conewise linear systems non zenoness and observability conewise linear systems are dynamical systems in which the state space is partitioned into a finite number of nonoverlapping polyhedral cones on each of which the dynamics of the system is described by a linear differential equation this class of dynamical systems represents a large number of piecewise linear systems most notably linear complementarity systems with the p property and their generalizations to affine variational systems which have many applications in engineering systems and dynamic optimization the challenges of dealing with this type of hybrid system are due to two major characteristics mode switchings are triggered by state evolution and states are constrained in each mode in this paper we first establish the absence of zeno states in such a system based on this fundamental result we then investigate and relate several state observability notions short time and t time or finite time local global observability for the short time observability notions constructive finitely verifiable algebraic both sufficient and necessary conditions are derived due to their long time mode transitional behavior which is very difficult to predict only partial results are obtained for the t time observable states nevertheless we completely resolve the t time local observability for the bimodal conewise linear system for finite t and provide numerical examples to illustrate the difficulty associated with the long time observability

intrinsic fluctuations and a phase transition in a class of large populations of interacting oscillators a theory of intrinsic fluctuations is developed of a phase ordering parameter for large populations of weakly and uniformly coupled limit cycle oscillators with distributed native frequencies in particular it is shown that the intensity as well as the correlation time of fluctuations exhibit power law divergence at the onset of mutual entrainment with critical exponents which depend on whether the coupling strength approaches the threshold from below or above this peculiar feature is demonstrated by numerical simulations mainly through finite size scaling analyses in the course of exploring its origin we encounter a new concept termed a correlation frequency which provides a natural interpretation of the finite size scaling laws a comment is given on a recent theory by kuramoto and nishikawa to clarify why it contradicts our results

necessary conditions of asymptotic stability for unilateral dynamical systems in this paper we develop a mathematical tool that can be used to state necessary conditions of asymptotic stability of isolated stationary solutions of a class of unilateral dynamical systems more precisely nonlinear evolution variational inequalities are considered instability criteria are also given applications can be found in mechanics or electrical circuits

strongly regular differential variational systems a differential variational system is defined by an ordinary differential equation ode parameterized by an algebraic variable that is required to be a solution of a finite dimensional variational inequality containing the state variable of the system this paper addresses two system theoretic topics for such a nontraditional nonsmooth dynamical system namely non zenoness and local observability of a given state satisfying a blanket strong regularity condition for the former topic which is of contemporary interest in the study of hybrid systems we extend the results in our previous paper where we have studied zeno states and switching times in a linear complementarity system lcs as a special case of the differential variational inequality dvi the lcs consists of a linear time invariant ode and a linear complementarity problem the extension to a nonlinear complementarity system ncs with analytic inputs turns out to be non trivial as we need to use the lie derivatives of analytic functions in order to arrive at an expansion of the solution trajectory near a given state further extension to a differential variational inequality is obtained via its equivalent karush kuhn tucker formulation for the second topic which is classical in system theory we use the non zenoness result and the recent results in a previous paper pertaining to the b differentiability of the solution operator of a nonsmooth ode to obtain a sufficient condition for the short time local observability of a given strongly regular state of an ncs refined sufficient conditions and necessary conditions for local observability of the lcs satisfying the p property are obtained

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

a fixed point iteration approach for multibody dynamics with contact and small friction acceleration force setups for multi rigid body dynamics are known to be inconsistent for some configurations and sufficiently large friction coefficients a painleve paradox this difficulty is circumvented by time stepping methods using impulse velocity approaches which solve complementarity problems with possibly nonconvex solution sets we show that very simple configurations involving two bodies may have a nonconvex solution set for any nonzero value of the friction coefficient we construct two fixed point iteration algorithms that solve convex subproblems and that are guaranteed for sufficiently small friction coefficients to retrieve at a linear convergence rate the unique velocity solution of the nonconvex linear complementarity problem whenever the frictionless configuration can be disassembled in addition we show that one step of one of the iterative algorithms provides an excellent approximation to the velocity solution of the original possibly nonconvex problem if for all contacts we have that either the friction coefficient is small or the slip velocity is small

