plot , omitting agn galaxies with significant point source emission at 24@xmath1 m . red circles identify a subset of these galaxies that are also in the sample of trager et al . ( 2000a , b ) which have been observed at both 24 and 70@xmath1 m but omitting two that are identified as agns in table 1 , ngc 0315 and ngc 4261 . , title="fig:",width=672 ] .7 in and stellar metallicity @xmath16 $ ] for the trager et al . ( 2000a , b ) sample of e galaxies . upper and lower panels show the linear relation with metallicities values derived in the @xmath19 and @xmath20 aperture respectively where @xmath21 is the effective radius in the @xmath22-band . two galaxies identified as agns in table 1 ( ngc 315 and ngc 4261 ) are not included in either panel . in the lower panel we also exclude the outlying ( and very uncertain ) value @xmath16 = 1.13 $ ] for ngc 720 . , title="fig:",width=432 ] .7 in vs. @xmath9 for elliptical galaxies ( @xmath37 ) in the tmb09b sample . galaxies marked in red all have excess extended dust and the large red circles indicate galaxies in which the spatial extension has been observed at 70@xmath1 m . vertical green arrows show the approximate estimated increase in @xmath8 due to excess cold dust in ngc 5044 and 4636 . , title="fig : " ] .7 in . galaxies in red and circled in red are identical with those in figure 6 , but now appear along the right boundary of the lower banana . as in figure 6 the horizontal green arrows show the trajectories of ngc 5044 and 4636 when extended cold dust is added to 70@xmath1 m emission produced only by local agb stellar mass loss . , title="fig : " ] .7 in against @xmath8 as in the bottom panel of figure 1 but without the @xmath9 normalization . symbols are identical to those in that panel . filled squares show computed steady - state emission from diffusely distributed interstellar dust in five representative elliptical galaxies ( ngc 4472 , 1404 4636 , 1399 & 5044 in order of decreasing @xmath7 ) . the star formation locus of sings galaxies ( crosses ) is @xmath74 . , title="fig : " ] .7 in

we show that this correlation is significantly tightened if galaxies with central agn emission are removed , but the cosmic scatter of elliptical galaxies in both 24 and 70 micron luminosities remains significant along the correlation . we find that the 24 micron variation among ellipticals correlates with stellar metallicity , reflecting emission from hot dust in winds from asymptotic giant branch stars of varying metallicity . some elliptical galaxies cold interstellar dust emitting at 70 and 160 microns may arise from recent gas - rich mergers . however , we argue that most of the large range of 70 micron luminosity in elliptical galaxies is due to dust transported from galactic cores by feedback events in ( currently ir - quiet ) active galactic nuclei .

the hubble morphological sequence from early to late galaxies corresponds to an increasing rate of specific star formation . the hubble sequence also follows a banana - shaped correlation between 24 and 70 micron luminosities , both normalized with the k - band luminosity . we show that this correlation is significantly tightened if galaxies with central agn emission are removed , but the cosmic scatter of elliptical galaxies in both 24 and 70 micron luminosities remains significant along the correlation . we find that the 24 micron variation among ellipticals correlates with stellar metallicity , reflecting emission from hot dust in winds from asymptotic giant branch stars of varying metallicity . infrared surface brightness variations in elliptical galaxies indicate that the k - 24 color profile is u - shaped for reasons that are unclear . in some elliptical galaxies cold interstellar dust emitting at 70 and 160 microns may arise from recent gas - rich mergers . however , we argue that most of the large range of 70 micron luminosity in elliptical galaxies is due to dust transported from galactic cores by feedback events in ( currently ir - quiet ) active galactic nuclei . cooler dusty gas naturally accumulates in the cores of elliptical galaxies due to dust - cooled local stellar mass loss and may accrete onto the central black hole , releasing energy . agn - heated gas can transport dust in cores 5 - 10 kpc out into the hot gas atmospheres where it radiates extended 70 micron emission but is eventually destroyed by sputtering . this , and some modest star formation , defines a cycle of dust creation and destruction . elliptical galaxies evidently undergo large transient excursions in the banana plot in times comparable to the sputtering time or agn duty cycle , 10 myrs . normally regarded as passive , elliptical galaxies are the most active galaxies in the ir color - color correlation .

cond-mat0305137

c

although the gravitational field is often neglected in the description of physicochemical processes , it may have noticeable influence on such biological heavy objects as microtubules or actin filaments , essential components of living cells . the equilibrium properties of such objects is influenced even by the earth gravitational acceleration . the fields in an ultracentrifuge can multiple the effect of gravity . in this paper we focus on the major effects of the gravitational field on the process of self - assembly of linear aggregates . it is shown , that the concentration gradient induced by the gravitational field leads to the redistribution of aggregates of different lengths ( and thus , masses ) on different heights : the local concentration of the self - assembled rods interacting via the second virial coefficient decreases _ linearly _ with height in contrast to barometric distribution of aggregates with fixed length . this prediction can be directly checked experimentally in the rotating clinostat experiments . in turn , the average length of the aggregates has a square root dependence in contrast to hyperbolic dependence found for ideal aggregates.@xcite we also show , that except the redistribution of aggregates with height , the gravity induces the _ overall growth _ of the aggregates . the stiffness of the aggregates enhance the growth under gravity . strong enough gravitational field can provoke the isotropic to nematic phase transition , which is reflected in the significant broadness of the phase coexistence region . the transition manifests itself in the precipitation of the aggregates from the isotropic to the nematic phase regardless their length . furthermore , the length distribution of the aggregates is found to be very sensitive to the gravitational field : the gravity induces considerable polydispersity in the nematic phase . taken together , the effect of gravity can lead to a series of experimentally relevant observations which are interesting from fundamental point of view .

the influence of the gravitational field on the reversible process of assembly and disassembly of linear aggregates is focus of this paper . the gravitational field facilitates the isotropic to nematic phase transition reflecting in a broader transition region . . the fields in an ultracentrifuge can only reinforce the effect of gravity , so the present description can be applied to a wider range of systems .

the influence of the gravitational field on the reversible process of assembly and disassembly of linear aggregates is focus of this paper . even the earth gravitational field can affect the equilibrium properties of heavy biological aggregates such as microtubules or actin filaments . the gravity gives rise to the concentration gradient which results in the distribution of aggregates of different lengths with height . strong enough gravitational field induces the _ overall growth _ of the aggregates . the gravitational field facilitates the isotropic to nematic phase transition reflecting in a broader transition region . coexisting phases have notedly different length distributions and the phase transition represent the interplay between the growth in the isotropic phase and the precipitation into nematic phase . the fields in an ultracentrifuge can only reinforce the effect of gravity , so the present description can be applied to a wider range of systems .

1111.3176

i

complex network theory has opened the way for exploring many dynamical processes on large - scale systems consisting of individual components connected in a nontrivial topology . one of the most widely studied phenomena occurring on complex networks are spreading processes , with a prominent example attracting widespread attention being the spread of viruses in social or computer networks @xcite . there are several approaches being used in the analysis of epidemic spreading . one popular approach is the heterogeneous mean - field ( hmf ) prescription by coarse - graining nodes within degree classes and relaxing the problem by assuming that all nodes in a degree class have the same dynamical properties @xcite . however , it has been shown that hmf can result in different levels of accuracy @xcite . a more successful approach in determining the outcome of an infection was introduced by chakrabarti et.al @xcite where the sis epidemic model was analyzed by using a system of probability equations , which in fact , represents a deterministic non - linear dynamical system ( nlds ) . this approach was also used in @xcite , where a family of sis epidemic models is examined , parameterized by the number of stochastic contact trials per unit time , that range from contact processes ( where the contagion expands at a certain rate from an infective vertex to one neighbor at a time ) to reactive processes ( in which an infective individual effectively contacts all its neighbors to expand the epidemics ) . using a deterministic model , referred to as the microscopic markov - chain approach ( mmca ) , which is virtually equivalent to nlds , the whole phase diagram of the different infection models is constructed and their critical properties are determined . it is worth noting that using different number of stochastic contagion per unit time extends the usability of the model , since this number can surely vary for different real - world problems @xcite . recently , a mixed approach using both nlds and hmf was proposed in @xcite which lead to a nonperturbative formulation enhancing the predictive power of the classical hmf approach . heterogeneous environments have also been extensively studied . one such is an epidemic model with inhomogeneous infection probabilities on a graph with prescribed degree distribution @xcite where model s dynamics are derived for i.i.d . weights and for weights that are functions of the degrees . with the help of these theoretical frameworks , the role of network topology in the spreading process has been repeatedly emphasized , yielding the result of a finite threshold for the spreading process in networks with exponentially bounded degree distributions , and a vanishing threshold in infinite uncorrelated networks with a power - law degree distribution . a recent addition to these findings is that for the sis epidemic model , the vanishing threshold has nothing to do with the scale - free nature of the degree distribution , but is the result of the largest hub being a self - sustainable source for the infection @xcite ( see also @xcite ) . however , the currently established connections are very rough with a topology - related threshold differentiating between two extreme outcomes of the model . with the threshold being satisfied , there is still a large spectrum for different spreading parameters and the poorly understood role of the network s topology there motivated our work . in this paper we adopt the approach proposed in @xcite and study the deterministic epidemic model on graphs , in which the dynamics of individual nodes is described by a discrete - time markov chain . in the sis model , a node can be in one of two states : susceptible ( s ) or infective ( i ) . infective nodes can infect other neighbouring nodes , and each node can be randomly cured with probability @xmath2 per unit time . at each time step , an infective node makes a number of trials per unit time to transmit the disease to its neighbours with probability @xmath3 . we consider two specific cases : ( i ) the contact process , which involves a single stochastic contagion per infective node per unit time , and ( ii ) the reactive process , which involves as many stochastic contagions per unit time as neighbours a node has . the work in this paper extends that of @xcite . we derive upper and lower bounds on the probability of a node to be infective , and determine how tight the bounds are around the probability that a node is infective . for both processes the bounds are derived using the @xmath0hop neighbourhood of each node . the larger the considered neighbourhood the more topological information one uses to determine the bounds , hence the bounds are tighter . we use the difference between the upper and lower bound averaged over all nodes to determine the influence of the network topology on the spreading process and compute numerical results for a real - world e - mail network . for additional clarity , figure [ fig : plotedgraphs ] depicts the @xmath4-hop and @xmath5-hop neighborhood of a particular node in the enron e - mail network with degree 10 , together with the calculated bounds for its probability of infection derived using only its respective subgraph information . the outline of the paper is the following . section [ sec:2 ] gives the definition of the model and recovers known results . the contributions of this paper are contained in sections [ sec:3 ] and [ sec:4 ] . in section [ sec:3 ] the upper and lower bounds on the probability of being infective are derived for the reactive process , and numerical results for the e - mail network are presented . section [ sec:4 ] gives the bounds for the contact process , along with the corresponding numerical results . section [ sec : conc ] concludes the paper and points out future research directions .

the influence of the network s structure on the dynamics of spreading processes has been extensively studied in the last decade . our findings are complemented by numerical results for a real - world e - mail network . a very good estimate for the infection density @xmath1

the influence of the network s structure on the dynamics of spreading processes has been extensively studied in the last decade . important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network , such as the largest eigenvalue of a topology related matrix . however , little is known about the direct influence of the network topology on microscopic level , such as the influence of the ( neighboring ) network on the probability of a particular node s infection . to answer this question , we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible - infective - susceptible model for two cases of spreading processes : reactive and contact processes . the bounds are derived by considering the @xmath0hop neighborhood of the node ; the bounds are tighter as one uses a larger @xmath0hop neighborhood to calculate them . consequently , using local information for different neighborhood sizes , we assess the extent to which the topology influences the spreading process , thus providing also a strong macroscopic connection between the former and the latter . our findings are complemented by numerical results for a real - world e - mail network . a very good estimate for the infection density @xmath1 is obtained using only 2-hop neighborhoods which account for 0.4% of the entire network topology on average .

1111.3176

c

in this paper we have derived the upper and lower bounds on the probability that a node is infective for the sis model of infection spreading on networks , where the behavior of a node is modeled with a discrete - time markov chain sis model . we have considered the reactive and the contact process as two cases of the spreading process . for both processes we use the difference between upper and lower bounds on microscopic level to assess the dependence of the spreading processes on network topology . numerical results are given on the enron e - mail network . for both processes , the bounds are progressively better as one considers a larger @xmath0hop neighborhood of a node . for the reactive process , both bounds on the probability that a node is infective are tighter as @xmath152 and their difference is largest for nodes with average degree . conversely , the bounds on the probability that a node is infective for the contact process are tighter as @xmath153 . one of the main implications of the paper is that if @xmath3 is larger than its critical value ( when @xmath3 is close to @xmath148 the probability of a node to be infective is anyway close to zero ) , one can estimate the probability of being infective using only local information ( considering only @xmath0hop local topology , for small @xmath73 ) , without knowing the whole network . consequently , from this local information one can also estimate the density of being infective on the whole network , as well as assess the extend to which the topology affects the outcome of the infection on macroscopic level . the results of this paper are easily extendable to other ergodic models ( such as sirs , for example ) and are related to all types of spreading ( idea , failure , rumor ) @xcite , regardless on the type of the spread agent . how these results can be extended to sir model by considering sirs model and taking one of its parameters to approach zero ( or one ) so that sirs model in this limit approaches sir model is a question for further research .

, we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible - infective - susceptible model for two cases of spreading processes : reactive and contact processes . the bounds are derived by considering the @xmath0hop neighborhood of the node ; the bounds are tighter as one uses a larger @xmath0hop neighborhood to calculate them . consequently , using local information for different neighborhood sizes , we assess the extent to which the topology influences the spreading process , thus providing also a strong macroscopic connection between the former and the latter .

the influence of the network s structure on the dynamics of spreading processes has been extensively studied in the last decade . important results that partially answer this question show a weak connection between the macroscopic behavior of these processes and specific structural properties in the network , such as the largest eigenvalue of a topology related matrix . however , little is known about the direct influence of the network topology on microscopic level , such as the influence of the ( neighboring ) network on the probability of a particular node s infection . to answer this question , we derive both an upper and a lower bound for the probability that a particular node is infective in a susceptible - infective - susceptible model for two cases of spreading processes : reactive and contact processes . the bounds are derived by considering the @xmath0hop neighborhood of the node ; the bounds are tighter as one uses a larger @xmath0hop neighborhood to calculate them . consequently , using local information for different neighborhood sizes , we assess the extent to which the topology influences the spreading process , thus providing also a strong macroscopic connection between the former and the latter . our findings are complemented by numerical results for a real - world e - mail network . a very good estimate for the infection density @xmath1 is obtained using only 2-hop neighborhoods which account for 0.4% of the entire network topology on average .

astro-ph0207113

i

white dwarfs are the most common end points of stellar evolution . since they are long - lived and well understood objects , they constitute an invaluable tool to study the evolution and structure of our galaxy in general and of the galactic halo in particular ( isern et al . moreover , the discovery of microlenses towards the large magellanic cloud ( alcock et al . 2000 ; lasserre et al . 2001 ) has generated a large controversy about the possibility that white dwarfs could be responsible for these microlensing events and , thus , could provide a significant contribution to the mass budget of our galactic halo . however , white dwarfs as viable dark matter candidates are not free of problems , since an excess of them would imply as well an overproduction of red dwarfs and type ii supernovae . in order to overcome this problem adams & laughlin ( 1996 ) proposed a non standard initial mass function in which the formation of both low and high mass stars was suppresed . besides the lack of evidence for such biased initial mass functions , they also present additional problems . the formation of an average mass ( @xmath0 ) white dwarf is accompanied by the injection into the interstellar medium of a sizeable amount of mass ( typically @xmath1 ) per white white dwarf . since in turn type ii supernovae are suppressed in biased initial mass functions , there is not enough energy to eject this matter into the intergalactic medium and a mass that is roughly three times the mass of the resulting white dwarf has to be accomodated into the galaxy ( isern et al . 1998 ) . furthermore , the mass ejected in the process of formation of a white dwarf is significantly enriched in metals ( abia et al . 2001 ; gibson & mould 1997 ) . finally , an excess of white dwarfs may translate into an excess of binaries containing such stars . if there are many white dwarfs in binaries then the secondary can not be a red dwarf because these would these would be easily detected . therefore , we are then forced to assume that these binaries are double degenerates , which are one of the currently proposed scenarios for type ia supernovae . hence we are forced to face the subsequent increase of type ia supernova rates which , consequently , results in an increase in the abundances of the elements of the iron peak ( canal , isern & ruiz lapuente 1997 ) . however , other explanations , such as self lensing in the lmc ( wu 1994 ; salati et al . 1999 ) , or background objects ( green & jedamzik 2002 ) are possible and have not been yet totally ruled out . the debate of whether or not white dwarfs contribute significantly to the galactic halo dark matter has motivated a large number of observational searches ( knox , hawkins & hambly 1999 ; ibata et al . 1999 ; oppenheimer et al . 2001 ; majewski & siegel 2002 , nelson et al . 2002 ) and theoretical works ( reyl , robin & crez 2001 ; koopmans & blandford 2002 ; flynn , holopainen & holmberg 2002 ) and is still open . among the observational surveys perhaps the most extensive one is that of oppenheimer et al . ( 2001 ) who discovered 38 faint white dwarfs with large proper motions in digitized photographic plates from the supercosmos sky survey . oppenheimer et al . ( 2001 ) claimed that these white dwarfs are indeed halo white dwarfs since they have very large tangential velocities ( in excess of @xmath2 km s@xmath3 ) . based on this assumption , they derived a space density of 2% of the galactic dark halo density , which is smaller than previous claims ( alcock et al . 1997 ) for halo dark matter in the form of @xmath4 objects , but still significant . however , reid , sahu & hawley ( 2001 ) challenged this claim by noting that the kinematics of these white dwarfs is consistent with the high velocity tail of the thick disk . hansen ( 2001 ) provided evidence that this sample presents a spread in age that makes it more likely to belong to the thick disk population . reyl et al . ( 2001 ) and flynn et al . ( 2002 ) also support this interpretation . koopmans & blanford ( 2002 ) find that the contribution of these white dwarfs to the local halo dark matter density is smaller , of the order of 0.8% , which is in good agreement with the theoretical results of isern et al . ( 1998b ) and the observational findings of the eros team ( goldman et al . 2002 ) . in this paper we reexamine this issue by making use of a monte carlo simulator ( garca berro et al . 1999 ; torres et al . the paper is organized as follows . in section 2 we present the main properties of our monte carlo simulator . in 3 we discuss the effect of the color magnitude calibration on the distances of the white dwarfs in the sample of oppenheimer et al . ( 2001 ) whereas in 4 we analyze which is the probability of this sample to be drawn from a halo population . finally in 5 our conclusions are summarized .

