rigidity for anosov actions of higher rank lattices this is the simplest example of a large class of analytic standard actions of lattices in semisimple lie groups on locally homogeneous spaces a basic problem is to understand the differentiable actions near to such a standard action in terms of their geometry and dynamics cf 13 50 51 a cr action so if x x x of a group f on a compact manifold x is said to be anosov if there exists at least one element yh e f such that p yh is an anosov diffeomorphism of x we begin in this paper to study the anosov differentiable actions of lattices including many standard algebraic examples and especially to study their stability properties our main theme is that either the cr rigidity or the cr deformation rigidity of an anosov action for 1 r cr or even for the real analytic case can be shown just by studying the behavior of the periodic orbits for the action there are two notions of structural stability that appear in this paper rigidity and deformation rigidity a cl perturbation of a cr action so is simply another cr action spl such that for a finite set of generators 81 ad of f the cr diffeomorphisms p 8i and pl 8i are cl close for all i an action so is said to be cr rigid or topologically rigid if r 0 if every sufficiently small c perturbation of so is cr conjugate to so for 0 r oo or r w in the case of real analytic actions a cl deformation of an action so is a continuous path of cr actions pt defined for some 0 t e with spo sd an action sd is said to be cr deform

stationary and dynamical properties of a zero range process on scale free networks we study the condensation phenomenon in a zero range process on scale free networks we show that the stationary state property depends only on the degree distribution of underlying networks the model displays a stationary state phase transition between a condensed phase and an uncondensed phase and the phase diagram is obtained analytically as for the dynamical property we find that the relaxation dynamics depends on the global structure of underlying networks the relaxation time follows the power law ensuremath tau ensuremath sim l z with the network size l in the condensed phase the dynamic exponent z is found to take a different value depending on whether underlying networks have a tree structure or not

existence theorem for a minimum problem with free discontinuity set we study the variational problem where is an open set in n n 2g l q l 1 q o andh n 1 is the n 1 dimensional hausdorff measure

finite size effects in dynamics of zero range processes the finite size effects prominent in zero range processes exhibiting a condensation transition are studied by using continuous time monte carlo simulations we observe that well above the thermodynamic critical point both static and dynamic properties display fluidlike behavior up to a density c l which is the finite size counterpart of the critical density c c l we determine this density from the crossover behavior of the average size of the largest cluster we then show that several dynamical characteristics undergo a qualitative change at this density in particular the size distribution of the largest cluster at the moment of relocation the persistence properties of the largest cluster and the correlations in its motion are studied

size of the largest cluster under zero range invariant measures we study the finite zero range process with occupancy dependent rate function g under the invariant measure which can be written explicitly in terms of g particles are distributed over sites and we regard all particles at a fixed site as a cluster in the density one case that is equal numbers of particles and sites we determine asymptotically the size of the largest cluster as the number of particles tends to infinity and determine its dependence on the rate function

a model for the quasi static growth of brittle fractures existence and approximation results we give a precise mathematical formulation of a variational model for the irreversible quasi static evolution of brittle fractures proposed by g a francfort and j j marigo and based on griffith s theory of crack growth in the two dimensional case we prove an existence result for the quasi static evolution and show that the total energy is an absolutely continuous function of time although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities this existence result is proved by a time discretization process where at each step a global energy minimization is performed with the constraint that the new crack contains all cracks formed at the previous time steps this procedure provides an effective way to approximate the continuous time evolution

dynamics of the condensate in zero range processes for stochastic processes leading to condensation the condensate once it is formed performs an ergodic stationary state motion over the system we analyse this motion and especially its characteristic time for zero range processes the characteristic time is found to grow with the system size much faster than the diffusive time scale but not exponentially fast this holds both in the mean field geometry and on finite dimensional lattices in the generic situation where the critical mass distribution follows a power law the characteristic time grows as a power of the system size

lower semicontinuity properties of functionals with free discontinuities this paper is concerned with functionals with free discontinuities considered as depending on the set variable a splitting operation divides the sets in which the functional takes low values in the union of a noise part and a macroscopic part then we show lower semicontinuity results on the limit of the macroscopic parts by hausdorff distance along minimizing sequences