differential variational inequalities this paper introduces and studies the class of differential variational inequalities dvis in a finite dimensional euclidean space the dvi provides a powerful modeling paradigm for many applied problems in which dynamics inequalities and discontinuities are present examples of such problems include constrained time dependent physical systems with unilateral constraints differential nash games and hybrid engineering systems with variable structures the dvi unifies several mathematical problem classes that include ordinary differential equations odes with smooth and discontinuous right hand sides differential algebraic equations daes dynamic complementarity systems and evolutionary variational inequalities conditions are presented under which the dvi can be converted either locally or globally to an equivalent ode with a lipschitz continuous right hand function for dvis that cannot be so converted we consider their numerical resolution via an euler time stepping procedure which involves the solution of a sequence of finite dimensional variational inequalities borrowing results from differential inclusions dis with upper semicontinuous closed and convex valued multifunctions we establish the convergence of such a procedure for solving initial value dvis we also present a class of dvis for which the theory of dis is not directly applicable and yet similar convergence can be established finally we extend the method to a boundary value dvi and provide conditions for the convergence of the method the results in this paper pertain exclusively to systems with index not exceeding two and which have absolutely continuous solutions

regularized gap functions and error bounds for generalized mixed weak vector quasivariational inequality problems in fuzzy environments abstract in this paper we establish gap functions for a new class of generalized mixed weak vector quasivariational inequality problems in fuzzy environments in short mqvipf these functions are constructed through terms of regularized gap functions using the method of nonlinear scalarization functions moreover error bounds are provided for mqvipf via regularized gap functions under suitable assumptions the main results obtained in this paper improve and extend some corresponding known results some examples are given to illustrate our results

on the regularization of zeno hybrid automata fundamental properties of hybrid automata such as existence and uniqueness of executions are studied particular attention is devoted to zeno hybrid automata which are hybrid automata that take infinitely many discrete transitions in finite time it is shown that regularization techniques can be used to extend the zeno executions of these automata to times beyond the zeno time different types of regularization may however lead to different extensions a water tank control problem and a bouncing ball system are used to illustrate the results

on mean field fluctuations in globally coupled logistic type maps abstract we consider mean field fluctuations in globally coupled map x n 1 i f x n i 1 n j 1 n x n j when the local map f has a flat power law top e g f x 1 a x with 1 it is shown that in the thermodynamic limit n the amplitude of mean field fluctuations is o 1 1 for 1 which is in good agreement with numerical calculations we also demonstrate the relation between this problem and behaviour of averages as functions of the parameter a in 1d maps for the latter we give both theoretical grounds and experimental evidence that the mean deviation of an average value behaves as a power of the deviation of the parameter e g x a a x a d a a 1

on a new class of differential variational inequalities and a stability result this paper addresses a new class of differential variational inequalities that have recently been introduced and investigated in finite dimensions as a new modeling paradigm of variational analysis to treat many applied problems in engineering operations research and physical sciences this new subclass of general differential inclusions unifies ordinary differential equations with possibly discontinuous right hand sides differential algebraic systems with constraints dynamic complementarity systems and evolutionary variational systems the purpose of this paper is two fold firstly we show that these differential variational inequalities when considering slow solutions and the more general level of a hilbert space contain projected dynamical systems another recent subclass of general differential inclusions this relation follows from a precise geometric description of the directional derivative of the metric projection in hilbert space which is based on the notion of the quasi relative interior secondly we are concerned with stability of the solution set to this class of differential variational inequalities here we present a novel upper set convergence result with respect to perturbations in the data including perturbations of the associated set valued maps and the constraint set here we impose weak convergence assumptions on the perturbed set valued maps use the monotonicity method of browder and minty and employ mosco convergence as set convergence also as a consequence we obtain a stability result for linear complementarity systems

on the optimality of the discrete karhunen loeve expansion a short proof of the optimality of the discrete karhunen loeve expansion as the best linear approximation in the quadratic mean is presented

on the exceedance point process for a stationary sequence it is known that the exceedance points of a high level by a stationary sequence are asymptotically poisson as the level increases under appropriate long range and local dependence conditions when the local dependence conditions are relaxed clustering of exceedances may occur based on poisson positions for the clusters in this paper a detailed analysis of the exceedance point process is given and shows that under wide conditions any limiting point process for exceedances is necessarily compound poisson more generally the possible random measure limits for normalized exceedance point processes are characterized sufficient conditions are also given for the existence of a point process limit the limiting distributions of extreme order statistics are derived as corollaries