( 2001 ) is still controversial . whereas these authors claim that they have finally found the elusive ancient halo white dwarf population that contributes significantly to the mass budget of the galactic halo , there have been several other contributions that argue that these white dwarfs are not genuine halo members but , instead , thick disk stars . stars : white dwarfs stars : luminosity function , mass function galaxy : stellar content galaxy : dark matter galaxy : structure galaxy : halo

the interpretation of the old , cool white dwarfs recently found by oppenheimer et al . ( 2001 ) is still controversial . whereas these authors claim that they have finally found the elusive ancient halo white dwarf population that contributes significantly to the mass budget of the galactic halo , there have been several other contributions that argue that these white dwarfs are not genuine halo members but , instead , thick disk stars . we show here that the interpretation of this sample is based on the adopted distances , which are obtained from a color magnitude calibration , and we demonstrate that when the correct distances are used a sizeable fraction of these putative halo white dwarfs belong indeed to the disk population . we also perform a maximum likelihood analysis of the remaining set of white dwarfs and we find that they most likely belong to the thick disk population . however , another possible explanation is that this sample of white dwarfs has been drawn from a 1:1 mixture of the halo and disk white dwarf populations . stars : white dwarfs stars : luminosity function , mass function galaxy : stellar content galaxy : dark matter galaxy : structure galaxy : halo

astro-ph0207113

c

we have presented evidence that the distances of the white dwarfs in the sample of oppenheimer et al . ( 2001 ) have not been correctly determined . the ultimate reason of this is that the authors used a calibration which is not appropriate for the halo white dwarf population . once the correct calibration is adopted it turns out that the distances to the most luminous white dwarfs in the sample have been underestimated , whereas the distances to the white dwarfs with small luminosities have been overestimated . we have also found that some white dwarfs in the sample can not have hydrogen dominated atmospheres , since their position in the color magnitude diagram is beyond the turn - off . as a consequence , once the corrected distances are taken into account , a good fraction of these putative halo white dwarfs have significantly smaller tangential velocities and can be safely discarded as genuine halo members . the remaining fraction of the sample of oppenheimer et al . ( 2001 ) has been analyzed using our monte carlo simulator . we have computed monte carlo models for the disk and the halo populations . the disk simulation naturally recovers both the thin and the thick disk populations . then we have computed the probability of the stars of the sample of oppenheimer et al . ( 2001 ) to belong to a randomly selected sample of both halo or disk white dwarfs . our results indicate that this subset of the sample of oppenheimer et al . ( 2001 ) does not belong exclusively to either the halo or the disk population at the 95% confidence level . regarding the disk population _ as a whole _ our results were not conclusive because of the small fraction of thick disk stars in a typical monte carlo simulation . however once the stars with small birth times ( @xmath74 2 gyr ) , corresponding to the thick disk , are selected we find that the number of stars in the sample nicely reproduces the values found by oppenheimer et al . ( 2001 ) , in agreement with the results of flynn et al . ( 2002 ) and reyl et al . there is yet another possibility which has not been previously explored . namely that the sample of oppenheimer et al . ( 2001 ) is drawn from a mixture of both the halo and the ( thick ) disk populations . we have found that in this case the probability is maximum for a 1:1 to ratio . hence , we conclude that the claim by oppenheimer et al . ( 2001 ) that , finally , the elusive halo white dwarf population has been found should be taken with caution and more observational searches and theoretical work are still needed . finally we have re - derived , using the distances obtained in this work , the number density of halo white dwarfs predicted by the sample of oppenheimer et al . we have found that a safe upper limit to this density is @xmath75 pc@xmath69 , assuming that _ all _ the white dwarfs found by oppenheimer et al . ( 2001 ) are true halo white dwarfs . if , as suggested by our simulations , we assume that only half of these stars are genuine halo members we find a number density of @xmath76 pc@xmath69 , which is in good agreement with previous independent determinations . _ acknowledgements . _ this work has been supported by the dges grant pb981183c0302 , by the mcyt grant aya20001785 , by the mcyt / daad grant ha20000038 and by the cirit grants 1995sgr-0602 and 2000aces-00017 . we would like to acknowledge the advise of nigel hambly in transforming our cooling sequences to the appropiate photometric passbands . we also would like to acknowledge the very valuable comments of our referee , chris flynn , which greatly improved the original version of the manuscript . abia , c. , domnguez , i. , straniero , o. , limongi , m. , chieffi , a. , & isern , j. , 2001 , , 557 , 126 adams , f.c . , & laughlin , g. , 1996 , , 468 , 686 alcock , c. , allsman , r.a . , alves , d. , axelrod , t.s . , becker , a.c . , bennett , d.p . , cook , k.h . , freeman , k.c . , griest , k. , guern , j. , lehner , m.j . , mashall , s.l . , peterson , b.a . , pratt , m.r . , quinn , p.j . , rodgers , a.w . , stubbs , c.w . , sutherland , w. , & welch , d.l . , 1997 , , 486 , 697 alcock , c. , allsman , r.a . , alves , d.r . , axelrod , t.s . , becker , a.c . , bennett , d.p . , cook , k.h . , dalal , n. , drake , a.j . , freeman , k.c . , geha , m. , griest , k. , lehner , m.j . , marshall , s.l . , minniti , d. , nelson , c.a . , peterson , b.a . , popowski , p. , pratt , m.r . , quinn , p.j . , stubbs , c.w . , sutherland , w. , tomaney , a.b . , vandehei , t. , & welch , d. , 2000 , , 542 , 281 bergeron , p. , ruiz , m.t . & leggett , s.k . , 1997 , , 108 , 339 bessell , m.s . , 1986 , , 98 , 1303 blair , m. , gilmore , g. , 1982 , , 94 , 742 bravo , e. , isern , j. , & canal , r. , 1993 , , 270 , 288 canal , r. , isern , j. , & ruiz - lapuente , p. , 1997 , , 1997 , 488 , 35 dehnen , w. & binney , j. , 1997 , , 294 , 429 dehnen , w. & binney , j. , 1997 , , 298 , 387 flynn , c. , holopainen , j. , & holmberg , j. , 2002 , , submitted , astro - ph/0202244 garca berro , e. , torres , s. , isern , j. , & burkert , a. , 1999 , , 302 , 173 gibson , b.k . , & mould , j.r . , 1997 , , 482 , 98 goldman , b. , afonso , a. , alard , ch . , albert , j .- n . , amadon , a. , andersen , j. , ansari , r. , aubourg , . , bareyre , p. , bauer , f. , beaulieu , j .- ph . , blanc , g. , bouquet , a. , char , s. , charlot , x. , couchot , f. , coutures , ch . , derue , f. , ferlet , r. , fouqu , p. , glicenstein , j .- f . , gould , a. , graff , d. , gros , m. , hassinski , j. , hamadache , c. , hamilton , j .- ch . , hardin , d. , kat , j. de , kim , a. , lasserre , th . , le guillou , l. , lesquoy , . , loup , c. , magneville , ch . , mansoux , b. , marquette , j .- b . , maurice , . , maury , a. , milsztajn , a. , moniez , m. , palanque - delabrouille , n. , perdereau , o. , prvot , l. , regnault , n. , rich , j. , spiro , m. , tisserand , p. , vidal - madjar , a. , vigroux , l. , & zylberajch , s. , 2002 , , in press , astro - ph/0205537 gould , a. , flynn , c. , & bahcall , j.n . , 1998 , , 499 , 728 green , a.m. , jedamzik , k. , , submitted , astro - ph/0203495 hansen , b.m.s . , 1999 , , 520 , 680 hansen , b.m.s . , 2001 , , 558 , l39 ibata , r.a . , richer , h.b . , gilliland , r.l . , & scott , d. , 1999 , , 524 , l95 isern , j. , garca berro , e. , hernanz , m. , mochkovitch , r. , & burkert , a. , 1995 , in _ white dwarfs _ d. koester & k. werner ( springer verlag ) , 19 isern , j. , garca berro , e. , hernanz , m. , mochkovitch , r. , & torres , s. , 1998a , , 503 , 239 isern , j. , garca berro , e. , hernanz , m. , & salaris , m. , 1998b , in `` the galactic halo : from field stars to globular clusters '' , ed . : a. noels , p. magain , d. caro , e. jehin , g. parmentier , & a. thoul , 347 knox , r.a . , hawkins , m.r.s . , & hambly , n.c . , 1999 , , 306 , 736 koopmans , l.v.e . , & blandford , r.d . , 2002 , , in press , astro - ph/0107358 lasserre , t. afonso . c. , albert , j.n . , andersen , j. , ansari , r. , aubourg , ' e. , bareyre , p. , bauer , f. , beaulieu , j.p . , blanc , g. , bouquet , a. , char , s. , charlot , x. , couchot , f. , coutures , c. , derue , f. , ferlet , r. , glicenstein , j.f . , goldman , b. , gould , a. , graff , d. , gros , m. , haissinski , j. , hamilton , j.c . , hardin , d. , de kat , j. , kim , a. , lesquoy , ' e. , loup , c. , magneville , c. , mansoux , b. , marquette , j.b . , maurice , ' e. , milsztajn , a. , moniez , m. , palanque - delabrouille , n. , perdereau , o. , pr ' evot , l. , regnault , n. , rich , j. , spiro , m. , vidal - madjar , a. , vigroux , l. , & zylberajch , s. , 2001 , , 355 , l39 leggett , s.k . , ruiz , m.t . , & bergeron , p. , 1998 , , 497 , 294 majewski , s.r . , & siegel , m.h . , 2002 , , 569 , 432 markovi , d. , & sommer - larsen , j. , 1997 , , 288 , 733 mihalas , d. , & binney , j. , 1981 , _ galactic astronomy _ freeman & co. ) nelson , c.a . , cook , k.h . , axelrod , t.s . , mould , j.r . , & alcock , c. , 2002 , , in press , astro - ph/0112414 oppenheimer , b.r . , hambly , n.c . , digby , a.p . , hodgkin , s.t . , & saumon , d. , science , 292 , 698 reyl , c. , robin , a.c . , & crze , m. , 2001 , , l53 reid , n.i . , sahu , k.c . , & hawley , s.l . , 2001 , , 559 , 942 salati , p. , taillet , r. , aubourg , ' e. , palanque - delabrouille , n. , & spiro , 1999 , , 350 , l57 salaris , m. , garca berro , e. , hernanz , m. , isern , j. & saumon , d. , 2000 , , 544 , 1036 saumon , d. , & jacobson , s.b . , 1999 , , 511 , l107 scalo , j. , 1998 , in _ the stellar initial mass function _ , eds . g. gilmore & d. howell ( pasp conference series ) , vol . 142 , 201 schmidt , m. , 1968 , , 151 , 393 torres , s. , garca berro , e. , & isern , j .. 1998 , , 508 , l71 wood , m.a . , 1995 , in 9@xmath77 european workshop on white dwarfs , ed . d. koester & k. werner ( berlin : springer ) , 41 wu , x. , 1994 , , 435 , 66

we show here that the interpretation of this sample is based on the adopted distances , which are obtained from a color magnitude calibration , and we demonstrate that when the correct distances are used a sizeable fraction of these putative halo white dwarfs belong indeed to the disk population . we also perform a maximum likelihood analysis of the remaining set of white dwarfs and we find that they most likely belong to the thick disk population .

the interpretation of the old , cool white dwarfs recently found by oppenheimer et al . ( 2001 ) is still controversial . whereas these authors claim that they have finally found the elusive ancient halo white dwarf population that contributes significantly to the mass budget of the galactic halo , there have been several other contributions that argue that these white dwarfs are not genuine halo members but , instead , thick disk stars . we show here that the interpretation of this sample is based on the adopted distances , which are obtained from a color magnitude calibration , and we demonstrate that when the correct distances are used a sizeable fraction of these putative halo white dwarfs belong indeed to the disk population . we also perform a maximum likelihood analysis of the remaining set of white dwarfs and we find that they most likely belong to the thick disk population . however , another possible explanation is that this sample of white dwarfs has been drawn from a 1:1 mixture of the halo and disk white dwarf populations . stars : white dwarfs stars : luminosity function , mass function galaxy : stellar content galaxy : dark matter galaxy : structure galaxy : halo

0909.4304

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the majority of stars form in clusters of 100 or more members @xcite . the dynamics and distribution of stars within clusters have important ramifications for planet formation , stellar multiplicity , mass segregation , cluster disruption , and any other property of stars and planets that can be influenced by interactions between stars in the dense environment of a young cluster . for example , @xcite show that close encounters with neighboring stars can disrupt the outer parts of planetary systems ( however , see @xcite ) . at an earlier stage , protoplanetary disks in dense clusters are subject to dynamical disruption ( e.g. @xcite ) , photoevaporation ( e.g. @xcite ) , and contamination with short - lived radio - nuclides ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . on larger scales , radiation from neighboring stars in a cluster is an important feedback effect that can modify the stellar imf @xcite , while gravitational interactions among stars lead to mass segregation @xcite . all of these phenomena depend critically on the kinematics of newly formed stars , since this determines the frequency of star - star encounters . kinematics also influence the fraction of star clusters that remain bound rather than dissolving into the field ( e.g. * ? ? ? . observations of the kinematics of young stars are challenging because the stars spend much of their youth enshrouded by gas , making spectroscopy difficult . however , measurements have been possible in a few regions , most notably the orion nebula cluster ( onc ) , a particularly interesting and well - studied young star cluster containing thousands of optically revealed stars as well as traces of remnant molecular gas . the onc is observed to be centrally concentrated and mass segregated , with the most massive stars residing in the center ( e.g. @xcite ) . radial velocity measurements of stars within the onc indicate a substantial stellar velocity gradient and significant correlation between the local gas and star velocities @xcite . as a result , @xcite suggest that the onc is kinematically young and not dynamically relaxed , which they interpret as requiring that the parent cloud be in a state of dynamical collapse @xcite , rather than evolving in quasi - equilibrum @xcite . @xcite use n - body simulations to demonstrate that collapsing clusters with subvirial initial conditions can indeed generate such observational signatures . however , it is far from clear how to extrapolate from observations of stellar kinematics to the conditions within the host giant molecular cloud ( gmc ) , particularly since not all components of a gmc share the same velocity dispersion . instead , the dispersion of the line - of - sight ( centroid ) gas velocity decreases with density ( e.g. @xcite ) . gas velocity dispersions in prestellar cores are comparable to the sound speed and are much less than the global cloud virial velocity @xcite . furthermore , the dispersion of the bulk velocities of the cores themselves is found to be subvirial @xcite , indicating the the relative motion between cores is small . molecular gas in star forming regions such as perseus and ophiuchus also exhibits large - scale linear velocity gradients similar to those observed in the orion stellar population @xcite . perseus , in particular , resembles an elongated filament with a gradient of @xmath3 km s@xmath2 pc@xmath2 along its length , similar to the onc . these observations of dense gas suggest that one can not simply assume that , because stars are subvirial , the parent cloud must be too . indeed , for gas the opposite appears to be the case . all of these subvirial signatures for dense components coexist with large - scale velocity dispersions that are consistent with virial balance ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? simulations of turbulent , virialized clouds are able to reproduce the observed kinematics of dense gas @xcite , while simulations of clouds undergoing subvirial collapse have trouble producing quiescent cores like those we observe @xcite . nor do clouds appear to convert large fractions of their mass into stars in a single dynamical time , as expected for a subvirial collapse ( e.g. * ? ? ? * ; * ? ? ? instead , observations both of individual star - forming regions @xcite and entire galaxies @xcite show that , even for gas as dense as the cloud that formed the onc , @xmath4 of the mass per dynamical time can form stars . the complicated relationship between the kinematics of dense and diffuse gas in molecular clouds suggests that it would be profitable to perform a systematic investigation of how the kinematics of newborn stars relate to the properties of the clouds from which they formed . such an investigation is also of broader interest , since , as noted above , the kinematics of young clusters have a strong influence on planet formation , mass segregation , and other aspects of star and star cluster evolution . thus it is important to develop first - principles predictions for the expected motion of newborn stars as a function of parent cloud properties , a subject that has not been investigated prior to this work . in this letter , we use turbulent , self - gravitating , adaptive mesh refinement ( amr ) hydrodynamics simulations of star cluster formation to study the properties of the star clusters that form in clouds in a variety of dynamical states . in particular , we examine the stellar velocity dispersion , projected velocities , and velocity gradients . we compare the simulation results with recent observations of the onc and discuss the relevance to current modeling of star clusters . in [ parameters ] we describe our simulation methods and parameters . in [ results ] we present our results , and we summarize our findings in [ conclusions ] .

the kinematics of newly - formed star clusters are interesting both as a probe of the state of the gas clouds from which the stars form , and because they influence planet formation , stellar mass segregation , cluster disruption , and other processes controlled in part by dynamical interactions in young clusters . however , to date there have been no attempts to use simulations of star cluster formation to investigate how the kinematics of young stars change in response to variations in the properties of their parent molecular clouds . in this letter we report the results of turbulent self - gravitating simulations of cluster formation in which we consider both clouds in virial balance and those undergoing global collapse . we find that stars in these simulations generally have velocity dispersions smaller than that of the gas by a factor of @xmath0 , independent of the dynamical state of the parent cloud , so that subvirial stellar velocity dispersions arise naturally even in virialized molecular clouds . we conclude that star clusters should display subvirial velocity dispersions , large - scale velocity gradients , and strong gas - star velocity correlations regardless of whether their parent clouds are in virial balance , and , conversely , that observations of these features can not be used to infer the dynamical state of the parent gas clouds .

the kinematics of newly - formed star clusters are interesting both as a probe of the state of the gas clouds from which the stars form , and because they influence planet formation , stellar mass segregation , cluster disruption , and other processes controlled in part by dynamical interactions in young clusters . however , to date there have been no attempts to use simulations of star cluster formation to investigate how the kinematics of young stars change in response to variations in the properties of their parent molecular clouds . in this letter we report the results of turbulent self - gravitating simulations of cluster formation in which we consider both clouds in virial balance and those undergoing global collapse . we find that stars in these simulations generally have velocity dispersions smaller than that of the gas by a factor of @xmath0 , independent of the dynamical state of the parent cloud , so that subvirial stellar velocity dispersions arise naturally even in virialized molecular clouds . the simulated clusters also show large - scale stellar velocity gradients of @xmath1 km s@xmath2 pc@xmath2 and strong correlations between the centroid velocities of stars and gas , both of which are observed in young clusters . we conclude that star clusters should display subvirial velocity dispersions , large - scale velocity gradients , and strong gas - star velocity correlations regardless of whether their parent clouds are in virial balance , and , conversely , that observations of these features can not be used to infer the dynamical state of the parent gas clouds .

1610.01021

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the lagrange - mesh method @xcite is a simple and often accurate method for solving quantum - mechanical problems . it can be seen as an approximate variational calculation using a basis of lagrange functions associated with a mesh and the gauss quadrature associated with this mesh to evaluate most of the matrix elements . for reasons not perfectly understood @xcite , the lagrange - mesh method is in many applications as accurate as the corresponding variational approach . however , the success of the lagrange - mesh method relies ultimately on the validity of the gauss quadrature . therefore , when the quality of the gauss - quadrature approximation is poor , the lagrange - mesh method is inaccurate . in particular , it happens when the potential is singular but surprisingly , only for the lowest partial waves @xcite . for some problems , the high accuracy of the lagrange - mesh method can be restored by means of a regularization technique @xcite . for other problems , such a regularization technique is not available , yet . it is the case for instance for the study of a coulomb system with more than three particles . in the case of three particles , the presence of singularities in the potential restricts the high quality of the lagrange - mesh method to some specific systems of coordinates @xcite . a better understanding of the regularization process , its effects and its necessity , could help to develop new regularization techniques and thus , broaden the scope of applicability of the lagrange - mesh method . in this paper , a regularized lagrange mesh based on orthonormal lagrange - laguerre functions is developed and applied to bound - state calculations . a comparison with other lagrange meshes provides interesting insight into the regularization process . the lagrange - mesh method is also extended to the phase - shift calculations by evaluating integral relations derived from the kohn variational principle and adapted from @xcite . the integral relations are computed with the gauss quadrature associated with the lagrange mesh , which make their evaluation particularly easy . the accuracy of the approach is analyzed . in sec . [ s2 ] , the application of the lagrange - mesh method to the study of bound states and to the calculation of phase shifts is outlined . the lagrange meshes considered in this work are defined in sec . formulae associated with these meshes and newly derived are given . in sec . [ s4 ] , the lagrange - mesh method is applied to different test cases and the obtained results are discussed . concluding remarks are given in sec . finally , in the appendix , the lagrange - mesh method is applied to a somehow exotic but illuminating problem : the study of bound states in a two dimensional space .

although this method provides accurate results in many problems with small number of mesh points , its accuracy can be strongly reduced by the presence of singularities in the potential term . in this paper , a new regularized lagrange - laguerre mesh , based on _ exactly _ orthonormal lagrange functions , is devised . the analysis of these results and a comparison with other lagrange - mesh calculations lead to a simple rule to predict in which cases a singularity does induce or not a significant loss of accuracy in lagrange - mesh calculations . in addition , the lagrange - laguerre - mesh approach is applied to the evaluation of phase shifts via integral relations . _ keywords _ : lagrange - mesh method , gauss quadrature , potential model , bound states and continuum

the lagrange - mesh method is an approximate variational approach having the form of a mesh calculation because of the use of a gauss quadrature . although this method provides accurate results in many problems with small number of mesh points , its accuracy can be strongly reduced by the presence of singularities in the potential term . in this paper , a new regularized lagrange - laguerre mesh , based on _ exactly _ orthonormal lagrange functions , is devised . it is applied to two solvable radial potentials : the harmonic - oscillator and coulomb potentials . in spite of the singularities of the coulomb and centrifugal potentials , accurate bound - state energies are obtained for all partial waves . the analysis of these results and a comparison with other lagrange - mesh calculations lead to a simple rule to predict in which cases a singularity does induce or not a significant loss of accuracy in lagrange - mesh calculations . in addition , the lagrange - laguerre - mesh approach is applied to the evaluation of phase shifts via integral relations . small numbers of mesh points suffice to provide very accurate results . _ keywords _ : lagrange - mesh method , gauss quadrature , potential model , bound states and continuum

physics0007061

i

the conceptual design of the tesla linear collider with integrated x - ray laser facility @xcite requires that one of the two 15 km long super - conducting linear accelerator has to provide beams for high energy physics ( hep ) experiments and beams for the x - ray free electron laser ( fel ) facility . linear accelerator of the tesla linear collider with integrated x - ray laser facility . , width=294 ] fig . [ overview ] shows the e@xmath1 linear accelerator which is used to accelerate the hep - beam to 250 gev and the fel - beam to energies up - to 50 gev . there are 25 gev and 50 gev extraction points in the linac . the hep beam is injected from the dog - bone damping ring into the main linear accelerator while the fel beam is generated with an rf - gun and accelerated to 5 gev in an injector linac before it is also injected into the main linear accelerator . the first part of the e@xmath1 linear accelerator is operated at a duty cycle of 10 hz providing hep ( 2882 bunches ) and fel ( 11315 bunches ) pulses in a alternating way . the pulse structure is illustrated in fig . [ pulse ] . the fel - pulses are accelerated at the same gradient of 17 mv / m but are ejected at 25 gev or 50 gev beam energy to be used for different undulators . the basic optical building block is a fodo cell with a length of 65 m for the first half of the linac ( up - to 125 gev ) and a length of 97 m for the second half . two cryo - modules , housing 12 ( 7-cell ) cavities each , will fit between two quadrupoles of the 65 m long fodo cell , while three cryo - modules will fit between the quadrupoles of the 97 m long cell . the quadrupole strength @xmath2 ( @xmath3 the gradient of the magnet , @xmath4 the momentum of the beam ) is different for the fel and hep beams due to the different accelerating gradients : @xmath5 . a betatron phase advance of 60@xmath0 is chosen for the hep beam optics . this corresponds to a phase advance of about 90@xmath0 for the fel beam since the focusing is stronger than that of the hep beam due to the lower momentum . for the availability of the beams it is important that a power supply failure or even a magnet failure does not cause a significant down time of the linac . in the next section it will be shown how the lattice can be matched with a quadrupole `` missing '' in the case of the 60@xmath0-fodo lattice . finally it is demonstrated that it is possible to match the lattice _ simultaneously _ for both beams .