condensation in a zero range process on weighted scale free networks we study the condensation phenomenon in a zero range process on weighted scale free networks in order to show how the weighted transport influences the particle condensation instead of the approach of grand canonical ensemble which is generally used in a zero range process we introduce an alternate approach of the mean field equations to study the dynamics of particle transport we find that the condensation on the scale free network is easier to occur in the case of weighted transport than in the case of weight free networks in the weighted transport especially a dynamical condensation is even possible for the case of no interaction among particles which is impossible in the case of weight free networks

existence and convergence for quasi static evolution in brittle fracture this paper investigates the mathematical well posedness of the variational model of quasi static growth for a brittle crack proposed by francfort and marigo in 15 the starting point is a time discretized version of that evolution which results in a sequence of minimization problems of mumford and shah type functionals the natural weak setting is that of special functions of bounded variation and the main difficulty in showing existence of the time continuous quasi static growth is to pass to the limit as the time discretization step tends to 0 this is performed with the help of a jump transfer theorem which permits under weak convergence assumptions for a sequence un of sbv functions to its bv limit u to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence un in particular it is shown that the notion of minimizer of a mumford and shah type functional for its own jump set is stable under weak convergence assumptions furthermore our analysis justifies numerical methods used for computing the time continuous quasi static evolution 2003 wiley periodicals inc

zero range processes with multiple condensates statics and dynamics the steady state distributions and dynamical behaviour of zero range processes with hopping rates which are non monotonic functions of the site occupation are studied we consider two classes of non monotonic hopping rates the first results in a condensed phase containing a large but subextensive number of mesocondensates each containing a subextensive number of particles the second results in a condensed phase containing a finite number of extensive condensates we study the scaling behaviour of the peak in the distribution function corresponding to the condensates in both cases in studying the dynamics of the condensate we identify two timescales one for creation the other for evaporation of condensates at a given site the scaling behaviour of these timescales is studied within the arrhenius law approach and by numerical simulations

infinitesimal rigidity for the action of sl n ℤ on n let r sl n z or any subgroup of finite index then the action of r on tn by automorphisms is infinitesimally rigid for n 7 i e the cohomology h i r vec tn 0 where vec t n denotes the module of c vector fields on t

smooth classification of cartan actions of higher rank semisimple lie groups and their lattices let g be a connected semisimple lie group without compact factors whose real rank is at least 2 and let g be an irreducible lattice we provide a c classification for volume preserving cartan actions of an d g also if g has real rank at least 3 we provide a c classification for volume preserving multiplicity free trellised anosov actions on compact manifolds

on livsic s theorem superrigidity and anosov actions of semisimple lie groups we prove a generalization of livsic s theorem on the vanishing of the cohomology of certain types of dynamical systems as a consequence we strengthen a result due to zimmer concerning algebraic hulls of anosov actions of semisimple lie groups combining this with topological superrigidity we find a holder geometric structure for multiplicity free anosov actions

a density result in two dimensional linearized elasticity and applications we show that in a two dimensional bounded open set whose complement has a finite number of connected components the vector fields u h 1 2 are dense in the space of fields whose symmetrized gradient e u is in l 2 4 this allows us to show the continuity of some linearized elasticity problems with respect to variations of the set with applications to shape optimization or the study of crack evolution

factorized steady states in mass transport models on an arbitrary graph we study a general mass transport model on an arbitrary graph consisting of l nodes each carrying a continuous mass the graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass chosen from a site dependent distribution is transported between the nodes at each time step the dynamics conserves the total mass and the system eventually reaches a steady state this general model includes as special cases various previously studied models such as the zero range process and the asymmetric random average process we derive a general condition on the stochastic mass transport rules valid for arbitrary graph and for both parallel and random sequential dynamics that is sufficient to guarantee that the steady state is factorizable we demonstrate how this condition can be achieved in several examples we show that our generalized result contains as a special case the recent results derived by greenblatt and lebowitz for d dimensional hypercubic lattices with random sequential dynamics

on a regularity problem occurring in connection with anosov diffeomorphisms let be ac manifold and s and u be two holder foliations transverse and with uniformlyc leaves if a functionf is uniformlyc along the leaves of the two foliations then it isc on the proof is elementary