stochastically stable globally coupled maps with bistable thermodynamic limit we study systems of globally coupled interval maps where the identical individual maps have two expanding fractional linear onto branches and where the coupling is introduced via a parameter common to all individual maps that depends in an analytic way on the mean field of the system we show 1 for the range of coupling parameters we consider finite size coupled systems always have a unique invariant probability density which is strictly positive and analytic and all finite size systems exhibit exponential decay of correlations 2 for the same range of parameters the self consistent perron frobenius operator which captures essential aspects of the corresponding infinite size system arising as the limit of the above when the system size tends to infinity undergoes a supercritical pitchfork bifurcation from a unique stable equilibrium to the coexistence of two stable and one unstable equilibrium

convergence of regularized time stepping methods for differential variational inequalities this paper provides convergence analysis of regularized time stepping methods for the differential variational inequality dvi which consists of a system of ordinary differential equations and a parametric variational inequality pvi as the constraint the pvi often has multiple solutions at each step of a time stepping method and it is hard to choose an appropriate solution for guaranteeing the convergence in l han a tiwari m k camlibel and j s pang siam j numer anal 47 2009 pp 3768 3796 the authors proposed to use least norm solutions of parametric linear complementarity problems at each step of the time stepping method for the monotone linear complementarity system and showed the novelty and advantages of the use of the least norm solutions however in numerical implementation when the pvi is not monotone and its solution set is not convex finding a least norm solution is difficult this paper extends the tikhonov regularization approximation to the p 0 function dvi whi

existence results of partial differential mixed variational inequalities without lipschitz continuity abstract the aim of this paper is to use order theoretic approaches to investigate a class of partial differential mixed variational inequalities pdmvis for short which are receiving much attention recently to this end the order preservation properties of proximity mapping are explored applying these order preservation properties and combining with the knaster tarski fixed point theorem we prove the existence of solutions and the order preservation properties of solution mapping for mixed variational inequalities on hilbert lattices relying on the above obtained results as well as some order theoretic techniques the existence of mild solutions to pdmvi is established in contrast to many existing results on pdmvis the order theoretic approaches are new and the results obtained in this paper do not require the lipschitz continuity of the mapping associated to nonlinear evolution equation

solution dependence on initial conditions in differential variational inequalities in the first part of this paper we establish several sensitivity results of the solution x t to the ordinary differential equation ode initial value problem ivp dx dt f x x 0 as a function of the initial value for a nondifferentiable f x specifically we show that for xi t equiv x t xi 0 0 leq t leq t a if f is b differentiable on xi t then so is the solution operator x t at 0 b if f is semismooth on xi t then so is x t at 0 c if f has a linear newton approximation on xi t then so does x t at 0 moreover the linear newton approximation of the solution operator can be obtained from the solution of a linear differential inclusion in the second part of the paper we apply these ode sensitivity results to a differential variational inequality dvi and discuss a the existence uniqueness and lipschitz dependence of solutions to subclasses of the dvi subject to boundary conditions via an implicit function theorem for semismooth equations and b the convergence of a nonsmooth shooting method for numerically computing such boundary value solutions

estimating the probability of a rare event let x 1 y 1 x 2 y 2 x n y n be a random sample from a bivariate distribution function f which is in the domain of attraction of a bivariate extreme value distribution function g a subset c of r 2 is given which contains none of the observations we shall give an asymptotic confidence interval for pr x i y i c under certain conditions

solving cone constrained convex programs by differential inclusions a differential inclusion is designed for solving cone constrained convex programs the method is of subgradient projection type it involves projection penalties and lagrangian relaxation nonsmooth data can be accommodated a novelty is that multipliers converge monotonically upwards to equilibrium levels an application to stochastic programming is considered

remarks on the mean field dynamics of networks of chaotic elements abstract fluctuations of the mean field of a globally coupled dynamical systems are discussed the origin of hidden coherence is related with the instability of the fixed point solution of the self consistent perron frobenius equation collective dynamics in globally coupled tent maps are re examined both with the help of direct simulation and the perron frobenius equation collective chaos in a single band state and bifurcation against initial conditions in a two band state are clarified with the return maps of the mean field lyapunov spectra and also the newly introduced lyapunov exponent for the perron frobenius equation future problems on the collective dynamics are discussed

globally coupled circle maps abstract a network of circle maps is investigated successive transitions are found among coherent ordered partially ordered po and turbulent phases in the ordered phase two cluster attractors with similarity have a large basin volume which are reduced to a unique circle map through a scaling transformation with two parameters the po phase is characterized by the increase of partition complexity in the phase chaotic itinerancy is observed whose dynamics consists of quasistationary high dimensional chaotic motion low dimensional attractor ruins and switching among them dependence of the diffusion constant on the size and the nonlinearity clearly deviates from that by a random phase approximation suggesting remaining correlation among elements even in the turbulent phase

constructive approximations to densities invariant under nonexpanding transformations let 0 1 0 1 be a piecewise monotonic nonexpanding map which has an invariant densityg and is topologically conjugate to a piecewise monotonic expanding map where the conjugacy is absolutely continuous an effective computable method is presented for approximatingg