the lattice for the present design of the tesla linear collider with integrated x - ray laser facility is basically a fodo structure with constant beta - function . there are more than 800 individually powered superconducting quadrupoles to focus the beam in the two main linear accelerators ( each with a length of 15 km ) . for the availability of the beams it is important that a power supply failure or even a magnet failure does not cause a significant down time of the linac . it is demonstrated that the beta - function can be matched with a quadrupole `` missing '' . one part of the main linac ( up - to 50 gev ) will be used to accelerate the high energy physics beam and the free electron laser drive beam with different accelerating gradients . therefore the betatron phase advance will be 60@xmath0 or 90@xmath0 depending on the beam energy . it is shown that even in that case it is possible to match the lattice simultaneously for both beams with a quadrupole missing .

the lattice for the present design of the tesla linear collider with integrated x - ray laser facility is basically a fodo structure with constant beta - function . there are more than 800 individually powered superconducting quadrupoles to focus the beam in the two main linear accelerators ( each with a length of 15 km ) . for the availability of the beams it is important that a power supply failure or even a magnet failure does not cause a significant down time of the linac . it is demonstrated that the beta - function can be matched with a quadrupole `` missing '' . one part of the main linac ( up - to 50 gev ) will be used to accelerate the high energy physics beam and the free electron laser drive beam with different accelerating gradients . therefore the betatron phase advance will be 60@xmath0 or 90@xmath0 depending on the beam energy . it is shown that even in that case it is possible to match the lattice simultaneously for both beams with a quadrupole missing .

astro-ph0212063

i

the longstanding problem of the generation of turbulence in various hydrodynamically stable situations has found a solution in recent years with the mhd shear flow instability , also called magnetorotational instability ( mri ) , in which the presence of a magnetic field has a destabilizing effect on a differentially rotating flow with the angular velocity decreasing outwards . the mri has been formulated decades ago @xcite for ideal taylor - couette flow , but its importance as the source of turbulence in accretion discs with differential ( keplerian ) rotation was first recognized by balbus and hawley , @xcite . however , the mri has never been observed in the laboratory @xcite . after goodman and ji @xcite was the absence of mri due to the small magnetic prandtl number approximation used in @xcite . the magnetic prandtl number pm is really very small under laboratory conditions ( @xmath10 and smaller , see table [ tab0 ] ) . let us now concentrate to the small magnetic prandtl number for liquid sodium , i.e. pm @xmath11 . we start with the results for containers with insulating walls and outer cylinders at rest , ( fig . there are then linear instabilities even without magnetic fields . for ha@xmath12 solutions for @xmath13 ( re@xmath14 ) and @xmath15 ( re@xmath16 ) are known , see @xcite . the axisymmetric mode possesses the lowest eigenvalue . this is also true for nonvanishing magnetic field ; we do not find any crossover of the instability lines for axisymmetric and nonaxisymmetric modes . the same is true for containers with rotating outer cylinder ( fig . [ for growing @xmath17 the reynolds number for the hydrodynamic solution moves upwards , reaching infinity for @xmath18 ( here ) . the mri is represented by characteristic minima , in our case for @xmath19 at hartmann numbers of order @xmath20 and reynolds numbers of order @xmath9 . the exact coordinates of the minima are given in table [ tab1 ] . in order to characterize the hartmann numbers note that for liquid sodium @xmath21 hence , for @xmath22 the magnetic field and the hartmann number have the same numerical values . with @xmath23 @xmath24/s and @xmath25=0.5 it follows from ( [ re ] ) and ( [ ha ] ) f_in= 64re/10 ^ 6(r_out/10cm)^2 hz [ fff ] for the frequency of the inner cylinder . hence , a container with an outer radius of 22 cm ( see above ) and an inner radius of 11 cm filled with liquid sodium and embedded in vacuum requires a _ rotation of about 19 hz _ in order to find the mri . following ( [ b2.22 ] ) the required magnetic field is about 1400 gauss . the results for containers with _ conducting walls _ are given in fig . note that the minimal reynolds numbers given in fig . [ f2]b are higher than for insulating cylinder walls . the influence of the boundary conditions is not as small as expected . the main difference between the two sorts of boundary conditions , however , is the existence of crossovers of the instability lines for @xmath13 and @xmath15 in case of conducting walls . for both resting and rotating outer cylinder hartmann numbers exist above which the nonaxisymmetric mode possesses a lower reynolds number than the axisymmetric mode . we have already shown the existence of such crossovers for conducting walls for @xmath26 in @xcite . it is now clear that the occurrence of nonaxisymmetric solutions as the preferred modes is a rather general phenomenon for containers with conducting walls which can become important for the design of future dynamo experiments ( cowling theorem ) . there are not only stationary patterns of flow and field possible but the instability can also onset in form of oscillating solutions . this effect is called overstability . in case of rotating convection between two layers heated from below the onset of the instability in form of oscillating solutions even possesses the lowest eigenvalues for certain prandtl numbers , @xcite . we find a very similar behavior for the mhd taylor - couette flow between conducting cylinders for resting outer cylinder ( see fig . [ over ] ) . it is a pair of waves traveling in positive and negative @xmath27-direction . note that the cylinder considered here has no bound in vertical direction . if the cylinder is finite , however , the possibility exists that traveling waves might be combined to standing waves . e. p. velikhov , sov . jetp * 9 * , 995 ( 1959 ) . s. chandrasekhar , _ _ h__ydrodynamic and hydromagnetic stability ( clarendon , oxford , 1961 ) . s. a. balbus and j. f. hawley , astrophys . j. * * 3**76 , 214 ( 1991 ) . r. j. donnelly and m. ozima , phys . rev . lett . * 4 * , 497 ( 1960 ) . r. j. donnelly and m. ozima , proc . a * * 2**66 , 272 ( 1962 ) . r. j. donnelly and d. r. caldwell , j. fluid . mech . * * 1**9 , 257 ( 1964 ) . a. brahme , physica scripta * 2 * , 108 ( 1970 ) . j. goodman and h. ji , j. fluid mech . * * 4**62 , 365 ( 2002 ) . k. noguchi , v. i. pariev , s. a. colgate , h. f. beckley and j. nordhaus , astrophys . j. * * 5**75 , 1151 ( 2002 ) . d. richard and j .- p . zahn , astron . astrophys . * * 3**47 , 734 ( 1999 ) . f. wendt , ing . arch . * 4 * , 577 ( 1933 ) . f. schultz - grunow , zamm * * 3**9 , 101 ( 1959 ) . d. a. shalybkov , g. rdiger and m. schultz , astron . astrophys . * * 3**95 , 339 ( 2002 ) . which is unknown in the hydrodynamic regime , counter rotation excluded , see e. r. krger , a. gross and r. c. diprima , j. fluid mech . * * 2**4 , 521 ( 1966 ) . d. elstner , r. meinel and g. rdiger , geophys . fluid dyn . * * 5**0 , 85 ( 1990 ) . g. rdiger , differential rotation and stellar convection : sun and solar - type stars ( gordon & breach science publishers , new york , 1989 ) . a. p. willis and c. f. barenghi , astron . astrophys . * * 3**88 , 688 ( 2002 ) . g. rdiger and d. a. shalybkov , phys . e * * 6**6 , 016307 ( 2002 ) . .- k . chen and m. chang , j. fluid mech . * * 3**66 , 135 ( 1998 ) .

the linear stability of mhd taylor - couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic prandtl number pm of order of @xmath0 . the calculations are performed for a container with @xmath1 with an axial uniform magnetic field excluding counter rotating cylinders . the sign of the constant @xmath2 in the basic rotation law @xmath3 strongly influences the presented results . it is negative for resting outer cylinder . the main point here is that the subcritical excitation which occurs for large pm disappears for small pm ( cf . fig . [ minima ] ) . this is the reason that the existence of the magnetorotational instability remained unknown over decades . for rotating outer cylinder the limiting case @xmath4 ( i.e. @xmath5 ) plays an exceptional role . the hydrodynamic instability starts to disappear while the hydromagnetic instability exists with minimal reynolds numbers at certain hartmann numbers of the magnetic field . these reynolds numbers exactly scale with pm@xmath6 resulting in moderate values of order @xmath7 for pm=10@xmath8 . however , already for the smallest positive value of @xmath2 the reynolds numbers start to scale as 1/pm leading to much higher values of order @xmath9 for pm=10@xmath8 . hence , for outer cylinders rotating faster than the limit @xmath4 it is exclusively the _ magnetic _ reynolds number rm which directs the excitation of the instability . they are resulting as lower for insulating walls ( ` vacuum ' ) than for conducting walls . generally , the magnetic reynolds numbers for liquid sodium have to exceed values of order 10 leading to frequencies of about 20 hz for the rotation of the inner cylinder if containers with ( say ) 10 cm radius are considered . the required magnetic fields are about 1000 gauss . also nonaxisymmetric modes have been considered . with vacuum boundary conditions their excitation is always more difficult than the excitation of axisymmetric modes ; we never observed a crossover of the lines of marginal stability . for conducting walls , however , such crossovers exist for both resting and rotating outer cylinders , and this might be essential for future dynamo experiments . in this case , however , the instability also can onset in form of _ oscillating _ axisymmetric patterns of flow and field and the reynolds numbers of these solutions are lower than the reynolds numbers for the stationary solutions .

the linear stability of mhd taylor - couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic prandtl number pm of order of @xmath0 . the calculations are performed for a container with @xmath1 with an axial uniform magnetic field excluding counter rotating cylinders . the sign of the constant @xmath2 in the basic rotation law @xmath3 strongly influences the presented results . it is negative for resting outer cylinder . the main point here is that the subcritical excitation which occurs for large pm disappears for small pm ( cf . fig . [ minima ] ) . this is the reason that the existence of the magnetorotational instability remained unknown over decades . for rotating outer cylinder the limiting case @xmath4 ( i.e. @xmath5 ) plays an exceptional role . the hydrodynamic instability starts to disappear while the hydromagnetic instability exists with minimal reynolds numbers at certain hartmann numbers of the magnetic field . these reynolds numbers exactly scale with pm@xmath6 resulting in moderate values of order @xmath7 for pm=10@xmath8 . however , already for the smallest positive value of @xmath2 the reynolds numbers start to scale as 1/pm leading to much higher values of order @xmath9 for pm=10@xmath8 . hence , for outer cylinders rotating faster than the limit @xmath4 it is exclusively the _ magnetic _ reynolds number rm which directs the excitation of the instability . they are resulting as lower for insulating walls ( ` vacuum ' ) than for conducting walls . generally , the magnetic reynolds numbers for liquid sodium have to exceed values of order 10 leading to frequencies of about 20 hz for the rotation of the inner cylinder if containers with ( say ) 10 cm radius are considered . the required magnetic fields are about 1000 gauss . also nonaxisymmetric modes have been considered . with vacuum boundary conditions their excitation is always more difficult than the excitation of axisymmetric modes ; we never observed a crossover of the lines of marginal stability . for conducting walls , however , such crossovers exist for both resting and rotating outer cylinders , and this might be essential for future dynamo experiments . in this case , however , the instability also can onset in form of _ oscillating _ axisymmetric patterns of flow and field and the reynolds numbers of these solutions are lower than the reynolds numbers for the stationary solutions .

1509.00965

i

one of the formidable tasks in heavy - ion physics is to identify a precise understanding of the jet - medium dynamics , the jet - medium interactions , and the jet - energy loss formalism . below , we study the influence of the details of the jet - medium coupling and the medium background on the simultaneous description of the nuclear modification factor ( @xmath1 ) and the high-@xmath0 elliptic flow ( @xmath2 ) measured at rhic and lhc @xcite for a radiative pqcd energy - loss ansatz @xcite . we contrast media determined via the viscous hydrodynamic approach vish2 + 1 @xcite with the parton - cascade bamps @xcite as well as a jet - medium coupling depending on the collision energy with a jet - medium coupling influenced by the energy of the jet , the temperature of the medium and non - equilibrium effects around the phase transition . besides this , we compare the jet - energy loss based on radiative pqcd @xcite with the hybrid ads energy - loss ansatz of ref . we contrast the pion nuclear modification factor obtained via the radiative pqcd - energy loss @xcite and the hybrid ads energy - loss ansatz with a parton - jet nuclear modification factor that can be considered as an idealized lo jet @xmath1 at rhic and lhc energies . the pqcd - based energy loss model studied is parametrized as @xcite @xmath3 with the jet - energy dependence @xmath4 , the path - length dependence @xmath5 , and the energy dependence @xmath6 . in the following , the jet - medium coupling @xmath7 will depend either on the collision energy @xmath8 or the energy of the jet and the temperature of the background medium considered @xmath9 . the jet - energy loss fluctuations are distributed via @xmath10 , allowing for an easy interpolation between non - fluctuating ( @xmath11 ) , uniform dirac distributions and distributions increasingly skewed towards small @xmath12 . the jets are spread according to a transverse initial profile specified by the bulk flow fields given by the vish2 + 1 and bamps backgrounds considered @xcite . on the other hand , the jet - energy loss of the hybrid ads energy - loss ansatz @xcite is based on falling strings @xcite where @xmath13 the initial jet energy is given by @xmath14 and the string stopping distance for quark and gluon jets is determined via @xmath15 with the jet - medium coupling @xmath16 for quarks and @xmath17 for gluons , including the respective casimir operators @xmath18 and @xmath19 . this energy loss ansatz has been integrated into our existing model @xcite . please note that ref . @xcite uses natural units , @xmath20 . for a direct comparison , we quote our results below using a dimensionless coupling . the main differences between the two energy - loss descriptions is the square - root dependence that leads to the formation of a bragg peak with the explosive burst of energy close to the end of the jet s evolution . there have been discussions in literature @xcite on the impact of the bragg peak . in line with previous findings @xcite we will show below that there is a difference between the hybrid ads energy - loss ansatz featuring a bragg peak and the pqcd model without a bragg peak , however , this difference is only marginal .

we extend our jet - energy loss model that is coupled to state - of - the - art hydrodynamic prescriptions to backgrounds generated by the parton cascade bamps . unfortunately , the results for both the pion and a parton - jet nuclear modification factor are insensitive to the jet - path dependence of the models considered . jet quenching , viscous hydrodynamics , transport model , jet holography

the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies are compared to results from a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we find that the high-@xmath0 ellitic flow requires to include realistic medium transverse flow fields and a jet - medium coupling including the effects of the energy of the jet , the temperature of the bulk medium , and non - equilibrium effects close to the phase transition . we extend our jet - energy loss model that is coupled to state - of - the - art hydrodynamic prescriptions to backgrounds generated by the parton cascade bamps . we demonstrate that the results for the hydrodynamic and the parton - cascade backgrounds show a remarkable similarity . unfortunately , the results for both the pion and a parton - jet nuclear modification factor are insensitive to the jet - path dependence of the models considered . jet quenching , viscous hydrodynamics , transport model , jet holography

1509.00965

c

we compared the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies to results obtained by a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we found that the simultaneous description of the @xmath1 and @xmath2 requires a jet - medium coupling that depends on the energy of the jet , the temperature of the medium @xcite , and non - equilibrium effects around the phase transition . we also contrasted a hydrodynamic background ( vish2 + 1 ) @xcite with a medium obtained from the parton cascade bamps @xcite and showed that the influence of the underlying bulk medium considered is suprisingly small . unfortunately , neiter the pion nor the lo jet @xmath1 are sensitive to the difference in the path - length between pqcd and ads models .

the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies are compared to results from a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we find that the high-@xmath0 ellitic flow requires to include realistic medium transverse flow fields and a jet - medium coupling including the effects of the energy of the jet , the temperature of the bulk medium , and non - equilibrium effects close to the phase transition .

the measured data on the nuclear modification factor for pions and reconstructed jets as well as on the high-@xmath0 elliptic flow at rhic and lhc energies are compared to results from a linear pqcd and a highly non - linear hybrid ads holographic model of jet - energy loss . we find that the high-@xmath0 ellitic flow requires to include realistic medium transverse flow fields and a jet - medium coupling including the effects of the energy of the jet , the temperature of the bulk medium , and non - equilibrium effects close to the phase transition . we extend our jet - energy loss model that is coupled to state - of - the - art hydrodynamic prescriptions to backgrounds generated by the parton cascade bamps . we demonstrate that the results for the hydrodynamic and the parton - cascade backgrounds show a remarkable similarity . unfortunately , the results for both the pion and a parton - jet nuclear modification factor are insensitive to the jet - path dependence of the models considered . jet quenching , viscous hydrodynamics , transport model , jet holography

hep-ph0410291

i

the physics potential of a photon collider @xcite is very rich and complementary to the physics program of the and hadron - hadron colliders . it is an ideal place to study the mechanism of the electroweak symmetry breaking ( ewsb ) and the properties of the higgs - boson . in paper @xcite we performed a realistic simulation of the standard model ( sm ) higgs - boson production at the photon collider for @xmath0 and @xmath1 decay channels , for higgs - boson masses above 150 gev . from the combined analysis of @xmath0 and @xmath1 invariant mass distributions the @xmath2 partial width of the higgs boson , , can be measured with an accuracy of 3 to 8% and the phase of @xmath3 amplitude , , with an accuracy between 30 and 100 mrad . in paper @xcite we extended this analysis to the generalised standard model - like scenario @xmath4 of the two higgs doublet model ii , 2hdm(ii ) , with and without cp - violation . in case of the solution @xmath4 with a weak cp violation via @xmath5 mixing , the mixing angle @xmath6 can be constrained to about 100 mrad for low values of @xmath7 . we found that for a general 2hdm ( ii ) with cp violation , only the combined analysis of lhc , lc and photon collider measurements allows for the precise determination of higgs - boson couplings and of cp - violating @xmath5 mixing angle @xcite . in this paper our aim is to establish cp - property of the higgs - boson in a generic model with a direct cp - violation . the measurement of the higgs - boson properties at the photon collider at tesla is studied in detail for masses between 200 and 350 gev , using realistic luminosity spectra and detector simulation . the model with generic , cp - violating higgs - boson couplings to vector bosons @xcite leads to different angular distributions for a scalar- and pseudoscalar - type of couplings . from a combined analysis of invariant mass distributions and angular distributions of the @xmath0 and @xmath8 decay - products the cp - parity of the observed higgs state can be determined independently on a production mechanism @xcite . results given in this paper supersede results presented in the second part of our earlier work @xcite .

understanding of the detector performance turns out to be crucial , as the influence of the acceptance corrections is similar to the effects of cp violation . from the combined measurement of invariant mass distributions and various angular distributions the phase describing a cp violation can be determined to about 50 mrad after one year of photon collider running .

the model - independent determination of the higgs - boson cp properties at the photon collider at tesla has been studied in detail , for masses between 200 and 350 gev , using realistic luminosity spectra and detector simulation . we consider a generic model with the cp violating higgs tensor couplings to gauge bosons . we introduce a new variable describing angular distributions of the secondary ww and zz decay products which is very sensitive to the cp properties of the higgs - boson . understanding of the detector performance turns out to be crucial , as the influence of the acceptance corrections is similar to the effects of cp violation . from the combined measurement of invariant mass distributions and various angular distributions the phase describing a cp violation can be determined to about 50 mrad after one year of photon collider running .

1503.08527

i

various effects of flooding can drastically alter an ecosystem . some of the factors that could potentially harm trees include alteration of soil factors , disturbance of plant life , and degeneration of habitat . during a flood , soil is altered by erosion , deoxygenation , and reconfiguration ( kozlowski 1997 ; lake 2011 ) . erosion is caused by the continuous circular and turbulent motion of the water . this motion carries particles of the soil away , resulting in a loss of topsoil , loss of nutrients , and an exposure of plant roots ; all three of these factors severely harm plants ( shafroth et al . the topsoil is reconfigured with the finer particles that were carried with the flood , such as sand and silt , which may to compact into finer arrangements . this compacted soil restricts the ability to hold gases such as oxygen , causing deoxygenation of the soil ( parrett 1964 ) . flooding disturbs not only the abiotic factors of the environment , but also the biotic factors . plants suffocate and decompose due to the flood waters ( parolin & wittmann 2010 ) . this can result in stunting , damaging , or even killing of trees ( joly & crawford 1982 ) . the warm , stagnant water is a suitable habitat for several bacteria and fungi . this can cause tree rot as the bacteria and fungi in the water inhibit the trees natural ability to carry nutrients and water ( coder 1994 ) . because the part of a tree is submerged , the tree is likely to undergo suffocation if it is submerged for a long period of time . the suffocation of trees is caused by the lack of oxygen in the stagnant flood waters . if there is a faster flowing current , the water can also damage a tree s structure by breaking off branches or uprooting it altogether . considering both abiotic and biotic factors , flooding substantially distorts the original environment . damage to native plant life during the flood and the change in soil configuration after the flood may provide a more suitable environment for foreign species ( yanosky 1982 ) . since the postdiluvian soil determines the species of plants present , a flood can restructure an ecosystem ( bratkovich 1993 ) . minot , north dakota , is positioned in the souris river valley . the souris river originates in canada , flows south into the united states at north dakota , passes through minot , and then turns north again to re - enter canada . flooding of varying severity is common along the souris river . despite numerous previous floods , none were as large as the flood of 2011 . record water levels from the 1969 flood were surpassed as water rose to 457.8 m above sea level . this record flood event submerged houses and crested bridges . warm , stagnant , and hypoxic waters from summer rains covered the valley for approximately 23 days in june and july ( `` timeline ... '' ) . the river banks are presently wider and contain more silt than the antediluvian banks ; this was caused by erosion of the banks . the flood has also affected the plant life present in the flood plain . vast areas of the minot flood plain were drastically over - saturated during the flood , causing a degeneration of suitable habitats for most indigenous plant species ( `` timeline ... '' ) . studying tree species in minot has allowed for better understanding of the extent of damage suffered by trees during floods . by determining which trees are best adapted to survive in flooding situations , informed decisions can be made when planting trees in areas prone to flooding . this knowledge will allow for the least sustained damage of habitats after future floods . here , we analyze data collected regarding the impact of a flood event on tree damage . we hypothesize that tree height , genus , and maximum water level are all determining factors in the severity of damage sustained by a tree in a flood event .

we hypothesized that tree height , identity , origin , and maximum water height affect in the severity of damage sustained by a tree in a flood event . the results from this research can influence planting practices in valleys and other flood prone areas to mitigate future damage .

the objective of this research was to identify factors affecting tree damage in the historical minot flood of 2011 . we hypothesized that tree height , identity , origin , and maximum water height affect in the severity of damage sustained by a tree in a flood event . all these factors were significant but highly interactive . the results from this research can influence planting practices in valleys and other flood prone areas to mitigate future damage .

astro-ph9711043

i

the rise of magnetic flux from the deep levels of the solar convection zone to the photosphere is a complex phenomenon involving many different magnetic and hydrodynamical processes . particular attention has been devoted in the past @xmath5 years to the time - evolution of a single buoyant magnetic flux tube considered as a one - dimensional object ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ; @xcite . further references and a recent review can be found in the paper by @xcite ) . these calculations incorporate several aspects of the basic physics of the rise of the magnetic tubes ( buoyancy , magnetic and rotational forces , external stratification , etc ) . they have been successful in predicting morphological and kinematic features of the resulting active regions which are observed at the surface of the sun . yet , the assumption of one - dimensionality of the magnetic region is certainly a drastic simplification . from laboratory and numerical experiments in different contexts we know of the complicated hydrodynamical and magnetic structure within and outside a tubular object which is moving with respect to the surrounding fluid . the one - dimensional numerical models mentioned above , in particular , do not contain two ingredients which turn out to be fundamental in studying the rise of buoyant magnetized plasma regions , to wit , the vorticity of the velocity field and the twist of the field lines around the main axis of the tube . vorticity and transverse field components may be crucial for the formation of the tubes in the first place ( @xcite ; @xcite ; @xcite ) . they also play a central role in the time evolution of the rising magnetic region . a clear warning in this sense came from the work of schssler ( 1979 ) , who showed how the cross section of a straight , buoyant magnetic tube initially with the same temperature of its surroundings develops an _ umbrella _ shape ( two side lobes connected on their upper side by an arch ) . the side lobes rotate in opposite directions around a horizontal axis , each thus constituting a vortex tube ; they finally detach from each other and from the arch above them . the whole process occurs at the beginning of the rise , namely before the tube has risen across a height equivalent to a few times its own diameter . the physics involved has been considered in detail by longcope , fisher & arendt ( 1996 ) . these authors have studied the boussinesq problem , including untwisted and very weakly twisted magnetic tubes . they clearly show how the two rotating side lobes , when detached from the rest , are subjected to a downward - pointing lift force , as a result of their flow being non - circulation free . the lift ends up cancelling the buoyancy force , this being the reason for their horizontal asymptotic motion . if this were a universal mechanism operating on all rising magnetic flux tubes , then magnetic buoyancy should no longer be considered an efficient mechanism to bring magnetic flux to the photosphere . in the present paper we consider in detail the more general case of a buoyant magnetic flux tube with an arbitrary initial twist of the field lines ( but still horizontal and with uniform values of all variables along the direction of the axis ) . the transverse magnetic field ( i.e. , the component of the field vector normal to the tube axis ) imparts a certain rigidity to the tube cross section . if strong enough , it can prevent the conversion of the tube into a vortex tube pair . the minimum amount of twist necessary for that corresponds to an average pitch angle of order @xmath6 the external pressure scaleheight , and @xmath7 the density difference between tube and surroundings ( see [ sec_tube_unity ] ) . this approximate criterion is indeed fulfilled by magnetic tubes with the classical parker magnetic buoyancy , as shown in a preliminary presentation of this paper ( @xcite ) . in the present article , we explore in more detail the physics involved in that process , discussing a number of ( m)hd processes occurring inside the tube , in the boundary layer at its periphery and in the trailing wake . we also show how the results of schssler ( 1979 ) and longcope ( 1996 ) can be seen as the limiting case in which the trailing wake in fact engulfs most of the original rising tube . the pitch angle just mentioned thus signals the borderline between the weak and strong twist regimes : a buoyant tube with an initial twist above that level rises without being strongly deformed and is followed by a wake containing only a small fraction of the initial total magnetic flux . additionally to the work of moreno - insertis & emonet ( 1996 ) , there is another paper in the recent literature dealing with a related subject ( cargill et al . the authors have studied the interaction of a twisted tube with a magnetized medium in the absence of gravity when the tube is subjected to an ad - hoc , spatially uniform acceleration . special emphasis was put on the reconnection of the ambient magnetic field with the tube s own one . buoyancy , stratification , or different degrees of twist were not studied in that paper . two further papers , submitted simultaneously with the present one , deal with the rise of buoyant twisted magnetic tubes ( @xcite ; hughes , falle & joarder , 1998 ) . the first authors , in particular , study the interaction between tubes rising in pairs . the results of both papers concerning the rise of single tubes are in general agreement with those of moreno - insertis & emonet ( 1996 ) . the layout of the paper is as follows . after a brief presentation of the equations and the numerical procedure in [ sec_equations ] , the basic features of the physical problem are considered ( [ sec_parameters ] ) . this includes the main parameters and a discussion of the amount of twist necessary to prevent the deformation of the tube and its conversion into vortex rolls . in [ sec_rise ] , the simulation of the rise of a tube with that amount of twist is presented . in particular , the initial acceleration phase , the internal torsional oscillations and the later asymptotic phase are discussed . section [ sec_interface ] deals with the structure of the magnetic boundary layer around the tube , and [ sec_wake ] examines the trailing wake . finally , the transition between the twisted and untwisted case is explained in [ sec_split ] . a general discussion follows in [ sec_discussion ] .

the physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical mhd code . , the minimum amount of twist necessary corresponds to an average pitch angle of order @xmath3 $ ] . most of the initial tube is turned into vortex rolls . at the opposite end ( strong initial twist ) , the tube rises with only a small deformation and no substantial loss of magnetic flux .

the physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical mhd code . the problem considered is fully compressible ( no boussinesq approximation ) , includes ohmic resistivity , and is two dimensional , i.e. , there is no variation of the variables in the direction of the tube axis . we study a high plasma @xmath0 case with small ratio of radius to external pressure scaleheight . the results obtained can therefore be of relevance to understand the transport of magnetic flux across the solar convection zone . we confirm that a sufficient twist of the field lines around the tube axis can suppress the conversion of the tube into two vortex rolls . for a tube with relative density deficit of order @xmath1 ( the classical parker buoyancy ) and radius smaller than a pressure scale - height ( @xmath2 ) , the minimum amount of twist necessary corresponds to an average pitch angle of order @xmath3 $ ] . the evolution of a tube with this degree of twist is studied in detail , including the initial transient phase , the internal torsional oscillations and the asymptotic , quasi - stationary phase . during the initial phase , the outermost , weakly magnetized layers of the tube are torn off its main body and endowed with vorticity . they yield a trailing magnetized wake with two vortex rolls . which fraction of the total magnetic flux is brought to the wake is a function of the initial degree of twist . in the weakly twisted case , most of the initial tube is turned into vortex rolls . at the opposite end ( strong initial twist ) , the tube rises with only a small deformation and no substantial loss of magnetic flux . the formation of the wake and the loss of flux from the main body of the tube are basically complete after the initial transient phase . a sharp interface between the tube interior and the external flows is formed at the tube front and sides ; it has the characteristic features of a magnetic boundary layer . its structure is determined as an equilibrium between ohmic diffusion and field advection through the external flows . it is the site of vorticity generation via the magnetic field during the whole tube evolution . from the hydrodynamical point of view , this problem constitutes an intermediate case between the rise of air bubbles in water and the motion of a rigid cylinder in an external medium . as in the first one , the tube is deformable and the outcome of the experiment ( shape of rising object and wake ) depends on the value of the weber number . several structural features obtained in the present simulation are also observed in rising air bubbles , like a central _ tail _ , and a _ skirt _ enveloping the wake . as in rigid cylinders , the boundary layer satisfies a no - slip condition ( provided for in the tube by the magnetic field ) , and secondary rolls are formed at the lateral edges of the moving object . # 1#2 # 1#2 # 1*#1 * # 1b^#1_bl # 1v_rel^#1 # 1v_rel^#1 # 1v^#1_term # 1v^#1_apex # 1v^#1_rise # 1c_s^#1 # 1re_m^#1 # 1 # 1#2 to 0pt12.0 cm @xmath4

astro-ph9711043

c

the results presented in this paper can be discussed from a twofold perspective . first , they can be applied to the theory of the magnetic activity in the sun , trying to understand different aspects of the rise of magnetic flux across the convection zone . on the other hand , the simulations described here bear a strong resemblance to the results of laboratory and numerical experiments on the motion of air bubbles and rigid cylinders ; it would be as well to clarify similarities and differences . the following subsections discuss different aspects of those topics . the numerical calculation of the present paper is necessarily idealized . the calculations were done in a high - beta regime with small ratio of radius to pressure scaleheight . in thus far , they are within the parameter regime of expected for the magnetic tubes in the deep convection zone . the latter have a larger @xmath0 , by a factor between @xmath178 and @xmath126 , than adopted here but many qualitative features of the rise should be similar in both cases . the only diffusive process considered , though , the ohmic resistivity , together with the numerical viscosity and diffusion , yield laminar flows in and around the tube with reynolds number of a few hundred . this can not be expected to hold in the actual sun : there , the rise of the tube will be accompanied by turbulent flows ( with , in particular , a turbulent wake ) . in spite of the foregoing , a conclusion seems unavoidable : for the transport of the magnetic flux to the surface in the form of buoyant magnetic flux tubes to be effective , the latter must be twisted from the early stages of their rise . we have shown for a tube with a density deficit of order the full isothermal value ( @xmath201 ) that an average pitch angle around @xmath3 $ ] is indeed necessary for the tube to withstand the various deforming agents . otherwise , they lose most of their magnetic flux to the trailing wake . as shown by earlier authors , the vortex rolls of the wake can easily end up moving horizontally rather than rising . the condition on the minimum pitch angle may be less stringent , though , if we consider that the rise may actually be driven by the parker instability in tubes which are stored in a neutrally buoyant equilibrium ( @xcite ) . the instability occurs with the upgoing mass elements being driven by a vertical force which remains well below @xmath202 while the amplitude is not too large . to a driving force of amount @xmath203 ( @xmath204 ) corresponds through ( [ eq_min_pitch ] ) a minimum pitch angle which is about a factor @xmath205 smaller than for isothermal straight tubes . for example , in the case discussed in the paper of @xcite , @xmath206 for the top of the rising loop in the lowermost @xmath207 km of the rise , i.e. , for distances equivalent to about @xmath136 times the tube radius . even if the tubes are strongly buoyant [ @xmath208 from the beginning , their time evolution may depend to some extent on the precise distribution of the density deficit in the tube at time @xmath18 . a gaussian profile , as used in this paper , yields a fast deformation of the initial magnetic configuration , followed by internal torsional oscillations . this is directly associated with the torque of the buoyancy force throughout the tube interior . a top - hat profile ( @xmath209 but @xmath210const ) , on the other hand , has no buoyancy torques associated except at the tube boundary . yet , the time evolution of such a tube for smooth pitch angle distributions like ( [ eq_pitchassympt ] ) or ( [ eq_pitchgauss ] ) is qualitatively similar to the cases studied in this paper , as has been tested through a series of numerical experiments . this can be understood in different ways : first , the hydrodynamic forces associated with the external flow depend on the speed of rise of the tube , which is a function of the average buoyancy rather than of the precise shape of the @xmath211 profile . to counteract them , one needs to have a sufficient pitch angle in the tube interior . on the other hand , the gravitational term in the vorticity equation ( [ eq_vort ] ) for a top - hat profile is concentrated at the periphery of the @xmath211 distribution , but is correspondingly more intense . to counteract it , it is necessary to have a large current density @xmath212 , which can only be achieved if @xmath62 is sufficiently intense , at least close to the tube boundary . through both arguments one arrives at criteria basically like eq . ( [ eq_min_pitch ] ) . if the magnetic tubes that yield active regions at the surface must be twisted already in the early stages of the rise , the sun should have a mechanism to routinely produce twisted tubes in the dynamo layers . if one relaxes the condition of symmetry along the tube imposed in the present paper , one may think that the twist could result through torsional shearing . this might come about as a natural subproduct of the generation of vorticity explained in this paper , if it took place at different rates on the different cross sections of the tube along the axis . this can be the case , for instance , if the originally horizontal tube develops an omega - loop shape in which a stretch of it rises while the rest remains at the original level . if the tube was originally untwisted ( or only weakly twisted ) , the rising sections would tend to turn into vortex tube pairs which contain most of the original magnetic flux . now , in contrast to the 2d case , this rotation produces a transverse field component in the flanks of the rising section of the loop . if enough @xmath62 is built up , the rotation in the vortices could be braked . yet , a simple calculation shows that for this mechanism to be at all effective , the footpoint separation , @xmath213 , of the omega loop has to be small , in fact smaller than one pressure scaleheight . more precisely , if we require that the tube develops a transverse component of the level required by the criterion ( [ eq_min_pitch ] ) after rising a distance equivalent to a few of its own radii , we obtain @xmath214 this is a very small footpoint separation : the ratio of the lorentz force associated with the curvature of the field lines to the buoyancy force in such a tube is at least of order @xmath215 . consequently , it is not easy to _ raise _ a loop that is narrow enough for a sufficient pitch angle to develop at all . this is an indication that the tubes possibly have to be formed with the necessary amount of twist before they start to rise . an interesting possibility for generating magnetic tubes with a non - zero total twist has been discussed by @xcite : they consider a rayleigh - taylor unstable slab of plasma with horizontal magnetic field such that the angle subtended by the field vector with a fixed horizontal axis monotonically changes with depth . upon development of the instability , the layer yields magnetic tubes with non - zero degree of twist . in their experiment , the authors showed how the resulting tubes were more resistant to deformation through the surrounding flows than in the corresponding untwisted case ( @xcite ) . a corresponding three - dimensional problem has been calculated by @xcite . they show how an unstable layer with a parallel horizontal field produces magnetic tubes with non - zero vorticity . through nonlinear interaction , these tubes arch as they rise in a vertical plane , thereby becoming twisted . another open question concerns the fate of a twisted tube as it rises across successive density scaleheights in the convection zone . the internal and external densities are essentially equal for most of the rise ( except for the small relative difference of order up to @xmath216 ) : the tube thus expands and its field intensity weakens by several orders of magnitude along the journey ( see @xcite , 1992 , 1997b ) . in fact , the beginning of this process can be seen by comparing the maximum field intensity of the three panels of fig . [ fig_pitch_angle ] . the rate of decrease associated with an off - axis expansion of the tube , though , is different for the longitudinal and transverse components of the field ( @xcite , 9 ) . a rough but simple argument based on the conservation of flux in 2d yields a rate of change of the twist following an approximate law @xmath217 . if so , the tubes could reach the upper convection zone with very large degrees of twist , possibly such that they can become kink unstable . yet , three - dimensional effects could render that simple law of little use . the stretching of the tube apex in the longitudinal direction , for instance , a phenomenon common in parker - unstable rising loops , may reduce the level of twist there . also , the conservation of the total helicity in the tube could put an upper limit to the number of turns of the field lines around the axis at any single place . however it is , large pitch angles should be a common appearance in rising tubes when they reach photospheric levels . the sheared field structures observed in emerging active regions ( @xcite , @xcite ) may be a consequence of this ( see also @xcite , @xcite and @xcite ) . [ [ magnetic - tubes - air - bubbles - and - rigid - cylinders - similarities - and - differences ] ] magnetic tubes , air bubbles and rigid cylinders : similarities and differences ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ along this paper we have compared our results to the laboratory experiments of flow past rigid cylinders and air bubbles at @xmath218 @xmath219 . in the following we summarize the similarities and differences found . _ magnetic tubes and air bubbles . _ remarkable similarities are : ( a ) the general shape and structural features ( skirt , central tail ) ( b ) the _ protection _ of the interior of the rising object through surface tension . these similarities are all the more striking given the difference in buoyancy [ density deficit @xmath220 for the tubes , @xmath221 for the bubbles ] and in the physical source of the surface tension ( capillary effects vs. jump in the tangential field component ) . as a result , defining the weber number on the basis of the corresponding surface tension mechanism , one can formulate a common law of dependence of structural properties on @xmath100 . _ magnetic tubes and rigid cylinders . _ a clear similarity concerns the boundary layer : both objects have a no - slip condition along the boundary . consequently , the relative jump of the tangential velocity across the boundary layer is large , @xmath222/v_{tg}^ { } \sim \hbox{o}(1)$ ] . in contrast , there is a zero - tangential stress condition along the fluid / air interface of a bubble ; correspondingly , @xmath222/v_{tg}^ { } \sim \hbox{o}(re^{-1/2})$ ] . as a result of the no - slip condition , both buoyant magnetic tubes and rigid cylinders produce ( and shed downstream ) secondary rolls near the point of separation of the boundary layer . _ features specific to the buoyant magnetic tubes with twist . _ in the magnetic tubes of the present simulations , the wake is formed in the initial phases of the rise out of material bodily transported from the initial tube thus , the wake is magnetized and maintains a magnetic connection to the head of the rising tube along time . the kind of behavior followed by the magnetic rope depends directly on the amount of magnetic flux incorporated into the wake , which , in turn , depends on the initial twist . in the case of an initially highly twisted tube ( @xmath223 ) , the magnetic rope is almost rigid and its shape and the flow around it strongly remind those of a _ solid cylinder_. if the initial pitch angle is closer to the threshold ( [ eq_min_pitch ] ) , then the tube deforms and adopt a _ bubble_-like shape ( though it still satisfies a no - slip condition along its boundary ) . finally , if @xmath50 is very small , the tube behaves like a rising _ thermal _ ( longcope et al . 1996 ) . this work was partially funded through the dges project no . 95 - 0028-c of the spanish ministry of education and culture . the numerical calculations were carried out using the computing resources of the instituto de astrofsica de canarias and of the centre de computaci i comunicacions de catalunya . the authors are grateful to m. kaisig for providing the numerical code and for his subsequent help with it . thanks are also due to a large number of scientists in hao , jila and cora in boulder ( colorado ) as well as in the university of chicago for interesting discussions on the topic of this paper . batchelor , g.k . , 1967 , an introduction to fluid dynamics , ( cambridge : cup ) bouard , r. , coutanceau , m. , 1980 , j. fluid mech . 101 , 583 caligari , p. , moreno - insertis , f. , schssler , m. , 1995 , , 441 , 886 cargill , p.j . , chen , j. , spicer , d.s . , zalesak , s.t . , 1996 , , 101 , 4855 cattaneo , f. , hughes , d.w . , 1988 , j. fluid mech . , 196 , 323 cattaneo , f. , chiueh , t. , hughes , d.w . , 1990 , j. fluid mech . , 219 , 1 collins , r. , 1965 , chem . , 20 , 851 collins , w.m . , dennis , s.c.r . , 1973a , quart . j. mech . , 26 , 53 collins , w.m . , dennis , s.c.r . , 1973b , j. fluid mech . , 60 , 105 choudhuri , a.r . , 1989 , , 123 , 217 christov , c.i , volkov , p.k . , 1985 , j. fluid mech . , 158 , 341 dandy , d.s . , leal , l.g . , 1989 , j. fluid mech . , 208 , 161 davies , r.m . , taylor , g.i . lond . , a 200 , 375 dsilva , s. , choudhuri , a.r . , 1993 , , 272 , 621 emonet , t. , moreno - insertis , f. , 1996 , , 458 , 783 fan , y. , fisher , g.h . , deluca e.e . , 1993 , , 405 , 390 fan , y. , fisher , g.h . , mcclymont , a.n . , 1994 , , 436 , 907 fan , y. , zweibel , e.g. , lantz , s.r . , 1997 , , submitted . hnat , j.g . , buckmaster , j.d . , 1976 , fluids , vol . 19 , no . 2 , 182 hughes , d.w . , falle , s.a.e.g . , joarder , p. , 1998 , , submitted . kaisig , m. , tajima , t. , shibata , k. , nozawa , s. , matsumoto , r. , 1990 , , 358 , 698 kurokawa , h. , 1989 , spa . rev , 51 , 49 leka , k.d . , canfield , r.c . , mcclymont , a.n . , van driel - gesztelyi , l , 1996 , , 462 , 547 lites , b.w . , low , b.c . , martnez pillet , v. , seagraves , p. , skumanich , a. , 1995 , , 446 , 877 . longcope , d.w . , fisher , g.h . , arendt , s. , 1996 , , 464 , 999 matthews , p.c . , hughes , d.w . , proctor , m.r.e . , 1995 , , 448 , 938 moreno - insertis , f. , 1983 , , 122 , 241 moreno - insertis , f. , 1986 , , 166 , 291 moreno - insertis , f. , 1992 , in sunspots , theory and observations , eds . j.h.thomas and n.o.weiss , p. 385 ( dordrecht : kluwer ) . moreno - insertis , f. , 1997a , in _ the inconstant sun _ , c. marmolino and g. cauzzi , eds . astr . it . * 68*. moreno - insertis , f. , 1997b , in _ solar magnetic fields _ , viggo hansteen , ed . , university of oslo , p. 330 . moreno - insertis , f. , emonet , t. 1996 , , 472 , l53 nordlund , , stein , r.f . 1990 , comput . commun . , 59 , 119 parlange , j .- y . , 1969 , _ j. fluid mech . _ , 37 , 257 parker , e.n . , 1979 , cosmical magnetic fields , ( oxford : oxford university press ) , chap . 9 richtmyer , r.o . , morton , k.w . 1967 , difference methods for initial - value problems ( 2d ed . ; new york : interscience ) , chap . 13 ryskin , g. , leal , l.g . , 1984a , j. fluid mech . , 148 , 1 ryskin , g. , leal , l.g . , 1984b , j. fluid mech . , 148 , 19 rubin , e.l . , burstein , s.z . , 1967 , phys . , 2 , 178 rust , d.m . , kumar , a. , 1996 , , 464 , l199 schssler , m. , 1979 , , 71 , 79 shibata , k. 1983 , , 35 , 263 shibata , k. , tajima , t. , steinolfson , r.s . , matsumoto , r. 1989 , , 345 , 584 stone , h.a . , 1994 , ann . fluid mech . , 26 , 65 ta phuoc loc , 1980 , j. fluid mech . , 100 , 111 ta phuoc loc , bouard , r. , 1985 , j. fluid mech . , 160 , 93 tanaka , k. , 1991 , , 136 , 37 tsinganos , k.c . , 1980 , , 239 , 746 wegener , p.p . , parlange , j .- y . , 1973 , annual rev . fluid mech . , 5 , 79