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

ergodic properties of invariant measures for piecewise monotonic transformations during the last decade a lot of research has been done on onedimensional dynamics different kinds of invariant measures for certain classes of piecewise monotonic transformations have been considered in most of these cases the perron frobenius operator plays an important role in this paper we try to unify these different examples which are discussed in detail below first we give a discription of the results proved in this paper

a stability result for differential inclusions in banach spaces on etablit un resultat de stabilite pour les inclusions differentielles definies sur un espace de banach separable

evolutionary problems driven by variational inequalities abstract in this paper we introduce the differential system obtained by mixing an evolution equation and a variational inequality eevi for short first by using kkm theorem and monotonicity arguments we prove the superpositional measurability and upper semicontinuity for the solution set of a general variational inequality then we establish that the solution set of eevi is nonempty and compact our approach is based on the theory of semigroups filippov implicit function lemma and fixed point theory for set valued mappings

non zenoness of a class of differential quasi variational inequalities the zeno phenomenon of a switched dynamical system refers to the infinite number of mode switches in finite time the absence of this phenomenon is crucial to the numerical simulation of such a system by time stepping methods and to the understanding of the behavior of the system trajectory extending a previous result for a strongly regular differential variational inequality this paper establishes that a certain class of non strongly regular differential variational inequalities is devoid of the zeno phenomenon the proof involves many supplemental results that are of independent interest specialized to a frictional contact problem with local compliance and polygonal friction laws this non zenoness result is of fundamental significance and the first of its kind

on the equivalence between complementarity systems projected systems and differential inclusions in this note we prove the equivalence under appropriate conditions between several dynamical formalisms projected dynamical systems two types of differential inclusions and a class of complementarity dynamical systems each of these dynamical systems can also be considered as a hybrid dynamical system this work both generalizes previous results and sheds some new light on the relationship between known formalisms besides it exclusively uses tools from convex analysis

optimization based simulation of nonsmooth rigid multibody dynamics we present a time stepping method to simulate rigid multibody dynamics with inelastic collision contact and friction the method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program we prove that a solution sequence of the method converges to the solution of a measure differential inclusion we present numerical results for a few examples and we illustrate the difference between the results from our scheme and previous linear complementarity based time stepping schemes

models and inference for uncertainty in extremal dependence conventionally modelling of multivariate extremes has been based on the class of multivariate extreme value distributions more recently other classes have been developed allowing for the possibility that whilst dependence is observed at finite levels the limit distribution is independent a number of articles have shown this development to be important for accurate estimation of the extremal properties both of theoretical processes and observed datasets it has also been shown that so far as dependence is concerned the choice between modelling with either asymptotically dependent or asymptotically independent distributions can be far more influential than model choice within either of these two classes in this paper we explore the issue of modelling across both classes examining in particular the effect of uncertainty caused by lack of knowledge about the status of asymptotic dependence this is achieved by new multivariate models whose parameter spaces are such that asymptotic dependence occurs on a boundary standard techniques in bayesian inference implemented through markov chain monte carlo enable inferences to be drawn that assign posterior probability mass to the boundary region the techniques are illustrated on a set of oceanographic data for which previous analyses have shown that it is difficult to resolve the question of asymptotic dependence status which is however important in model extrapolation

solvability of parabolic variational hemivariational inequalities involving space fractional laplacian abstract the paper is devoted to investigate a new kind of variational hemivariational inequality of parabolic type driven by a generalized space fractional laplace operator and two multivalued terms which are expressed by the clarke generalized gradient and convex subgradient respectively an existence theorem of weak solutions to the problem is established by applying a surjectivity theorem for the sum of operators combined with results from nonsmooth analysis

piecewise smoothness local invertibility and parametric analysis of normal maps this paper is concerned with properties of the euclidean projection map onto a convex set defined by finitely many smooth convex inequalities and affine equalities under a constant rank constraint qualification we show that the projection map is piecewise smooth pc1 hence bouligand differentiable or directionally differentiable and a relatively simple formula is given for the b derivative these properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps using a new characterization of invertibility of a pc1 function in terms of its b derivative an extension of the implicit function theorem which does not require local uniqueness is also presented degree theory plays a major role in the analysis of both the locally unique case and its extension