we study a high plasma @xmath0 case with small ratio of radius to external pressure scaleheight . the results obtained can therefore be of relevance to understand the transport of magnetic flux across the solar convection zone . the evolution of a tube with this degree of twist is studied in detail , including the initial transient phase , the internal torsional oscillations and the asymptotic , quasi - stationary phase . during the initial phase , the outermost , weakly magnetized layers of the tube are torn off its main body and endowed with vorticity . they yield a trailing magnetized wake with two vortex rolls . which fraction of the total magnetic flux is brought to the wake is a function of the initial degree of twist . in the weakly twisted case ,

the physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical mhd code . the problem considered is fully compressible ( no boussinesq approximation ) , includes ohmic resistivity , and is two dimensional , i.e. , there is no variation of the variables in the direction of the tube axis . we study a high plasma @xmath0 case with small ratio of radius to external pressure scaleheight . the results obtained can therefore be of relevance to understand the transport of magnetic flux across the solar convection zone . we confirm that a sufficient twist of the field lines around the tube axis can suppress the conversion of the tube into two vortex rolls . for a tube with relative density deficit of order @xmath1 ( the classical parker buoyancy ) and radius smaller than a pressure scale - height ( @xmath2 ) , the minimum amount of twist necessary corresponds to an average pitch angle of order @xmath3 $ ] . the evolution of a tube with this degree of twist is studied in detail , including the initial transient phase , the internal torsional oscillations and the asymptotic , quasi - stationary phase . during the initial phase , the outermost , weakly magnetized layers of the tube are torn off its main body and endowed with vorticity . they yield a trailing magnetized wake with two vortex rolls . which fraction of the total magnetic flux is brought to the wake is a function of the initial degree of twist . in the weakly twisted case , most of the initial tube is turned into vortex rolls . at the opposite end ( strong initial twist ) , the tube rises with only a small deformation and no substantial loss of magnetic flux . the formation of the wake and the loss of flux from the main body of the tube are basically complete after the initial transient phase . a sharp interface between the tube interior and the external flows is formed at the tube front and sides ; it has the characteristic features of a magnetic boundary layer . its structure is determined as an equilibrium between ohmic diffusion and field advection through the external flows . it is the site of vorticity generation via the magnetic field during the whole tube evolution . from the hydrodynamical point of view , this problem constitutes an intermediate case between the rise of air bubbles in water and the motion of a rigid cylinder in an external medium . as in the first one , the tube is deformable and the outcome of the experiment ( shape of rising object and wake ) depends on the value of the weber number . several structural features obtained in the present simulation are also observed in rising air bubbles , like a central _ tail _ , and a _ skirt _ enveloping the wake . as in rigid cylinders , the boundary layer satisfies a no - slip condition ( provided for in the tube by the magnetic field ) , and secondary rolls are formed at the lateral edges of the moving object . # 1#2 # 1#2 # 1*#1 * # 1b^#1_bl # 1v_rel^#1 # 1v_rel^#1 # 1v^#1_term # 1v^#1_apex # 1v^#1_rise # 1c_s^#1 # 1re_m^#1 # 1 # 1#2 to 0pt12.0 cm @xmath4

1106.4175

i

cavity polaritons are bound light - matter states that appear due to the strong coupling of 2d excitons and photons in semiconductor microcavities.@xcite the optically driven system of polaritons behaves like a weakly imperfect bose gas , which results in a spectacular row of polariton collective phenomena such as multistability,@xcite parametric scattering,@xcite pattern formation,@xcite self - organization effects,@xcite dynamical bose - einstein condensation.@xcite polariton multistability attracts much attention as a potential candidate for very fast picosecond range optical switching on a micron size scale.@xcite moreover , the sharp transitions in intra - cavity field , stemming from the multistability , can proceed concurrently with inter - mode parametric scattering , which determines interesting ways of polariton self - organization under pumping near the inflection point of the lower polariton branch ( the `` magic angle'').@xcite the polariton bistability has recently been studied in the `` scalar '' approximation neglecting the spin degrees of freedom.@xcite because of the mutual interaction of polaritons , their energy effectively depends on the intra - cavity field magnitude . the repulsion between excitons leads to the blueshift of polariton energy . when the pump is itself blue - detuned from the polariton resonance , a strong positive feedback loop between the resonance energy and the field amplitude is created in a certain range of system parameters , resulting in sharp jumps in the intra - cavity field and , hence , in the cavity transmission . consequently , the transmission signal can exhibit a prominent hysteresis in the dependence on continuous - wave ( cw ) pump intensity.@xcite the response of the optically excited polariton system becomes more complicated with allowance made for exciton spin degrees of freedom ( that corresponds to arbitrary optical polarization of the intra - cavity field ) . in the general case the system has up to four stable states under a given cw pump , whereas the actual state of the system is determined by the history of the excitation process.@xcite in critical points , where a number and/or stability of stationary solutions change , the system can exhibit sharp jumps in both the amplitude and polarization of the intra - cavity field . under a spatially inhomogeneous ( e.g. , gaussian shaped ) cw excitation the system can also exhibit a nontrivial spatial distribution of polarization of the luminescence signal , like the `` spin ring '' patterns,@xcite due to the same underlying phenomena . the strong multistability effect predicted in ref . has recently been observed experimentally,@xcite including the sharp jumps in the cavity transmission under a smooth variation of the pump polarization degree . the spin ring patterns under gaussian shaped excitation have also been reported.@xcite all these experiments were carried out under the cw excitation . thus , one of the still remaining questions is the dynamical peculiarities of the transitions in a multistable system , which could only be traced using the time - resolved techniques . particularly , the characteristic switching times between different stability branches call for the experimental study , for they can have a crucial impact upon the practical implementations . another question concerns the theoretical approach allowing to describe the observed multistability effect in microcavities . traditionally , the multistability is considered in terms of the self - acting classical fields corresponding to macro - occupied coherent polariton modes which appear under a coherent resonant excitation.@xcite although such an approach is supposed to be sufficient to describe the bistability in a circularly polarized system,@xcite it gives wrong predictions for the general case of elliptically polarized excitation.@xcite most probably , the incoherent states of the exciton reservoir which are inevitably excited in optical experiments have a substantial impact on the decay rates and energies of polaritons . for instance , the nonlinear decay of polaritons with different circular polarizations was taken into consideration in order to explain the experimental data in ref . . further , the nonequilibrium transitions reported in ref . can only be reproduced in calculations taking into account the reservoir induced shifts of the polariton energy . in the present work we report the experimental study of nonequilibrium transitions in the multistable cavity polariton system . unlike in recent refs . , we have studied the optically polarized system under a pulsed nanosecond - long excitation , which allowed us to trace the time - resolved dynamics of the intra - cavity field . the shifts in polariton energy were reflected by temporal variations in the transmission energy spectrum . thus , the employed technique is capable of visualizing the temporal correlations between the resonance energy and intensity of the intra - cavity field . we discuss in detail the time dependence of the transmission signal polarization , below as well as above the threshold , for several polarizations of the pump beam . the observed polarization behavior can not be reproduced within a semi - classical model based on the gross - pitaevskii equations considered in refs . . the experimental results allowed us to develop a phenomenological model to describe a multistable polariton system with a proper regard to the exciton reservoir . the reservoir excitons shift the polariton energy that , in turn , influences the thresholds of nonequilibrium transitions . both the linear and nonlinear mechanisms of exciton scattering into the reservoir are found to be significant within a sub - nanosecond time scale . while the nonlinear decay of cross - circularly polarized excitons leads to the levelling of the @xmath0 and @xmath1 jump points ( which has also been found in refs . in the cw pump regime ) , the linear decay mechanism leads to the temporal delay of the jumps with respect to the pump intensity peak . further , we apply the developed approach to simulate the parametric scattering under pumping at the magic angle . as we show , this model allows to explain self - consistently the temporal dependences of polarizations of both the driven mode and the scattering signal which appears at the polariton branch bottom . the paper is organized as follows . in sec . [ sec : theory ] the available models of the multistability effect are considered and compared with each other in view of the recent experimental results of refs . . [ experimental ] references the experimental setup . sec . [ sec : experiment ] contains the experimental results and compares them with the calculations performed in the framework of the suggested model , for the cases of pumping at normal incidence ( sec . [ sec : normal ] ) and at the magic angle ( sec . [ sec : magic ] ) , with a brief reference to some of the still unresolved issues ( sec . [ sec : discussion ] ) . the results are summarized in conclusion ( sec . [ sec : conclusions ] ) .

the observed dynamics can not be reproduced within the conventional semi - classical model based on the gross - pitaevskii equations . to explain the observed phenomena , it is necessary to take into account the unpolarized exciton reservoir which brings on additional blueshift of bright excitons , equal in the @xmath0 and @xmath1 polarization components .

the polarization dependence of nonequilibrium transitions in a multistable cavity - polariton system is studied under a nanosecond long resonant optical excitation at the normal and magic angle incidences with various polarizations of the pump beam . the temporal correlations between the frequency , intensity , and optical polarization of the intra - cavity field , which all undergo sharp threshold - like changes due to the spin dependent interaction of cavity polaritons , are visualized . the observed dynamics can not be reproduced within the conventional semi - classical model based on the gross - pitaevskii equations . to explain the observed phenomena , it is necessary to take into account the unpolarized exciton reservoir which brings on additional blueshift of bright excitons , equal in the @xmath0 and @xmath1 polarization components . this model explains the effect of polarization instability under both pulsed and continuous wave resonant excitation conditions , consistently with the spin ring pattern formation that has recently been observed under gaussian shaped excitation .

1106.4175

c

in the present work we have studied the non - equilibrium transitions in a multistable system of cavity polaritons under resonant nanosecond - long excitation . using the spectrally broadened pulses , we have visualized the temporal correlations between the effective resonant energy , intensity , and optical polarization of the intra - cavity field which all undergo the strong changes on reaching the threshold pump power . in the vicinity of the threshold , the dynamics of such system is strongly affected by the long - lived exciton reservoir ( excited due to polariton scattering ) which influences both the characteristic times of instability development and output signal polarization . the temporal behavior of the intra - cavity field is found to be not described in the conventional model based on the gross - pitaevskii equations written for purely coherent macro - occupied polariton states . most importantly , the observed phenomena can not be explained even qualitatively within a model with only the two exciton - exciton interaction constants ( @xmath14 ) allowed for . to explain the experiments , we have proposed the model for the macro - occupied polariton states coupled with an exciton reservoir . in spite of some limitations , this model provides a self - consistent description of the observed intra - cavity field dynamics under both pulse and continuous wave excitation conditions . authors thank m.s.skolnick for rendered samples , d.n.krizhanovskii for fruitful discussions , and a.v.larionov for assistance in the experiment . this work was supported by russian foundation for basic research and the russian academy of sciences .

the polarization dependence of nonequilibrium transitions in a multistable cavity - polariton system is studied under a nanosecond long resonant optical excitation at the normal and magic angle incidences with various polarizations of the pump beam . the temporal correlations between the frequency , intensity , and optical polarization of the intra - cavity field , which all undergo sharp threshold - like changes due to the spin dependent interaction of cavity polaritons , are visualized .

the polarization dependence of nonequilibrium transitions in a multistable cavity - polariton system is studied under a nanosecond long resonant optical excitation at the normal and magic angle incidences with various polarizations of the pump beam . the temporal correlations between the frequency , intensity , and optical polarization of the intra - cavity field , which all undergo sharp threshold - like changes due to the spin dependent interaction of cavity polaritons , are visualized . the observed dynamics can not be reproduced within the conventional semi - classical model based on the gross - pitaevskii equations . to explain the observed phenomena , it is necessary to take into account the unpolarized exciton reservoir which brings on additional blueshift of bright excitons , equal in the @xmath0 and @xmath1 polarization components . this model explains the effect of polarization instability under both pulsed and continuous wave resonant excitation conditions , consistently with the spin ring pattern formation that has recently been observed under gaussian shaped excitation .

1301.7061

c

the dynamics of quantum correlations , including entanglement and discord with its geometric measure , and classical correlation in two - qubit models are introduced for a open or closed quantum system . it is found that the dynamics of gmqd , qd , qe and cc differ . where , quantum discord and its geometric measure are exist in the region where the entanglement is zero , which is a strong signature for the presence of non classical correlations . system - reservoir coupling leads to : gmqd , qd and qe die asymptotically with larger system - reservoir coupling parameter . also , processes of quantum correlation loss and classical correlation gain are instantaneously happen . it is found that the purity of the initial states destroys the quantum correlations by exponential decay . therefore , in presence of the purity , one can determines a particular region in which there is no state have quantum correlations . 99 b. schumacher , m. d. westmoreland , _ phys . rev . _ a * 74*(2006 ) 042305 ; b. groisman , s. popescu , a. winter , _ phys . rev . _ a * 72 * ( 2005 ) 032317 . l. henderson and v. vedral , _ j. phys . a : math . * 34 * ( 2001 ) 6899 ; v. vedral , _ phys . rev . lett . _ * 90 * ( 2003 ) 050401 . d. yang , m. horodecki , z. d. wang _ phys . lett . _ * 101*(2008 ) 140501 . h. ollivier and w. h. zurek , _ phys . * 88 * ( 2001 ) 017901 . m. piani , p. horodecki , r. horodecki , _ phys . lett . _ * 100 * ( 2008)090502 ; m. piani , m. christandl , c. e. mora , p. horodecki , _ phys . lett . _ * 102*(2009 ) 250503 . b. wang , z .- y . xu , z .- q . chen , m. feng , _ phys . rev . _ a * 81 * ( 2010 ) 014101 . t. werlang , s. souza , f.f . fanchini , c. j. villas boas , _ phys . rev . _ a * 80 * ( 2009 ) 024103 . xing xiao , mao - fa fang , yan - ling li , guo - dong kang , chao wu , _ opt . * 283 * ( 2010 ) 3001 ; t. werlang , g. rigolin , _ phys . rev . _ a * 81 * ( 2010 ) 044101 . a .- a. mohamed , _ int j theor phys . _ * 51*(2012 ) 2779 . a. mohamed , _ phys . _ * 85 * ( 2012 ) 055013 . a. datta , a. shaji , c. m. caves , _ phys . lett . _ * 100*(2008 ) 050502 . lanyon , m. barbieri , m. p. almeida , a.g . white , _ phys . lett . _ * 101 * 200501 ( 2008 ) . f. f. fanchini , t. werlang , c. a. brasil , l. g. e. arruda , and a. o. caldeira , _ phys . rev . _ a * 81 * ( 2010 ) 052107 ; m.s . sarandy , _ phys . rev . _ a * 80 * ( 2009 ) 022108 . m. ali , a. r. p. rau , g. alber , _ phys . rev . _ a * 81 * ( 2010 ) 042105 ; s. luo , _ phys . rev . _ a * 77 * ( 2008 ) 042303 . b. dakic , v. vedral , and c. brukner , _ phys . * 105 * ( 2010)190502 . x. m. lu , z. j xi , z. sun and x. wang , _ quantum information and computation _ * 10 * ( 2010)0994 . f. altintas , _ opt . commun . _ * 283 * ( 2010)5264 . b. wang , z .- y . xu , z .- q . chen , m. feng , _ phys . _ a * 81 * ( 2010 ) 014101 . jun - qi li , j .- q . liang , _ phys . lett . _ a * 375 * ( 2011 ) 1496 . k. roszak , p. machnikowski , _ phys . rev . _ a * 73 * ( 2006 ) 022313 . a. mohamed , _ ann . _ * 327 * ( 2012 ) 3130 ; _ quantum inf process _ doi 10.1007/s11128 - 012 - 0460 - 1 . abdel - baset a. mohamed , _ journal of the egyptian mathematical society _ , doi 10.1016/j.joems.2012.10.005 . t. yu , j.h . * 93 * ( 2004 ) 140404 . t. yu , j.h . * 97 * ( 2006 ) 140403 ; t. yu , _ phys . lett . a _ ( 2007)361 . j. h. eberly , t. yu , _ science _ * 316 * ( 2007 ) 555 ; t. yu , j.h . eberly , _ science _ * 323 * ( 2009 ) 598 . m. p. almeida , f. de melo , m. hor - meyll , a. salles , s. p. walborn , p. h. ribeiro souto , l. davidovich , _ science _ * 316 * ( 2007 ) 579 . j. laurat , k. s. choi , h. deng , c. w. chou , h. j. kimble , _ phys . _ * 99 * ( 2007 ) 180504 . k. modi , t. paterek , w. son , v. vedral , m. williamson , _ phys . * 104 * ( 2010)080501 . s. luo , _ phys . _ a * 77 * ( 2008 ) 022301 ; s. luo and q. zhang , _ j. stat . * 131 * ( 2008)1169 . g. vidal , r. f. werner , _ phys . rev . _ a * 65*(2002 ) 032314 . a. blais , r .- s . huang , a. wallraff , s. girvin and r. schoelkopf , _ phys . rev . _ a * 69 * ( 2004 ) 062320 . r. f. werner , _ phys . _ a * 40 * ( 1989 ) 4277 . c. p. sun , x. x. yi , x. j. liu , _ fortschr . phys . _ * 43*(1995 ) 585 .

the quantum correlations , including entanglement and discord with its geometric measure , and classical correlation are studied for a bipartite partition of a open or closed quantum system . it is found that the purity of the initial state plays an important role in the dynamics of quantum and classical correlations . in the dephasing model

the quantum correlations , including entanglement and discord with its geometric measure , and classical correlation are studied for a bipartite partition of a open or closed quantum system . it is found that the purity of the initial state plays an important role in the dynamics of quantum and classical correlations . in the dephasing model , the quantum correlations loss and the classical correlation gain are instantaneously happen . while , the purity of the initial state destroys the quantum correlations which is resulted by the unitary interaction . therefore , with the purity parameter , a particular region in which there is no state have quantum correlations can be determined . + * keywords*:quantum discord ; geometric measure of quantum discord ; dephasing model

0805.1470

i

x - ray observations are often used to infer various properties of energetic electrons accelerated during the solar flares . the spatially integrated x - ray photon spectrum @xmath1 ( photons @xmath2 s@xmath3 kev@xmath3 ) is related to mean electron flux spectrum @xmath4 ( electrons @xmath2 s@xmath3 kev@xmath3 ) via the rather simple linear integral relation @xcite @xmath5 for source volume @xmath6 , mean plasma density @xmath7 , and isotropic bremsstrahlung cross - section per unit photon energy @xmath8 , @xmath9 @xcite . although the angular distribution of energetic electrons is generally unknown , the recent observations @xcite suggest rather close to isotropic distribution of electrons . the exact plasma density distribution and flaring volume are also poorly known and therefore value @xmath10 is normally inferred . the value @xmath11 is model independent @xcite , and the detailed energy structure of this is related to electron acceleration and propagation physics . radio emission spectrum of solar energetic particles , although normally only at above a few hundred kev energies , is an alternative approach to infer electron beam and plasma parameters @xcite . the spatially integrated spectrum of energetic electrons @xmath11 is often _ approximated _ as a sum of a isothermal maxwellian distribution and a non - thermal power - law distribution @xcite . the thermal component often dominates the overall spectrum at low energies @xmath12 kev and little can be said about the low - energy part of non - thermal distribution . however , the low - energy part of non - thermal spectra plays a crucial role in the solar flare diagnostics . most of the non - thermal electron energy is concentrated in this part , hence this defines the total energy budget of the flare . in addition , this part of the spectrum is more effectively influenced by various electron propagation effects like collisions @xcite or beam - plasma interactions @xcite , thus playing an important role in the electron transport diagnostics in the solar flares . various model - based methods to find the value of low energy cutoff have been used . requiring that the assumed thermal emission dominate over non - thermal emissions find a low energy cutoff of @xmath13 kev should be present . assuming `` theoretical neupert effect '' to be satisfied conclude that the low energy cutoff should be between @xmath14 kev and @xmath15 kev for four flares analysed in the paper . have used empirical relationship between the observed parameters of the photon power - law fit and the low - energy cutoff of the electron distribution and have found that the low - energy cutoffs in microflare events could range from @xmath16 to @xmath17 kev with the median being around @xmath18 kev . in this paper we will focus on the _ model - independent _ inference of low - energy cutoffs in the mean electron spectra . high resolution spectra observed by rhessi @xcite allows us to infer detailed structure of electron distribution often never seen before . have demonstrated that the mean electron spectrum @xmath10 has a statistically significant local minimum at approximately @xmath19 kev in the electron spectrum of goes x - class july 23 , 2002 solar flare , although this feature is likely to be an instrumental effect caused by a pulse pile - up . show that some electron spectra inferred from rhessi x - ray spectra free from pile - up issues seem inconsistent with a simple collisional thick - target model @xcite . however , the photon spectra of these events should be corrected for albedo - compton back - scattered x - rays @xcite . have shown that the spectrum of the august 20 , 2002 event with a puzzlingly large value of the low - energy cutoff @xmath20 kev can be understood in terms of the photospheric albedo . flares showing a weak thermal component allow us to scrutinize the low - energy part of the non - thermal distribution of electrons . the analysis can be done either by _ assuming _ a functional form of the electron spectrum @xcite or by using the regularised inversion techniques @xcite . it is known that flat x - ray spectra ( low value of photon spectral index ) can require low - energy cutoffs in the power - law distributions when a functional form is assumed @xcite , whereas the model independent approach , via the regularised inversion technique , @xcite may show a dip or a gap in the electron distribution @xcite . in this paper we present the results of a systematic search for dips in the mean electron flux distribution using the rhessi solar flare database for the period of feb 2002 - may 2006 . section [ analysis ] describes the selection criteria for the flare photon spectra and the application of the regularised inversion method for the determination of the corresponding mean electron flux spectra . section [ dips ] discusses energies and depths of the obtained statistically significant dips and their relation to the photospheric albedo . the analysis confirms previous suggestions that the isotropic albedo correction is capable of removing all statistically significant dips in the mean electron flux distribution . the obtained results are summarised in section [ summary ] .

the ramaty high energy solar spectroscopic imager ( rhessi ) x - ray data base ( february 2002 may 2006 ) has been searched to find solar flares with weak thermal components and flat photon spectra . using a regularised inversion technique we have found 18 cases which exhibit a statistically significant local minimum ( a dip ) in the range of 1020 kev . the positions and spectral indices of events with low - energy cutoff indicate that such features are likely to be the result of photospheric albedo . it is shown that if the isotropic albedo correction was applied , all low - energy cutoffs in the mean electron spectrum were removed and hence the low energy cutoffs in the mean electron spectrum of solar flares above @xmath012 kev can not be viewed as real features in the electron spectrum . if low - energy cutoffs exist in the mean electron spectra , the energy of low energy cutoffs should be less than @xmath012 kev .

the ramaty high energy solar spectroscopic imager ( rhessi ) x - ray data base ( february 2002 may 2006 ) has been searched to find solar flares with weak thermal components and flat photon spectra . using a regularised inversion technique , we determine the mean electron flux distribution from count spectra of a selection of events with flat photon spectra in the 1520 kev energy range . such spectral behaviour is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range , e.g. a low - energy cutoff in the mean electron spectra of non - themal particles . we have found 18 cases which exhibit a statistically significant local minimum ( a dip ) in the range of 1020 kev . the positions and spectral indices of events with low - energy cutoff indicate that such features are likely to be the result of photospheric albedo . it is shown that if the isotropic albedo correction was applied , all low - energy cutoffs in the mean electron spectrum were removed and hence the low energy cutoffs in the mean electron spectrum of solar flares above @xmath012 kev can not be viewed as real features in the electron spectrum . if low - energy cutoffs exist in the mean electron spectra , the energy of low energy cutoffs should be less than @xmath012 kev .

1507.08588

c

together , these measurements and calculations reveal that spin - orbit coupling induces a complex atomic- and momentum - dependent hierarchy of orbitally - polarised components of the underlying electronic structure in bitei , summarised schematically in fig . [ f : cd ] . our calculations additionally reveal how each orbital component is , in turn , coupled to a disparate spin texture . we illustrate this for the bi - derived states in fig . [ f : cd](b - d ) ; the te - derived component is additionally shown in supplementary fig . the in - plane spin - texture @xmath43 projected onto bi @xmath16 orbitals yields a conventional counter - rotating chiral spin texture of neighbouring cess at energies above the dirac point , characteristic of classic rashba systems @xcite and indeed observed experimentally for bitei @xcite . in contrast , the spin texture is significantly more complex for the @xmath19 and @xmath20 orbital projection , with the in - plane spin component switching between tangential and radial around the ces . this results from a coupling of the spin to the characteristic orbital textures , and is similar to that found recently for topological surface states @xcite . for example , combined with our uncovered tangential ( radial ) in - plane bi orbital texture above ( below ) the dp , this leads to a net clockwise spin rotation for the in - plane orbital projection of _ both _ the inner and outer cess . this is in strong departure from the conventional picture of rashba - like spin polarisation . such in - plane orbital textures likely also underlie the unconventional spin topology predicted for certain @xmath44-derived states in bi / cu(111 ) @xcite and pb / cu(111 ) @xcite surface alloys . they are also broadly consistent with recent first - principles calculations that suggest the rashba parameter can be orbital - dependent in bismuth tellurohalides @xcite , although here we reveal how orbital mixing can lock the spin components on the nominally `` spin - split '' cess together , stabilising pronounced components of the underlying wavefunction that host markedly non - rashba - like spin textures in this system . similar considerations hold for the te - derived components , although with additional variations in the magnitude of the spin components projected onto out - of - plane vs. in - plane orbital components between the cess due to a greater out vs. in - plane orbital polarisation for te ( supplementary figs . s2 and s3 ) . with each orbital component locked to a different spin texture , the fundamental requirement from time - reversal symmetry of spin - degeneracy at the kramer s point ( the dirac point formed in this system at @xmath4 ) ensures equal contribution of in - plane @xmath19 and @xmath20 orbitals at this point . thus , the vanishing of orbital polarisation at the dirac point observed experimentally above can be simply viewed as an orbital analogue of kramer s spin degeneracy in time - reversal symmetric systems . away from the dirac point , our calculations additionally predict a strong canting of the spin out of the surface plane for the bi - derived orbitals . this grows in magnitude with increasing energy away from the dirac point , where the cess become increasingly hexagonally warped @xcite . we show evidence for this through circular dichroism measurements . we attribute such dichroism as a signature of unquenched orbital angular momentum @xcite , which our calculations reveal is large and locked approximately opposite to the spin angular momentum due to the strong spin - orbit coupling . circular dichroism is known to show a complex dependence on photon energy in this system @xcite as well as in other layered compounds such as bi@xmath45te@xmath46 ( ref . ) , which can naturally arise as a consequence of inter - layer photoelectron interference @xcite . to simplify such effects , we again perform our measurements on - resonance , selectively enhancing states of bi character ( fig . [ f : cd](f ) ) . we find that the outer ( hexagonally - warped ) band in such measurements develops a pronounced six - fold modulation , which has previously been shown to reflect out - of - plane spin - canting in topological insulators @xcite . here , this provides the first experimental evidence for deviations from simple in - plane chiral spin textures in bitei . as evident in fig . [ f : cd](b - d ) , @xmath47 is substantially larger when projected onto the in - plane orbital components than for the @xmath16 projection . the emergence of a large out - of - plane spin canting in this system is thus intricately tied to the development of the in - plane orbital texture away from the dirac point observed here . together , our measurements and calculations establish a powerful role of in - plane atomic orbitals shaping the spin structure of the model rashba compound bitei , revealing a complex interplay between atomic makeup , anisotropic orbital textures , and spin - momentum locking . while small quantitative variations may occur due to near - surface potential contributions to the rashba spin splitting and possible surface - induced orbital reconstructions here , our findings should be broadly applicable to the spin - split bulk electronic structure of bitei as well as being generic to other strong spin - orbit rashba systems , suggesting new routes to control spin splitting through the orbital sector . for example , exploiting structure - property relations to tune the competition of atomic spin - orbit coupling and crystal field splitting will allow control over the ratio of in - plane and out - of - plane orbital polarisation , thus modulating the degree of non - rashba - like spin components and out - of - plane spin canting . together , this promises new prospects for the targeted design of optimised spintronic materials .

the rashba effect is one of the most striking manifestations of spin - orbit coupling in solids , and provides a cornerstone for the burgeoning field of semiconductor spintronics . combining polarisation - dependent and resonant angle - resolved photoemission measurements with density - functional theory calculations , we show that the two `` spin - split '' branches of the model giant rashba system bitei additionally develop disparate orbital textures , each of which is coupled to a distinct spin configuration . this necessitates a re - interpretation of spin splitting in rashba - like systems , and opens new possibilities for controlling spin polarisation through the orbital sector .

the rashba effect is one of the most striking manifestations of spin - orbit coupling in solids , and provides a cornerstone for the burgeoning field of semiconductor spintronics . it is typically assumed to manifest as a momentum - dependent splitting of a single initially spin - degenerate band into two branches with opposite spin polarisation . here , combining polarisation - dependent and resonant angle - resolved photoemission measurements with density - functional theory calculations , we show that the two `` spin - split '' branches of the model giant rashba system bitei additionally develop disparate orbital textures , each of which is coupled to a distinct spin configuration . this necessitates a re - interpretation of spin splitting in rashba - like systems , and opens new possibilities for controlling spin polarisation through the orbital sector .

cond-mat9809227

i

the role of electronic interactions on the observed properties of semiconductor quantum dots has increasingly been found to be of vital importance , as many of the papers in these proceedings and elsewhere illustrate . more and more , transport and capacitance experiments , as well as detailed studies of far - infrared response , require the consideration of interactions in order to understand the observed experimental features . since a number of experiments explore specifically the electronic level spectrum , it is of interest to contrast these studies with a detailed theoretical analysis of the role of interactions . we present here an analysis of the energy level statistics of a quantum dot system as function of variable interaction strength , and then as function of an applied magnetic field . as the level spectrum is considered in detail , the correspondence with the dynamical integrability of a classical system is also of interest . it is anticipated that as the coulomb interaction is introduced , the dynamics would in general become chaotic and this would in turn be reflected in various statistical properties of the level spectrum . it has been known for some time now that as a classical system becomes non - integrable @xcite , the corresponding quantum system exhibits a level spacing distribution given by the ` wigner surmise ' derived in the context of random matrix theory ( rmt ) @xcite . in fact , this behavior has been verified in a number of theoretical and experimental systems , although typically the classical non - integrability is due to disorder or boundary ( geometrical ) effects . examples discussed in the literature include small disordered metallic particles @xcite , particles moving in a variety of ` stadia ' @xcite , and in two - dimensional antidot arrays @xcite . rmt also has been used to make definite predictions on the statistical distribution of coulomb blockade peak amplitudes @xcite . this behavior has in fact been shown recently to be a good description of quantum dot systems in beautiful experimental realizations @xcite . one should also mention that recent work on interacting systems , some without an obvious classical counterpart , has also shown that these exhibit the level repulsion characteristic of quantum versions of non - integrable classical systems @xcite . moreover , recent analysis of the level spectrum of excitons in quantum wells ( via photoluminescence excitation spectroscopy ) has shown evidence of level repulsion @xcite . a level structure described by rmt has been sought recently in the charging ( or addition ) spectrum of quantum dots @xcite . detailed analysis of experimental charging energies , after proper subtraction , would be expected to yield the single - particle like _ excitation _ spectrum described by rmt . unfortunately , it appears that the extraction of this excitation spectrum is obscured by the systematic shift in the charging energies , and the resulting level spacing is described by a normal distribution , rather than by the rmt functions . this would then suggest that a more direct measurement of the excitation spectrum ( via perhaps nonlinear tunneling currents ) would be desirable ( although clearly difficult experimentally beyond the first few excitations @xcite ) . one should also mention here that it is believed that the nonlinear transport experiments explore mainly the excitations of the center of mass of the system ( in the typically parabolic quantum dots ) @xcite , due to the strong electronic correlations suppressing most of the tunneling ` channels ' . this prevalence of the center of mass excitations is however expected theoretically to diminish as the energy of the excitation increases @xcite . this regime would be reached only as the bias voltage is raised in transport experiments , and makes it then difficult to achieve in practice . we hope , however , that the results presented here would motivate more experimental work in this direction .

the role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures . we find that an otherwise simple system is made strongly non - integrable in the classical regime by the introduction of particle interactions . similarly , a corresponding two - dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields . + keywords : quantum dots , chaos , level statistics + sergio e. ulloa + e - mail : sulloa1@ohiou.edu + fax : ( 614 ) 5930433

the role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures . we find that an otherwise simple system is made strongly non - integrable in the classical regime by the introduction of particle interactions . in particular we present a two - particle classical system contained in a @xmath0-dimensional billiard with hard walls . similarly , a corresponding two - dimensional quantum dot problem with three particles is shown to have interesting spectral properties as function of the interaction strength and applied magnetic fields . + keywords : quantum dots , chaos , level statistics + sergio e. ulloa + e - mail : sulloa1@ohiou.edu + fax : ( 614 ) 5930433

1608.04851

i

the simulation of the movement of pedestrians and crowds in spatial structures is a consolidated research and application context that still presents challenges for researchers in different fields and disciplines : both the automated analysis and the synthesis of pedestrian and crowd behaviour , as well as attempts to integrate these complementary and activities @xcite , present open challenges as well as significant opportunities in a smart environment perspective @xcite . although the currently available commercial tools are used on a day - to - day basis by designers and planners , there is still room for innovations in models , to improve their effectiveness in modeling pedestrians and crowd phenomena , their expressiveness ( i.e. simplifying the modeling activity or introducing the possibility of representing phenomena that were still not considered by existing approaches ) and efficiency . moreover , and this is the particular focus of this paper , they are generally not integrated with existing monitoring and control infrastructures , that are employed by crowd managers and field operators . as testified by an analysis of a recent disaster related to a crowding situation @xcite , a more systemic perspective on the overall work flow leading from planning and preparation , to monitoring and control of a crowded event , can help preventing these kinds of situations . this idea of a more thorough and comprehensive computational support to crowd management is also discussed in @xcite . this paper introduces the notion of an integrated crowd management support system , a system encompassing both interfaces from and to a monitored and controlled environment ( respectively sensors and actuators ) as well as a set of software tools supporting the analysis of phenomena taking place in the environment , a faster than real - time simulation of the plausible evolution of the current situation in order to support forms of inference providing decision support to crowd managers , potentially directly controlling elements of the environment ( e.g. blocking turnstiles , escalators ) , communicating orders to operators on the field or trying to influence the pedestrians by means of dynamic signage or audible messages . the following section provides a brief discussion of the relevant state of the art in pedestrians and crowd automated analysis and synthesis , then some early works providing relevant examples of prototypes of systems partly implementing a crowd control center will be presented and discussed in order to sketch a general architecture . conclusions and future works end the paper .

the simulation of the dynamical behavior of pedestrians and crowds in spatial structures is a consolidated research and application context that still presents challenges for researchers in different fields and disciplines . despite currently available commercial systems for this kind of simulation are growingly employed by designers and planners for the evaluation of alternative solutions , this class of systems is generally not integrated with existing monitoring and control infrastructures , usually employed by crowd managers and field operators for security reasons . this paper introduces the essentials and the related computational framework of an integrated crowd management support system based on a collective artificial intelligence approach encompassing ( i ) interfaces from and to monitored and controlled environments ( respectively , sensors and actuators ) , ( ii ) a set of software tools supporting the analysis of pedestrians and crowd phenomena taking place in the environment to feed a ( iii ) faster than real - time simulation of the plausible evolution of the current situation in order to support forms of inference providing decision support to crowd managers , potentially directly controlling elements of the environment ( e.g. blocking turnstiles , escalators ) , communicating orders to operators on the field or trying to influence the pedestrians by means of dynamic signage or audible messages . pedestrians and crowd simulation , monitoring and control , crowd management

the simulation of the dynamical behavior of pedestrians and crowds in spatial structures is a consolidated research and application context that still presents challenges for researchers in different fields and disciplines . despite currently available commercial systems for this kind of simulation are growingly employed by designers and planners for the evaluation of alternative solutions , this class of systems is generally not integrated with existing monitoring and control infrastructures , usually employed by crowd managers and field operators for security reasons . this paper introduces the essentials and the related computational framework of an integrated crowd management support system based on a collective artificial intelligence approach encompassing ( i ) interfaces from and to monitored and controlled environments ( respectively , sensors and actuators ) , ( ii ) a set of software tools supporting the analysis of pedestrians and crowd phenomena taking place in the environment to feed a ( iii ) faster than real - time simulation of the plausible evolution of the current situation in order to support forms of inference providing decision support to crowd managers , potentially directly controlling elements of the environment ( e.g. blocking turnstiles , escalators ) , communicating orders to operators on the field or trying to influence the pedestrians by means of dynamic signage or audible messages . pedestrians and crowd simulation , monitoring and control , crowd management

1303.1450

i

the in - spiral and coalescence of binary neutron star systems is a topic of increasingly intensive research in observational and theoretical astrophysics . it is anticipated that the first direct detections of gravitational wave ( gw ) will be from compact binary mergers . binary neutron star ( bns ) mergers are also thought to produce short - hard gamma - ray bursts ( sgrb s ) @xcite . simultaneous detections of a prompt gravitational wave signal with a spatially coincident electromagnetic ( em ) counterpart dramatically increases the potential science return of the discovery . for this reason , there has been considerable interest as to which , if any , detectable em signature may result from the merger @xcite . other than sgrbs and their afterglows , including those viewed off - axis @xcite , suggestions include optical afterglows associated with the radio - active decay of tidally expelled r - process material@xcite ( though detailed calculations indicate they are faint @xcite ) , radio afterglows following the interaction of a mildly relativistic shell with the interstellar medium @xcite , and high - energy pre - merger emission from resistive magnetosphere interactions @xcite . merging neutron stars possess abundant orbital kinetic energy ( @xmath4ergs ) . a fraction of this energy is certain to be channelled through a turbulent cascade triggered by hydrodynamical instabilities during merger . turbulence is known to amplify magnetic fields by stretching and folding embedded field lines in a process known as the small - scale turbulent dynamo @xcite . amplification stops when the magnetic energy grows to equipartition with the energy containing turbulent eddies @xcite . an order of magnitude estimate of the magnetic energy available at saturation of the dynamo can be informed by global merger simulations . these studies indicate the presence of turbulence following the nonlinear saturation of the kelvin - helmholtz ( kh ) instability activated by shearing at the ns surface layers @xcite . the largest eddies produced are on the @xmath5 km scale and rotate at @xmath6 , setting the cascade time @xmath7 and kinetic energy injection rate @xmath8 at @xmath9ms and @xmath10 respectively . when kinetic equipartition is reached , each turbulent eddy contains @xmath11 of magnetic energy , and a mean magnetic field strength @xmath12 whether such conditions are realized in merging neutron star systems depends upon the dynamo saturation time @xmath13 and equipartition level @xmath14 . in particular , if @xmath15 then turbulent volumes of neutron star material will contain magnetar - level fields throughout the early merger phase . once saturation is reached , a substantial fraction of the injected kinetic energy , @xmath16 , is resistively dissipated @xcite at small scales . magnetic energy dissipated by reconnection in optically thin surface layers will accelerate relativistic electrons @xcite , potentially yielding an observable electromagnetic counterpart , independently of whether the merger eventually forms a relativistic outflow capable of powering a short gamma - ray burst . in this letter we demonstrate that the small - scale turbulent dynamo saturates quickly , on a time @xmath15 , and that @xmath17 g magnetic fields are present throughout the early merger phase . this implies that the magnetic energy budget of merging binary neutron stars is controlled by the rate with which hydrodynamical instabilities randomize the orbital kinetic energy . our results are derived from simulations of the small scale turbulent dynamo operating in the high - density , trans - relativistic , and highly conductive material present in merging neutron stars . we have carefully examined the approach to numerical convergence and report grid resolution criteria sufficient to resolve aspects of the small - scale dynamo . our letter is organized as follows . the numerical setup is briefly described in section 2 . section 3 reports the resolution criterion for numerical convergence of the dynamo completion time and the saturated field strength . in section 4 we asses the possibility that magnetic reconnection events may convert a sufficiently large fraction of the magnetic energy into high energy photons to yield a prompt electromagnetic counterpart detectable by high energy observatories including _ swift _ and _ fermi_. and @xmath18 . lower resolutions are shown in red and graduate to black with higher resolution . _ top _ : the root mean square magnetic field strength in units of @xmath19 . when a turbulent volume is resolved by @xmath20 zones , the small - scale dynamo proceeds so slowly that almost no amplification is observed in the first 1ms . _ middle _ : the magnetic energy in units of the rest mass @xmath21 shown on logarithmic axes . it is clear that the linear growth rate increases at each resolution . _ bottom _ : the kinetic energy ( upper curves ) shown again the magnetic energy ( lower curves ) again in units of @xmath21 . for all resolutions , the kinetic energy saturates in less than 1 @xmath7.,width=326 ]

the simultaneous detection of electromagnetic and gravitational wave emission from merging neutron star binaries would aid greatly in their discovery and interpretation . by studying turbulent amplification of magnetic fields in local high - resolution simulations of neutron star merger conditions , we demonstrate that magnetar - level ( @xmath0 g ) fields are present throughout the merger duration . we find that the small - scale turbulent dynamo converts 60% of the randomized kinetic energy into magnetic fields on a merger time scale .

the simultaneous detection of electromagnetic and gravitational wave emission from merging neutron star binaries would aid greatly in their discovery and interpretation . by studying turbulent amplification of magnetic fields in local high - resolution simulations of neutron star merger conditions , we demonstrate that magnetar - level ( @xmath0 g ) fields are present throughout the merger duration . we find that the small - scale turbulent dynamo converts 60% of the randomized kinetic energy into magnetic fields on a merger time scale . since turbulent magnetic energy dissipates through reconnection events which accelerate relativistic electrons , turbulence may facilitate the conversion of orbital kinetic energy into radiation . if @xmath1 of the @xmath2 erg of orbital kinetic available gets processed through reconnection , and creates radiation in the 15 - 150 kev band , then the fluence at 200 mpc would be @xmath3 , potentially rendering most merging neutron stars in the advanced ligo and virgo detection volumes detectable by _ swift _ bat .