differential mixed variational inequalities in finite dimensional spaces in this paper a differential vector variational inequality is introduced and studied in finite dimensional euclidean spaces the existence of a caratheodory weak solution for the differential vector variational inequality is presented under some suitable conditions furthermore the upper semicontinuity and the lower semicontinuity of the solution sets for the differential variational inequality are established when both the mapping and the constraint set are perturbed by two different parameters

on parametric evolution inclusions of the subdifferential type with applications to optimal control problems in this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear infinite dimensional optimal control problems the parameter appears in all the data of the problem including the subdifferential operator first we establish several continuity results for the solution multifunction of the subdifferential inclusion then we study how these results can be used to examine the sensitivity properties variational stability of certain broad classes of nonlinear infinite dimensional optimal control problems some examples are worked out in detail illustrating the applicability of our work these include obstacle problems with time varying obstacles optimal control of distributed parameter systems and differential variational inequalities

differential variational inequality approach to dynamic games with shared constraints the dynamic nash equilibrium problem with shared constraints nepsc involves a dynamic decision process with multiple players where not only the players cost functionals but also their admissible control sets depend on the rivals decision variables through shared constraints for a class of the dynamic nepsc we propose a differential variational inequality formulation using this formulation we show the existence of solutions of the dynamic nepsc and develop a regularized smoothing method to find a solution of it we prove that the regularized smoothing method converges to the least norm solution of the differential variational inequality which is a solution of the dynamic nepsc as the regularization parameter lambda and smoothing parameter mu go to zero with the order mu o lambda o numerical examples are given to illustrate the existence and convergence results

a class of generalized mixed variational hemivariational inequalities i existence and uniqueness results abstract we investigate a generalized lagrange multiplier system in a banach space called a mixed variational hemivariational inequality mvhvi for short which contains a hemivariational inequality and a variational inequality first we employ the minty technique and a monotonicity argument to establish an equivalence theorem which provides three different equivalent formulations of the inequality problem without compactness for one of operators in the problem a general existence theorem for mvhvi is proved by using the fan knaster kuratowski mazurkiewicz principle combined with methods of nonsmooth analysis furthermore we demonstrate several crucial properties of the solution set to mvhvi which include boundedness convexity weak closedness and continuity finally a uniqueness result with respect to the first component of the solution for the inequality problem is proved by using the ladyzhenskaya babuska brezzi lbb condition all results are obtained in a general functional framework in reflexive banach spaces

positive solutions to nonlinear nonhomogeneous inclusion problems with dependence on the gradient abstract the goal of the paper is to study a generalized elliptic inclusion problem driven by a nonhomogeneous partial differential operator with the dirichlet boundary condition and a convection multivalued term an existence theorem for positive solutions of the problem is established by applying the method of subsolution supersolution together with truncation and comparison techniques

on two parameter global bifurcation of periodic solutions to a class of differential variational inequalities abstract in this paper by using the method of integral guiding functions a multiparameter global bifurcation theorem for differential inclusions with the periodic condition is proved it is shown how the abstract result can be applied to the study of the two parameter global bifurcation of periodic solutions for a class of differential variational inequalities

large deviations from the thermodynamic limit in globally coupled maps abstract systems of a large number n of globally coupled maps have become popular as a relatively simple prototype of high dimensional dynamics showing many interesting and typical phenomena like synchronisation cluster formation and multistability and having potential applications in systems like josephson junction arrays or in biophysical models while much progress has been made in the explanation of the macroscopic behaviour of such systems in the limit n there is still need for a sound theory about the asymptotic behaviour of finite n systems as n approaches infinity this article introduces a method by which it is possible to obtain asymptotic estimates for finite size effects that show up as long term deviations from the thermodynamic limit behaviour this method works for systems of globally coupled noisy maps and is based upon the concept of quasipotentials originally developed by freidlin wentzell and others for describing the influence of small random perturbations on the long term behaviour of dynamical systems the problems of explicitly computing quasipotentials in the present context and potential approximation schemes are discussed all the concepts described in this article are illustrated with a simple example