1303.1450

c

in this letter we have determined the time scale and saturation level of the small - scale turbulent dynamo operating in the conditions of binary neutron star mergers . we have presented numerically converged simulations showing that magnetic fields are amplified to the @xmath93 g level within a small fraction of the merger dynamical time ( @xmath15 ) , independently of the seed field strength . if hydrodynamical instabilities create fluctuating velocities on the order of @xmath94 as indicated by global simulations , then each @xmath95 turbulent volume dissipates @xmath96 erg of magnetic energy per 0.1 ms . if @xmath97 represents the fraction of the merger remnant that contains such turbulence , the magnetic energy dissipated during the merger is at least @xmath98 a fraction of that dissipation will occur through magnetic reconnection in optically thin surface layers , supplying relativistic electrons which synchrotron radiate in the merger remnant magnetosphere . if 5% of that magnetic energy dissipation creates radiation in the 15 - 150 kev band , then the fluence at 200 mpc would be @xmath3 , potentially rendering most merging neutron stars in the advanced ligo and virgo detection volumes detectable by _ swift _ bat . if so , then merging neutron stars are accompanied by a prompt electromagnetic counterpart , independently of whether a later merger phase yields a collimated outflow capable of powering a short gamma - ray burst . we suggest that merger flares may be present in the current sample of short grbs and may be roughly isotropic on the sky since they are seen to distances where the cosmological matter distribution becomes homogeneous . searches for merger flares should seek to identify short flares , not unlike soft - gamma repeaters , among the short burst population . if mergers also produce short grbs short - hard grbs , then merger flares may constitute a precursor component of the emission . the presence of strong magnetic fields may also aid in the ejection of neutron - rich material from surface layers of the merger remnant , possibly enhancing the enrichment of inter - stellar medium by r - process nuclei @xcite . enhanced production of r - process nuclei also increases the likelihood of em detection by radio - active decay powered afterglows , or `` kilonovae '' @xcite . finally , it has been shown that magnetic fields will significantly influence the gravitational wave signature and remnant disk mass , if they exist at the @xmath99 g level @xcite . such strong fields are unlikely in older neutron star binaries , but our results suggest they may be revived , albeit at small scales , during the merger . to have significant influence , those fields would have to fill a considerable fraction of the merger volume . as we have shown in this letter , the overall magnetic energy budget is controlled by the prevalence ( @xmath97 ) and vigor ( @xmath100 ) of the turbulent volumes . this fact motivates the use of higher resolution global simulations aimed at measuring @xmath97 and @xmath100 . this research was supported in part by the nsf through grant ast-1009863 and by nasa through grant nnx10af62 g issued through the astrophysics theory program . resources supporting this work were provided by the nasa high - end computing ( hec ) program through the nasa advanced supercomputing ( nas ) division at ames research center .

since turbulent magnetic energy dissipates through reconnection events which accelerate relativistic electrons , turbulence may facilitate the conversion of orbital kinetic energy into radiation . if @xmath1 of the @xmath2 erg of orbital kinetic available gets processed through reconnection , and creates radiation in the 15 - 150 kev band , then the fluence at 200 mpc would be @xmath3 , potentially rendering most merging neutron stars in the advanced ligo and virgo detection volumes detectable by _ swift _ bat .

the simultaneous detection of electromagnetic and gravitational wave emission from merging neutron star binaries would aid greatly in their discovery and interpretation . by studying turbulent amplification of magnetic fields in local high - resolution simulations of neutron star merger conditions , we demonstrate that magnetar - level ( @xmath0 g ) fields are present throughout the merger duration . we find that the small - scale turbulent dynamo converts 60% of the randomized kinetic energy into magnetic fields on a merger time scale . since turbulent magnetic energy dissipates through reconnection events which accelerate relativistic electrons , turbulence may facilitate the conversion of orbital kinetic energy into radiation . if @xmath1 of the @xmath2 erg of orbital kinetic available gets processed through reconnection , and creates radiation in the 15 - 150 kev band , then the fluence at 200 mpc would be @xmath3 , potentially rendering most merging neutron stars in the advanced ligo and virgo detection volumes detectable by _ swift _ bat .

0912.4222

i

the cast ( cern axion solar telescope ) experiment is using a decommissioned lhc dipole magnet to convert solar axions into detectable x - ray photons . axions are light pseudoscalar particles that arise in the context of the peccei - quinn@xcite solution to the strong cp problem and can be dark matter candidates@xcite . stars could produce axions via the primakoff conversion of the plasma photons . the cast experiment is pointing at our closest star , the sun , aiming to detect solar axions . the detection principle is based on the coupling of an incoming axion to a virtual photon provided by the transverse field of an intense dipole magnet , being transformed into a real , detectable photon that carries the energy and the momentum of the original axion . the axion to photon conversion probability is proportional to the square of the transverse field of the magnet and to the active length of the magnet . using an lhc magnet ( @xmath7 t and @xmath8 m long ) improves the sensitivity by a factor 100 compared to previous experiments . the cast experiment has been taking data since 2003 providing the most restrictive limits on the axion - photon coupling @xcite for masses @xmath9ev . at this mass the sensitivity is degraded due to coherence loss . in order to restore coherence , the magnet can be filled with a buffer gas providing an effective mass to the photon@xcite . by changing the pressure of the buffer gas in steps , one can scan an entire range of axion mass values . at the end of 2005 the cast experiment started such a program , entering its phase ii by filling the magnet bore with he gas . from 2005 to 2007 , the magnet bore was filled with @xmath10 gas extending our sensitivity to masses up to @xmath11ev , final results will be presented here . from march 2008 onwards the magnet bore has been filled with @xmath12 and the sensitivity should be increased to sensivities up to @xmath13ev by the end of the @xmath12 run in 2010 .

the status of the solar axion search with the cern axion solar telescope ( cast ) will be discussed . results from the first part of cast phase ii where the magnet bores were filled with @xmath0 gas at variable pressure in order to scan @xmath1 up to 0.4 ev will be presented . from the absence of excess x - rays our search for axions with masses up to about 1.2 ev using @xmath6 as a buffer gas is , since last year , in progress in the second part of cast phase ii . expectations for sensibilities will be given .

the status of the solar axion search with the cern axion solar telescope ( cast ) will be discussed . results from the first part of cast phase ii where the magnet bores were filled with @xmath0 gas at variable pressure in order to scan @xmath1 up to 0.4 ev will be presented . from the absence of excess x - rays when the magnet was pointing to the sun , we set a typical upper limit on the axion - photon coupling of @xmath210@xmath3gev@xmath4 at 95% cl for @xmath1@xmath5 ev , the exact result depending on the pressure setting . our search for axions with masses up to about 1.2 ev using @xmath6 as a buffer gas is , since last year , in progress in the second part of cast phase ii . expectations for sensibilities will be given . near future perspectives as well as more long term options for a new helioscope experiment will be evoked .

nlin0602021

i

elucidating cooperative behavior of synchronization of coupled genetic oscillators has important biological implications and potential engineering applications from both theoretical and experimental viewpoints , and it is also essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels . so far many researchers have studied the synchronization in genetic networks from the aspects of experiment , numerical simulation and theoretical analysis . for instance , in @xcite , the authors experimentally investigated the synchronization of cellular clock in the suprachiasmatic nucleus ( scn ) ; in @xcite and @xcite , the collective dynamics of synchronization are theoretically studied in synthetic biological networks of identical genetic oscillators ; and in @xcite , the mechanism of synchronization in a population of identical hysteretic genetic oscillators is analyzed . biologically , the genetic oscillators , even in the same species , are usually nonidentical possibly due to asymmetrical nutrition conditions and fluctuated environments , and the nonidentical property can be modelled as parametric mismatches among oscillators . for example , in the suprachiasmatic nucleus ( scn ) , the periods of the circadian oscillators are not exactly the same , and it has been observed that isolated individual neurons are able to produce circadian oscillations with period ranging from 20 to 28 hours @xcite . in @xcite , the synchronization for nonidentical genetic oscillators is examined numerically . although many mathematical models have been developed to study the cooperative behaviors of cellular oscillation , there is no general theoretical method in analyzing the dynamics of the coupled genetic oscillators due to their inherent nonlinearity . genetic networks are biochemically dynamical systems , in which the nodes indicate the biochemicals , and the couplings represent the biochemical interactions @xcite . mathematically many genetic oscillators can be expressed in the form of multiple additive terms , each of which particularly is of linear , michaelis - menten or hill forms , such as the well - known goodwin model @xcite , repressilator @xcite , toggle switch @xcite , and the circadian oscillators @xcite . from the synthetic biology viewpoint , genetic oscillators with only linear , michaelis - menten and hill form terms can also be implemented easily . in this paper we explore such special structure of gene networks to show that these genetic oscillators can be transformed into lure form and can be further analyzed by using lure system method in control theory @xcite . the aim of this paper is to provide a general theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators with the above - mentioned structure . in studying the synchronization of genetic oscillators ( and other nonlinear systems ) , a general idea is to study the stability of the error equations among oscillators . however , there are two main difficulties for such method : ( 1 ) the difference of the oscillator dynamics usually can not be written into a function of the state error ; ( 2 ) due to the nonlinearity , there is no general efficient analysis method for the stability of the error system . we show in this paper that for genetic oscillators with the above - mentioned structure , we can overcome both of the above difficulties . since coupled nonidentical oscillators usually can not achieve complete synchronization , a synchronous error is required to evaluate the quality of the synchronization . in this paper , we present a theoretical result , which can not only guarantee the synchronization , but also estimates the bound of the synchronization error . besides , the obtained conditions can be represented in terms of linear matrix inequalities ( lmis ) @xcite , which are very easy to be verified . recently , it was found that many biological networks are complex networks with small - world and scale - free properties @xcite . our method is also applicable to genetic oscillator networks with complex topology , directed and weighted couplings . to demonstrate the effectiveness of the theoretical results , we present two simulation examples of coupled goodwin oscillators with linear and michaelis - menten couplings , respectively . finally , several remarks on the extensions of the proposed method are discussed . notation used in this paper as well as the detailed theoretical analysis are given in the appendix .

the study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels . we show in this paper that many genetic oscillators can be transformed into lure form by exploiting the special structure of biological systems . by using control theory approach , we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators . sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained . to demonstrate the effectiveness of our theoretical results , a population of genetic oscillators based on the goodwin model

the study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels . genetic oscillators are biochemical networks , which can generally be modelled as nonlinear dynamic systems . we show in this paper that many genetic oscillators can be transformed into lure form by exploiting the special structure of biological systems . by using control theory approach , we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators . sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained . to demonstrate the effectiveness of our theoretical results , a population of genetic oscillators based on the goodwin model are adopted as numerical examples .

1210.5011

r

the 323 neutron and proton doubly folded single - particle energy levels for @xmath0tl employed in the present calculations are obtained within the axially deformed woods - saxon potentials including the spin - orbit and coulomb interactions @xcite . the neutron spectrum spans a space of 157 doubly folded levels ( degenerated into 41 spherical orbitals ) , starting from the bottom at -38.36 mev up to 12.57 mev . the proton spectrum has 166 doubly folded levels ( degenerated into 44 spherical orbitals ) , starting from the bottom at around -34 mev , up to around 22.3 mev . they cover the energy intervals similar to those used in the calculations of gdr width in @xmath29pb @xcite . in the construction of the ce partition function ( [ zce ] ) one needs to include all the eigenvalues of the ground state as well as excited states . meanwhile , the fortran imsl subroutine for matrix diagonalization at the riken integrated cluster of clusters computing system implies that the numbers of levels @xmath127 and particles @xmath119 should satisfy the condition @xmath128 < 10 ^ 4 $ ] , which means it is impossible to carry out the exact diagonalization of the pairing hamiltonian ( [ hpair ] ) with the entire single - particle spectra @xcite . therefore , knowing that pairing has a significant effect around the fermi surface , we calculate the exact ce thermal gap ( [ gap ] ) only for 14 doubly folded neutron ( proton ) levels situated around the fermi one , @xmath129 , with 7 levels below and 7 levels above it . the selected levels belong to the group of 18 neutron ( proton ) levels within five @xmath130-folded spherical orbitals @xmath131 for the neutrons , and @xmath132 , @xmath133 for protons , as listed in table [ table1 ] . the pairing parameters @xmath134 0.182 mev for neutrons and @xmath135 = 0.37 mev for protons are chosen to reproduce the empirical values of the neutron and proton gaps @xmath136 , which are both equal to 1 mev for @xmath0tl according to fig . 2 - 5 of ref . this value agrees well with the three - point and five - point gaps calculated in ref . @xcite and shown in fig . 1 therein . the remaining 4 neutron levels ( two on @xmath137 and two on @xmath138 orbitals ) and 4 proton levels ( two on @xmath139 and two on @xmath133 orbitals ) of this group are assumed to have the same thermal neutron and proton pairing gaps , respectively . for the levels beyond this group , pairing is assumed to be negligible so that @xmath140 , @xmath141 , @xmath142 , and @xmath143 . .single - particle spherical orbitals obtained within woods - saxon potentials and used in the calculations of neutron and proton exact ce pairing gaps for @xmath0tl . [ table1 ] [ cols="^,^,^,^,^ " , ] the pdm assumes that the matrix elements of gdr coupling to @xmath15 configurations , causing the quantal width , are all equal to @xmath49 , whereas those of coupling to @xmath16 ( @xmath17 ) configurations , causing the thermal width at @xmath14 0 , are all equal to @xmath50 [ see sec . ii b of ref . @xcite for the detail discussion on the justification of this assumption . ] . the third parameter , @xmath35 , in the case of gdr ( @xmath144 ) , is chosen to be close to @xmath145 . because the mechanism of the spreading width @xmath146 at @xmath18 0 is known , which is owing to coupling to more complicate configurations @xmath147 configurations , the pdm has no ambition to calculate it microscopically but is interested only in its temperature dependence incorporated in the quantal width . therefore the parameter @xmath49 is selected to reproduce the gdr experimental width at @xmath18 0 , which is essentially the sum of the spreading width , @xmath146 , and the escape width , @xmath85 . the parameter @xmath50 is usually adjusted so that the gdr energy @xmath148 , found as the solution of eq . ( [ egdr ] ) , does not change appreciably with @xmath1 . because the gdr energy in @xmath0tl does not depend on @xmath1 , namely @xmath149 mev @xcite , for simplicity , we adopt in the present paper @xmath150 13.8 mev , and select @xmath50 so that the calculated width at @xmath13 2 mev matches the corresponding experimental value for the gdr width in @xmath29pb @xcite . and protons [ ( blue ) dashed line ] for @xmath0tl . [ gaptl201],width=510 ] shown in fig . [ gaptl201 ] are the exact ce neutron and proton pairing gaps for @xmath0tl as functions of @xmath1 . in different with the bcs gaps , the exact ce gaps do not collapse at @xmath151 0.57 mev for @xmath152 1 mev . instead , they both decrease as @xmath1 increases . in particular , the proton gap remains almost unchanged or even slightly increases in the region @xmath153 1 mev , and it is significantly larger than the neutron gap at the same value of @xmath1 already starting from @xmath13 0.5 mev . at @xmath18 1 mev the proton gap is still equal to around 1 mev whereas the neutron gap drops to 0.34 mev . at @xmath18 5 mev the proton gap remains as large as around 0.4 mev , whereas the neutron gap is depleted to 0.13 mev . versus experimental data . the ( red ) thick solid line is the gdr width for @xmath0tl obtained with the effect of exact ce pairing . the ( green ) thin solid line denotes the same width but obtained without pairing . the ( purple ) dashed line stands for the same quantity , but obtained by using the exact single - particle occupation numbers @xmath73 and effective @xmath154 discussed in the text . the dotted line represents the gdr width for @xmath29pb obtained previously in refs . the full circles and open boxes are experimental gdr widths for @xmath0tl @xcite and @xmath29pb @xcite , respectively . [ widthtl201],width=415 ] the gdr fwhm @xmath155 in @xmath0tl obtained within the pdm in three different approximations are plotted as functions of @xmath1 against the experimental data in fig . [ widthtl201 ] . in the first approximation , the zero - pairing one , the width @xmath155 is calculated by using eq . ( [ fwhm ] ) and the phonon damping given in eq . ( [ gamma_nopair ] ) . the single - particle occupation numbers @xmath73 are approximated with the fermi - dirac distribution @xmath156 + 1\}~ , \label{ffd}\ ] ] where the chemical neutron and proton potentials change with @xmath1 to conserve the particle numbers , according to the equation @xmath157 with @xmath158 . the calculations adopted the following values of the parameters for the @xmath15 and @xmath16 ( @xmath17 ) couplings : @xmath159 4.0@xmath16010@xmath161 mev and @xmath162 13.27@xmath16010@xmath161 mev . the gdr width predicted by this approximation ( thin solid line ) clearly overestimates three lowest experimental data points at @xmath18 0.82 , 0.84 and 0.97 mev . the overall temperature dependence of this width is similar to that obtained previously for the doubly closed - shell @xmath29pb ( dotted line ) except at @xmath8 3 mev , where it becomes larger than the gdr width in @xmath29pb , to saturate at @xmath8 4 mev at a value of 12.7 mev compared to that of around 10.5 mev for @xmath29pb . the small bump at @xmath163 0.3 mev occurs because of the neutron single - particle energies of the orbitals @xmath164 and @xmath165 , which are equal to 6.903 mev and 6.587 mev , respectively , and located just below the fermi level at @xmath18 0 . they cause a local minimum in the temperature dependence of the neutron chemical potential at @xmath18 0.3 mev as shown by the solid line in fig . [ widthtest ] ( a ) . a test by changing the energies of these levels to 7.903 and 7.587 mev , respectively , removes this local minimum and , consequently , flattens the gdr width at @xmath163 1 mev , as shown by the dash - dotted lines in figs . [ widthtest ] ( a ) and [ widthtest ] ( b ) , respectively . . in ( a ) the ( green ) solid line denotes the neutron chemical potentials as a function of @xmath1 obtained for @xmath0tl before modifying the energies of the orbitals @xmath164 and @xmath165 , whereas the ( blue ) dash - dotted line stands for the same quantity obtained after modifying the energies of these orbitals as specified in the text . in ( b ) the ( green ) solid and ( blue ) dash - dotted lines show the gdr widths for @xmath0tl obtained within the no - pairing approximation before and after this modification , respectively . [ widthtest],width=415 ] in the second approximation , we consider an effective way of taking thermal pairing into account , namely , in eq . ( [ gamma_nopair ] ) , the single - particle occupation numbers @xmath73 for the 18 selected levels around the fermi surface , which were discussed previously , are replaced with their exact ce values @xmath166 calculated by using eq . ( [ ef ] ) . the effective values of @xmath167 for these 18 levels are found by inverting the fermi - dirac distribution ( [ ffd ] ) to obtain @xmath168 $ ] . the calculations used @xmath169 2.45@xmath16010@xmath161 mev and @xmath162 14.83@xmath16010@xmath161 mev . starting at the same value equal to around 4 mev at @xmath18 0 , the width predicted by this approximation ( dashed line ) decreases as @xmath1 increases up to @xmath18 0.7 mev to perfectly match the three lowest data points at @xmath18 0.82 , 0.84 and 0.97 mev . at @xmath8 0.7 mev this width increases with @xmath1 but remains smaller than that obtained without pairing up to @xmath13 3.6 mev when they cross and reach the same value at @xmath18 5 mev . finally , thermal pairing is fully taken into account within the quasiparticle representation of the pdm by using eqs . ( [ fwhm ] ) and ( [ gamma ] ) , which include the exact ce thermal pairing gap for 18 levels around the fermi surface for neutrons and protons , separately , as has been discussed in sec . the gdr width predicted by this approach ( thick solid line ) nicely describes all the data points for @xmath0tl . its values at @xmath12 0.8 , 0.9 , 1.0 , 1.1 and 1.2 mev are found equal to 3.58 , 3.75 , 3.96 , 4.22 and 4.5 mev , respectively , to be compared with the corresponding experimental values of 3.4@xmath170 0.45 , 3.7@xmath170 0.45 , 3.8@xmath170 0.45 , 4.6@xmath170 0.45 and 4.5@xmath170 0.45 mev at @xmath18 0.82 , 0.94 , 0.97 , 1.09 and 1.12 mev , respectively . it also matches fairly well the experimental width for @xmath29pb at 1.3@xmath171 2 mev , although , up to @xmath13 3 mev , it remains smaller than the width predicted by the pdm for @xmath29pb ( dotted line ) . however , to obtain such description , the value for @xmath49 has to be smaller than that used in the case without pairing so that @xmath172 3 mev instead of 4 mev for the gdr width in @xmath29pb at @xmath173 , and , consequently , the value for @xmath50 has to be larger to reproduce the same data point at @xmath18 2 mev . eventually , this brings @xmath174 closer to the recent parametrization of the gdr width for quasipherical nuclei @xcite , which implies that the gdr fwhm for @xmath0tl at @xmath18 0 amounts to around 3.33 mev , rather than 4 mev as that of @xmath29pb . the slope of the width s increase as a function of @xmath1 also becomes slightly steeper , improving the agreement between theory and experiment within the entire region of @xmath1 . a value for @xmath49 that reproduces @xmath175 4 mev leads to an overestimation of the width in the entire temperature region of @xmath14 0 . the values for the coupling parameters used in this approximation are @xmath169 2.81@xmath16010@xmath161 mev and @xmath162 16.73@xmath16010@xmath161 mev . it is important to point out that , although one could fit the data points for @xmath0tl within the zero - pairing approximation by reducing the value of parameter @xmath49 from 4.0@xmath16010@xmath161 mev to 3.54@xmath16010@xmath161 mev , it is not possible by readjusting only parameters @xmath81 to achieve the overall agreement with both sets of data for the gdr widths in @xmath0tl and @xmath29pb as does the last approach that fully includes exact ce pairing gaps within the quasiparticle representation of the pdm . at @xmath8 2.5 mev the gdr width obtained by using such reduced parameter @xmath49 in the zero - pairing approximation becomes even smaller than that predicted by the second approximation ( of taking effectively thermal pairing into account ) . this indicates that the effect owing to thermal pairing on the gdr width has its microscopic origin , which can not be accounted for by simply adjusting model s parameters . tl obtained within the quasiparticle representation of the pdm ( red solid lines ) at @xmath12 0.8 1.2 mev as shown in the panels in comparison with the experimental linearized strength functions ( green data points ) @xcite at @xmath18 0.82 , 0.94 , 0.97 , 1.09 , and 1.12 mev from the bottom panel , ( e ) , to the top one , ( a ) , respectively . [ stre],width=377 ] the gdr strength functions obtained at @xmath18 0.8 1.2 mev by using eq . ( [ s ] ) within the quasiparticle representation of the pdm that includes exact ce pairing are displayed in fig . [ stre ] in comparison with the corresponding experimental data adapted from fig . 1(a ) of ref . @xcite . the theoretical strength functions have been renormalized so that the value at @xmath176 5 mev and the maximum at @xmath12 1.2 mev match the corresponding experimental values . this figure and fig . [ widthtl201 ] show that the pdm describes reasonably well not only the temperature dependence of the gdr width but also that of the gdr linearized shape .

the thermal pairing gap obtained by embedding the exact solutions of the pairing problem into the canonical ensemble is employed to calculate the width and strength function of the giant dipole resonance ( gdr ) within the phonon damping model . the results of calculations describe reasonably well the data for the gdr width as well as the gdr linearized strength function , recently obtained for @xmath0tl in the temperature region between 0.8 and 1.2 mev , which other approaches that neglect the effect of non - vanishing thermal pairing fail to describe .

the thermal pairing gap obtained by embedding the exact solutions of the pairing problem into the canonical ensemble is employed to calculate the width and strength function of the giant dipole resonance ( gdr ) within the phonon damping model . the results of calculations describe reasonably well the data for the gdr width as well as the gdr linearized strength function , recently obtained for @xmath0tl in the temperature region between 0.8 and 1.2 mev , which other approaches that neglect the effect of non - vanishing thermal pairing fail to describe .

1604.00977

i

we have presented two examples where time - resolved infrared investigations using step - scan fourier - transform spectroscopy provide insight in the molecular dynamics at the phase transition and molecular orientation . in the case of liquid crystals , the application of an electric field switches the orientation of the molecular dipoles changing the transmission of the cell for polarized infrared light . watching the time evolution of the pronounced molecular vibrational modes allows us to extract the time constant of approximately 2 ms and its dependence on the applied voltage . the neutral - ionic phase transition of ttf - ca can be photo - excited with a short laser pulse , creating domain walls that are mobile and eventually annihilate . we follow the time - dependence of the vibrational modes activated by the changed dimerization and ionicity . the relaxation back to the initial state strongly depends on the temperature and laser intensity , it extends from a 3 @xmath15s to almost 1 ms . for both examples we give details of the experimental setups and limitations . we demonstrate the applicability of step - scan fourier - transform spectroscopy in a large dynamical range . we thank f. schrg and f. giesselmann for providing the liquid crystals and g. untereiner for continuous help ; e. kurz and n. frhauf supported us when building the cell and use of their clean room . funding by the deutsche forschungsgemeinschaft ( dfg ) is acknowledged . thanks the carl - zeiss - stiftung for financial support . m. mitrano , g. cotugno , clark , s.r . , r. singla , s. kaiser , j. sthler , r. beyer , m. dressel , l. baldassarre , d. nicoletti , a. perucchi , t. hasegawa , h. okamoto , d. jaksch , a. cavalleri , phys . lett . * 112 * , 117801 ( 2014 )

the time - dependent optical properties of molecular systems are investigated by step - scan fourier - transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range . we present all details of the experimental setups and thoroughly discuss the technical challenges .

the time - dependent optical properties of molecular systems are investigated by step - scan fourier - transform spectroscopy in order to explore the dynamics at phase transitions and molecular orientation in the milli- and microsecond range . the electrical switching of liquid crystals traced by vibrational spectroscopy reveals a rotation of the molecules with a relaxation time of 2 ms . the photo - induced neutral - ionic transition in ttf - ca takes place by a suppression of the dimerization in the ionic phase and creation of neutral domains . the time - dependent infrared spectra depend on temperature and laser pulse intensity ; the relaxation of the spectra follows a stretched - exponential decay with relaxation times in the microsecond range strongly dependent on temperature and laser intensity . we present all details of the experimental setups and thoroughly discuss the technical challenges . example.eps gsave newpath 20 20 moveto 20 220 lineto 220 220 lineto 220 20 lineto closepath 2 setlinewidth gsave .4 setgray fill grestore stroke grestore

astro-ph0010115

c

we put forward a maximum likelihood technique , coupled to a variational calculus , which allows the robust , non - parametric reconstruction of the evolution of the star formation rate from the information contained in colour - magnitude diagrams . a full bayesian analysis is also applied to assess whether the best solutions found are also good fits to the data . its main limitation , at the moment , is the prior knowledge of the metallicity of the ensemble of stars in a cmd . for the first time , an objective reconstruction of star formation histories without any a priori or model - dependent information is applied to an homogeneous sample of dwarf spheroidals of the local group . we find a wide variety of sfhs , with bursts of activity uncorrelated to any special epoch or event , like perigalacticon passages . among many other things , this also implies that late accretion was not important in the formation of the galactic halo ( gilmore et al . 2000 ) . in the solar neighbourhood observed by hipparcos , we infer with an unprecedented resolution of 50 myr its star formation history over the past 3 gyr , finding a surprising regularity of star formation episodes separated by some 0.5 gyr . a possible explanation is that the solar neighbourhood interacted with two spiral arms or the galactic bar , triggering star formation at each interaction . these bursts are likely to induce the formation of massive star clusters which slowly dissolve into the galactic disc . amaral l.h . , lpine j.r.d . , 1997 , mnras , 286 , 885 aparicio a. , 1998 , in iau symp 192 , the stellar content of local group galaxies , ed . p. whitelock & r. cannon ( san francisco : asp ) , 20 asiain r. , figueras f. , torra j. , 1999 , a&a , 350 , 434 avedisova v.s . , 1989 , astrophys . 30 , 83 chereul e. , crz m. , bienaym o. , 1999 , a&a suppl . 135 , 5 dolphin , a. , 1997 , new ast . , 2 , 397 gallart c. , freedman w. , aparicio a. , bertelli g. , chiosi c. , 1999 , aj , 118 , 2245 gilmore g. , hernandez x. , valls - gabaud d. , 2000 , the galactic halo : from globular clusters to field stars , 35th lige conf . , ed . a. noels et al . in press ( astro - ph/9910409 ) held , e.v . et al . , 2000 , apj , 530 , l85 hernandez x. , valls - gabaud d. , gilmore g. , 1999 , mnras , 304 , 705 ( paper i ) hernandez x. , gilmore g. , valls - gabaud d. , 2000a , mnras , 317 , 83 ( paper ii ) hernandez x. , valls - gabaud d. , gilmore g. , 2000b , mnras , 316 , 605 ( paper iii ) hurley - keller d. , mateo m. , nemec j. , 1998 , aj , 115 , 1840 mateo m. , 1998 , ara&a , 36 , 435 mighell k.j . , 1997 , aj , 114 , 1458 mighell k.j . , burke , c.j . , 1999 , aj , 118 , 366 mishurov y.n . , pavloskaya e.d . , suchkov a.a . , 1979 , azh , 56 , 268 ng , y.k . , 1998 , a&as , 132 , 133 rocha - pinto h.j . , scalo j. , maciel w.j . , flynn c. , 2000a , apj , 531 , l115 rocha - pinto h.j . , maciel , w.j . , scalo j. , flynn c. , 2000b , a&a , submitted ( astro - ph/0001383 ) saha p. , 1998 , aj , 115 , 1206 sandage , a. 1986 , a&a , 161 , 89 skuljan , j. , hearnshaw , j.b . , cottrell , p.l . , 1999 , mnras , 308 , 731 tolstoy e. , 1999 , in dwarf galaxies and cosmology , ed . thuan , c. balkowski , v. cayatte , j. tran thanh van ( paris : editions frontires ) tolstoy e. , saha a. , 1996 , apj , 462 , 672 valle , j.p . , 1995 , apj , 454 , 119 vazquez e.c . , scalo j.m . , 1989 , apj , 343 , 644

we have developed a maximum likelihood technique , which coupled to a variational calculus allows us to make a robust , non - parametric reconstruction of the evolution of the star formation rate . a full bayesian analysis is also applied to assess whether the best solutions found are also good fits to the data . applying this new method to wfpc2 observations of five dsph galaxies of the local group we infer , with an unprecedented resolution of 50 myr , its star formation history over the past 3 gyr . these bursts possibly trigger the formation of massive star clusters which slowly dissolve into the galactic field .

the unprecedented quality of recent colour - magnitude diagrams of resolved stellar populations in nearby galaxies requires state - of - the - art techniques to infer the star formation histories which gave rise to the observed distributions . we have developed a maximum likelihood technique , which coupled to a variational calculus allows us to make a robust , non - parametric reconstruction of the evolution of the star formation rate . a full bayesian analysis is also applied to assess whether the best solutions found are also good fits to the data . applying this new method to wfpc2 observations of five dsph galaxies of the local group , we find a wide variety of star formation histories , with no particular epoch being dominant . in the case of the solar neighbourhood observed by hipparcos we infer , with an unprecedented resolution of 50 myr , its star formation history over the past 3 gyr . the surprising regularity of star formation episodes separated by some 0.5 gyr could be interpreted as the result of interactions with two spiral arms or the galactic bar . these bursts possibly trigger the formation of massive star clusters which slowly dissolve into the galactic field .

nucl-th9512023

c

in this work we have used @xmath36pt to calculate the effective pion - exchange current contribution to the @xmath294 reaction at threshold . as stated repeatedly , our aim here is to carry out a systematic treatment of @xmath143 up to chiral order @xmath171 [ see eq.([eq : calttrunc ] ) ] . however , in order to make contact with the expressions appearing in the literature @xcite , let us consider a very limited number of @xmath295 diagrams . to be specific , we consider a diagram in fig.2(b ) but with the @xmath296 ( @xmath10-wave ) @xmath100 vertex replaced with a @xmath72 ( @xmath4-wave ) vertex . then , instead of eq.([tp1r ] ) , we will obtain @xmath297 , \label{textra}\ ] ] which is the two - body transition operator used in ref.@xcite . thus , we do recover the usual phenomenological parameterization in @xmath36pt , but this is just one of many @xmath298 diagrams . our systematic @xmath299 calculation excludes all @xmath298 diagrams . we have also ignored the exchange current contributions from scalar and vector two - nucleon exchanges . following the @xmath36pt of refs . @xcite the vector meson exchange is largely accounted for via the four - nucleon contact terms illustrated in fig.4(a ) . if we had retained the last two terms of eq.([eq:11 ] ) , the pion - nucleon interaction @xmath300 , eq.([eq : hint1 ] ) , would have had an additional piece @xmath301 the @xmath301 term of fig.4(a ) has a @xmath303 structure , which means it describes @xmath10-wave pion production and therefore does not contribute to the threshold @xmath0 reaction . the @xmath4-wave pion production contact term , also belonging to the type of diagram illustrated in fig.4(a ) , enters as a @xmath304 recoil correction to @xmath301 and therefore is of chiral order @xmath64 = 2 . formally , the chiral order @xmath295 diagrams have no place in the present calculation limited to @xmath171 . however , in view of the great current interest in the possible large contribution of the heavy - meson exchange diagrams , we make a few remarks on the s - wave @xmath295 contact terms depicted in fig.4(a ) . we note that the coordinate representation of this contact term contains @xmath305 . meanwhile , in the threshold @xmath0 reaction the initial two - nucleon relative motion must be in @xmath10-wave ( because of parity ) and so its wavefunction vanishes at @xmath306 . thus , even in a chiral order @xmath295 calculation , the contact term fig.4(a ) corresponding to s - wave pion production will play no role . including meson loops corrections to these contact terms [ an example illustrated in fig.4(b ) ] would smear out the @xmath307-function behavior , allowing them to have a finite contribution to the threshold @xmath0 reaction . this involves , however , diagrams of even higher chiral order than @xmath295 . thus , in order to include the strong effective isoscalar - vector repulsion of the @xmath6-@xmath6 forces ( @xmath308 exchange ) contained in the four - nucleon contact terms of weinberg s @xcite and van kolck s _ et al . _ s @xcite @xmath36pt description , we have to go to chiral order @xmath309 . meanwhile , one may picture the effective heavy mesons " as generated by multi - pion exchange diagrams like those illustrated in fig.5 . these diagrams , which necessarily contain loops , represent a very limited class of @xmath310 diagrams . for example , an important part of the effective scalar exchange between two nucleons involve intermediate @xmath5-@xmath5 @xmath4-wave interaction which requires at least two loop diagrams like fig.5(c ) . thus , if we are to interpret the heavy - meson exchange diagrams of lee and riska@xcite in the framework of nuclear @xmath36pt , we must deal with terms with chiral order @xmath311 , which at present is beyond practical calculations . 1 . using @xmath36pt in a systematic fashion we have shown that the contribution of the pion rescattering term can be much larger than obtained in the traditional phenomenological calculations . this fact itself supports the suggestion of hernandez and oset @xcite that the off - shell @xmath4-wave pion - nucleon scattering should enhance the rescattering contribution significantly . however , the sign of the enhanced rescattering vertex obtained in @xmath36pt is _ opposite _ to that used in ref.@xcite , at least for the _ typical threshold kinematics _ defined in the text . this sign change in the coupling constant @xmath37 leads to a destructive interference between the born and rescattering terms instead of the constructive interference found in ref.@xcite . the significant cancelation between these terms give rise to the very small cross section for the near - threshold @xmath0 reaction calculated in this work . although our particular numerical results were obtained in what we call the _ fixed kinematics approximation _ , these results at least indicate that the large enhancement of @xmath293 obtained in ref.@xcite is open to more detailed examinations . the _ fixed kinematics approximation _ ( which is commonly used in the literature ) should be avoided . there are at least two reasons why this is not a good approximation for this reaction : ( i ) the initial- and final - state interactions play an essential role in the near - threshold @xmath0 reaction ; ( ii ) the theoretical cross section within the framework of the born plus rescattering terms is likely to depend on the delicate cancelation between these two terms . in a momentum space calculation @xcite , we can easily avoid the _ fixed kinematics approximation_. such a calculation will allow us to work with full off - shell kinematics , to incorporate the @xmath36pt form factors in the born term , and to reduce ambiguities in our calculation down to the level of uncertainties in the input parameters in @xmath36pt and the chiral counter terms . 3 . several works @xcite indicate that the two - nucleon scalar ( sigma ) exchange can be very important . we gave in the introduction a simple kinematical argument for its plausibility , and our dynamical calculation ( albeit of semiquantitative nature ) seems to indicate the necessity of the sigma exchange contribution in order to explain the observed cross sections for the threshold @xmath0 reaction . it is of great interest to see to what extent an improved @xmath36pt calculation based on momentum - space representation helps sharpen the conclusion on the necessity of the sigma exchange diagram . such a calculation is now in progress . if it is established that the heavy meson exchange diagrams play an essential role in the threshold @xmath0 reaction , it seems that we must resort to a modified version of @xmath36pt , for a brute force extension of our treatment to @xmath312 seems extremely difficult . an attempt to include vector meson degrees of freedoms explicitly can be found e.g. in ref.@xcite . a purely phenomenological approach as used in @xcite may also be a useful alternative . we are grateful to u. van kolck for the useful communication on ref . one of us ( b .- y . p ) is grateful for the hospitality of the nuclear theory group of the university of south carolina , where the main part of this work was done . this work is supported in part by the national science foundation , grant no . phys-9310124 . in practical calculations we will choose the nucleon rest frame @xmath314 in which case eq.([n ] ) corresponds to the standard non - relativistic reduction of a spinor into upper and lower components and the covariant spin operator of eq.([s ] ) is simply given by @xmath315 . in eq.(11a ) the sum over @xmath316 runs over the possible combinations of @xmath317- and @xmath318- matrices : @xmath319 , @xmath320 , @xmath321 , and @xmath322 . however , because of the fermi statistics ( fierz rearrangement ) , only two of the four coupling constants @xmath323 are independent . we may remark en passant that this standard value " for @xmath14 determined from @xmath127 , is numerically close to the contribution of the crossed born term , which in hff is grouped with the @xmath118 term in @xmath83 as @xmath324 . this remnant of the s - wave pion nucleon crossed born term in hff , appears in the second term in eq.([eq : kappa ] ) , and gives a value of @xmath127 , @xmath325 compatible with @xmath326 @xcite .

the usual theoretical treatments of the near - threshold @xmath0 reaction are based on various phenomenological lagrangians . in this work an important consequence of this energy - momentum dependence is that , for a representative threshold kinematics and within the framework of our semiquantitative calculation , the rescattering term interferes destructively with the born - term in sharp contrast to the constructive interference obtained in the conventional treatment . this destructive interference makes theoretical cross sections for @xmath0 much smaller than the experimental values , a feature that suggests the importance of the heavy - meson exchange contributions to explain the experimental data .

the usual theoretical treatments of the near - threshold @xmath0 reaction are based on various phenomenological lagrangians . in this work we examine the relationship between these approaches and a systematic chiral perturbation method . our chiral perturbation calculation indicates that the pion rescattering term should be significantly enhanced as compared with the traditional phenomenological treatment , and that this term should have substantial energy and momentum dependence . an important consequence of this energy - momentum dependence is that , for a representative threshold kinematics and within the framework of our semiquantitative calculation , the rescattering term interferes destructively with the born - term in sharp contrast to the constructive interference obtained in the conventional treatment . this destructive interference makes theoretical cross sections for @xmath0 much smaller than the experimental values , a feature that suggests the importance of the heavy - meson exchange contributions to explain the experimental data .

1603.09149

c

in this paper a portfolio optimization problem , without any consumption and transaction cost , where stock prices are modelled by multi dimensional geometric jump diffusion market model with semi - markov modulated coefficients is studied . we find the expression of optimal wealth for expected terminal utility method with risk sensitive criterion on finite time horizon . we have studied the existence of classical solution of hjb equation using a probabilistic approach . we have obtained the implicit expression of optimal portfolio . it is important to note that , the control is robust in the sense that the optimal control does not depend on the transition function of the regime . we have also implemented a numerical scheme to see the behaviour of solutions with respect to initial portfolio value , maturity and risk of aversion parameter . the results of the numerical scheme are in agreement with the theory of financial market . the corresponding problem in infinite horizon is needs further investigation . this would require appropriate results on large deviation principle for semi - markov processes which need to be carried out .

this article studies a portfolio optimization problem , where the market consisting of several stocks is modeled by a multi - dimensional jump diffusion process with age - dependent semi - markov modulated coefficients . we also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth , the maturity and the risk of aversion parameter . 1 true cm * key words * portfolio optimization , jump diffusion market model , semi - markov switching , risk sensitive criterion .

this article studies a portfolio optimization problem , where the market consisting of several stocks is modeled by a multi - dimensional jump diffusion process with age - dependent semi - markov modulated coefficients . we study risk sensitive portfolio optimization on the finite time horizon . we study the problem by using a probabilistic approach to establish the existence and uniqueness of the classical solution to the corresponding hamilton - jacobi - bellman ( hjb ) equation . we also implement a numerical scheme to investigate the behavior of solutions for different values of the initial portfolio wealth , the maturity and the risk of aversion parameter . 1 true cm * key words * portfolio optimization , jump diffusion market model , semi - markov switching , risk sensitive criterion .