on the bifurcation structure of the mean field fluctuation in the globally coupled tent map systems abstract a theoretical analysis on the behavior of the globally coupled tent map systems based on the kinetics of the mean field value is presented we investigated the nature of the mean field fluctuation in large system size limit and uncovered the existence of a complicated bifurcation structure that leads the appearance of collective motion with the increase of the coupling strength the way to the appearance of the collective motion sensitively depends on the gradient a of individual tent maps for a belonging to a set which is dense in 2 2 the collective motion appears when the coupling strength exceeds a certain threshold value while for a belonging to another dense set in 2 2 any non zero coupling will induce the collective motion the dependence of the amplitude of mean field fluctuation on the coupling strength is also obtained as a function of the parameter a and the coupling strength

partial differential variational inequalities involving nonlocal boundary conditions in banach spaces abstract in this paper we firstly introduce a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions which is called partial differential variational inequality pdvi for short then we show that the solution set of the mixed variational inequality involved in problem pdvi is nonempty bounded closed and convex moreover the upper semicontinuity and measurability properties for set valued mapping u 0 t e 2 c b v e 1 see 3 7 below are also established finally several existence results for pdvi are obtained by using a fixed point theorem for condensing set valued operators and theory of measure of noncompactness

existence result for differential variational inequality with relaxing the convexity condition abstract in this paper a class of differential variational inequalities are studied and a new approach is introduced to relax the convexity condition firstly an existence theorem of caratheodory weak solution for the differential variational inequalities is established secondly an algorithm for solving the problem is developed and the convergence analysis for the algorithm is given finally a numerical example is reported to illustrate the proposed algorithm

mean field fluctuation of a network of chaotic elements remaining fluctuation and correlation in the large size limit fluctuation of the mean field is studied for a network of chaotic elements with the use of globally coupled maps as the size n is increased the variance of the mean field decreases up to a crossover size nc but then stays constant where the remaining variance is roughly proportional to 1nc the distribution of the mean field approaches a gaussian form up to nc but keeps some deviation for n nc the breakdown of the law of large numbers implies some hidden coherence among elements confirmed by finite mutual information and lyapunov spectra the breakdown is also supported by the instability of the self consistent solution for the perron frobenius operator the anomalous effect of additional noise to our system is also reported results from other globally coupled maps suggest that the law of large numbers is generally broken in a turbulent phase with local stretching and contraction but is satisfied for a map with stretching only

hp fem convergence for unilateral contact problems with tresca friction in plane linear elastostatics abstract this paper is concerned with the convergence of the h p version of the finite element method h p fem for some nonsmooth unilateral problems in linear elastostatics we consider in particular the deformation of an elastic body unilaterally supported by a rigid foundation admitting tresca friction given friction along the rigid foundation solely subjected to body forces and surface tractions without being fixed along some part of its boundary for the discretization of the unilateral constraint and the nonsmooth friction functional we employ gauss lobatto quadrature we show convergence of the h p fem approximations for mechanically definite problems without imposing any regularity assumption moreover we treat the coercive case when the body is fixed along some part of the boundary based on an abstract cea falk estimate and operator interpolation arguments we establish an a priori error estimate in the energy norm under a reasonable regularity assumption

asymptotic periodicity of the iterates of markov operators on dit que p l 1 l 1 est un operateur de markov si 1 pf 0 pour f 0 et 2 pf f si f 0 on montre que tout operateur de markov p a une certaine decomposition spectrale si pout tout f l 1 avec f 0 et f 1 p n f 7b f quand n ou 7b f est un sous ensemble fortement compact de l 1

linear complementarity systems we introduce a new class of dynamical systems called linear complementarity systems the time evolution of these systems consists of a series of continuous phases separated by events which cause a change in dynamics and possibly a jump in the state vector the occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming the framework we describe is suitable for certain situations in which both differential equations and inequalities play a role for instance in mechanics electrical networks piecewise linear systems and dynamic optimization we present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions

linear complementarity systems zeno states a linear complementarity system lcs is a hybrid dynamical system defined by a linear time invariant ordinary differential equation coupled with a finite dimensional linear complementarity problem lcp the present paper is the first of several papers whose goal is to study some fundamental issues associated with an lcs specifically this paper addresses the issue of zeno states and the related issue of finite number of mode switches in such a system the cornerstone of our study is an expansion of a solution trajectory to the lcs near a given state in terms of an observability degree of the state on the basis of this expansion and an inductive argument we establish that an lcs satisfying the p property has no strongly zeno states we next extend the analysis for such an lcs to a broader class of problems and provide sufficient conditions for a given state to be weakly non zeno while related mode switch results have been proved by brunovsky and sussmann for more general hybrid systems our analysis exploits the special structure of the lcs and yields new results for the latter that are of independent interest and complement those by these two and other authors

convergence of a time stepping scheme for rigid body dynamics and resolution of painleve s problem this paper gives convergence theory for a new implicit time stepping scheme for general rigid body dynamics with coulomb friction and purely inelastic collisions and shocks an important consequence of this work is the proof of existence of solutions of rigid body problems which include the famous counterexamples of painleve the mathematical basis for this work is the formulation of the rigid body problem in terms of measure differential inclusions of moreau and monteiro marques the implicit time stepping method is based on complementarity problems and is essentially a particular case of the algorithm described in anitescu potra 2 which in turn is based on the formulation in stewart trinkle 47

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

on mean field fluctuations in globally coupled maps abstract we consider the mean field fluctuations in the globally coupled map x n 1 i f x n i 1 n j 1 n x n j with an expanding piecewise linear local map f in the thermodynamic limit n using the reduced master equation self consistent frobenius perron operator it is shown that correlations between the elements are absent in simultaneous ensembles and only arise in time series for small the equilibrium state with constant mean field is proved to be unstable so the mean field fluctuates corresponding to a complex attractor of the reduced master equation it is chaotic and its lyapunov exponent is estimated to be 2 the order of magnitude of stationary fluctuations is estimated as exp o 2 the theoretical approach used enables us to develop high precision numerical methods able to detect such tiny fluctuations

second order differential variational inequalities involving anti periodic boundary value conditions abstract this paper deals with a new class of second order nonlinear differential variational inequalities firstly we study the properties of a solution set for a variational inequality by using the kkm technique and a monotonicity property then we prove the existence of solutions to a second order nonlinear differential variational inequality with anti periodic boundary value conditions not assuming the lipschitz continuity of the nonlinear term our approaches which are essentially different from previous research methods in differential variational inequalities are based on the topological degree theory and the filippov implicit function lemma

convergence of time stepping method for initial and boundary value frictional compliant contact problems beginning with a proof of the existence of a discrete time trajectory this paper establishes the convergence of a time stepping method for solving continuous time boundary value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions our investigation complements the analysis of the initial value rigid body model with one frictional contact encountering inelastic impacts by stewart arch ration mech anal 145 1998 pp 215 260 and the recent analysis by anitescu optimization based simulation for nonsmooth rigid multibody dynamics argonne national laboratory argonne il 2004 using the framework of measure differential inclusions in contrast to the measure theoretic approach of these authors we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts applicable to both initial and affine boundary value problems our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small

bounds on the number of switchings for trajectories of piecewise analytic vector fields abstract we study the trajectories of systems x x x where x is a continuous extendably piecewise analytic vector field i e a continuous vector field x such that the domain of admits a locally finite partition i into sets such that for each a i there is a vector field xa which is analytic on a neighborhood of the closure of a and whose restriction to a coincides with that of x we prove that the trajectories are piecewise analytic with a priori bounds on the number of switchings for all trajectories that stay in a fixed compact set and whose duration does not exceed a fixed number t this result implies the existence of a regular synthesis for optimal control problems with a strictly convex lagrangian and a linear dynamics with polyhedral constraints on the controls

time stepping for three dimensional rigid body dynamics traditional methods for simulating rigid body dynamics involves determining the current contact arrangement e g each contact is either a rolling or sliding contact the development of this approach is most clearly seen in the work of haug et al mech machine theory 21 1986 401 425 and pfeiffer and glocker multibody dynamics with unilateral contacts wiley 1996 however there has been a controversy about the status of rigid body dynamics as a theory due to simple problems in the area which do not appear to have solutions the most famous if not the earliest is due to paul painleve c r acad sci paris 121 1895 112 115 recently a number of time stepping methods have been developed to overcome these difficulties these time stepping methods use integrals of the forces over time steps rather than the actual forces this allows impulsive forces without the need for a separate formulation or special procedures to cover this case the newest of these methods are developed in terms of complementarity problems the complementarity problems that define the time stepping procedure are solvable unlike previous methods for simulating rigid body dynamics with friction proof of the existence of solutions to the continuous problem can be shown in the sense of measure differential inclusions in terms of these methods in this paper a number of these variants will be discussed and their essential properties proven