synchronization in lattices of coupled oscillators abstract we consider coupled nonlinear oscillators with external periodic forces and the dirichlet boundary conditions we prove that synchronization occurs provided that the coupling is dissipative and the coupling coefficients are sufficiently large the synchronization here is of an obvious type the size of an attractor is comparable to the difference of the subsystems

box constrained quadratic programming with proportioning and projections two new closely related concepts are introduced that depend on a positive constant gamma an iteration is proportional if the norm of violation of the kuhn tucker conditions at active variables does not excessively exceed the norm of the part of the gradient that corresponds to free variables while a progressive direction determines a descent direction that enables the released variables to move far enough from the boundary in a step called proportioning an algorithm that uses the conjugate gradient method to explore the face of the region defined by the current iterate until a disproportional iteration is generated is proposed it then changes the face by means of the progressive direction it is proved that for strictly convex problems the proportioning is a spacer iteration so that the algorithm converges to the solution if the solution is nondegenerate then the algorithm finds the solution in a finite number of steps moreover a simple lower bound on gamma is given to ensure finite termination even for problems with degenerate solutions the theory covers a class of algorithms allowing many constraints to be added or dropped at a time and accepting approximate solutions of auxiliary problems preliminary numerical results are promising

stabilized interface methods for mechanical joints physics based models and variationally consistent embedding abstract this paper presents the application of a new method for interfacial modeling utilizing a merger of continuous galerkin and discontinuous galerkin concepts to simulate the behavior of mechanical joints the interfacial flux terms arising naturally from the discontinuous galerkin treatment provide a mechanism to embed friction models in a variationally consistent fashion due to the unbiased implementation of the interface facilitated by avoiding the master slave concept the deformation of the two interacting surfaces conforms to the local material and geometric attributes of the surfaces this results in a better preservation of physics in interface mechanics additionally the method is incorporated into a variational multiscale framework that comes equipped with a built in error estimation module providing numerical estimation of convergence and distinguishing discretization errors from modeling errors a series of quasi static numerical simulations of a lap joint under fretting conditions are conducted to compare the performance of two friction models i classical coulomb friction model and ii physics based multiscale model hysteresis study of a three dimensional double bolted lap joint for the two friction models is also presented and the computed results are shown to be consistent between conforming and nonconforming meshes

quasistatic normal compliance contact problem of visco elastic bodies with coulomb friction implemented by qp and sgbem the quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with coulomb friction at small strains in kelvin voigt rheology is considered the discretization is made by a semi implicit formula in time and the symmetric galerkin boundary element method sgbem in space assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient the obtained recursive minimization problem formulated only on the contact boundary has a nonsmooth cost function if the normal compliance responds linearly and the 2d problems are considered then the cost function is piecewise quadratic which after a certain transformation gets the quadratic programming qp structure however it would lead to second order cone programming in 3d problems finally several computational tests are presented and analysed with an additional discussion on numerical stability and convergence of the involved approximated poincare steklov operators

synchronization conditions and desynchronizing patterns in coupled limit cycle and chaotic systems many coupling schemes for both limit cycle and chaotic systems involve adding linear combinations of dynamical variables from various oscillators in an array of identical oscillators to each oscillator node of the array examples of such couplings are nearest neighbor diffusive coupling all to all coupling star coupling and random linear couplings we show that for a given oscillator type and a given choice of oscillator variables to use in the coupling arrangement the stability of each linear coupling scheme can be calculated from the stability of any other for symmetric coupling schemes in particular when there are desynchronization bifurcations our approach reveals interesting patterns and relations between desynchronous modes including the situation in which for some systems there is a limit on the number of oscillators that can be coupled and still retain synchronous chaotic behavior

synchronous chaos in coupled oscillator systems we investigate the synchronization of chaotic oscillations in coupled oscillator systems both theoretically and in analog electronic circuits particular attention is paid to deriving and testing general conditions for the stability of synchronous chaotic behavior in cases where the coupled oscillator array possesses a shift invariant symmetry these cases include the well studied cases of nearest neighbor diffusive coupling and all to all or global coupling an approximate criterion is developed to predict the stability of synchronous chaotic oscillations in the strong coupling limit when the oscillators are coupled through a single coordinate scalar coupling this stability criterion is illustrated numerically in a set of coupled r ossler like oscillators synchronization experiments with coupled r ossler like oscillator circuits are also carried out to demonstrate the applicability of the theory to real systems

robust control of markov decision processes with uncertain transition matrices optimal solutions to markov decision problems may be very sensitive with respect to the state transition probabilities in many practical problems the estimation of these probabilities is far from accurate hence estimation errors are limiting factors in applying markov decision processes to real world problems we consider a robust control problem for a finite state finite action markov decision process where uncertainty on the transition matrices is described in terms of possibly nonconvex sets we show that perfect duality holds for this problem and that as a consequence it can be solved with a variant of the classical dynamic programming algorithm the robust dynamic programming algorithm we show that a particular choice of the uncertainty sets involving likelihood regions or entropy bounds leads to both a statistically accurate representation of uncertainty and a complexity of the robust recursion that is almost the same as that of the classical recursion hence robustness can be added at practically no extra computing cost we derive similar results for other uncertainty sets including one with a finite number of possible values for the transition matrices we describe in a practical path planning example the benefits of using a robust strategy instead of the classical optimal strategy even if the uncertainty level is only crudely guessed the robust strategy yields a much better worst case expected travel time

error bounds for finite step approximations for solving infinite horizon controlled markov set chains this note considers finite step approximations for solving an infinite horizon controlled markov set chain problem with finite state and action spaces we develop a value iteration type algorithm based on the optimality equation developed by kurano et al and analyze an error bound relative to the optimal value that satisfies the optimality equation from the successive approximation we further analyze an error bound of the approximate control policy defined from a finite step approximate value by applying the value iteration type algorithm

robust dynamic programming in this paper we propose a robust formulation for discrete time dynamic programming dp the objective of the robust formulation is to systematically mitigate the sensitivity of the dp optimal policy to ambiguity in the underlying transition probabilities the ambiguity is modeled by associating a set of conditional measures with each state action pair consequently in the robust formulation each policy has a set of measures associated with it we prove that when this set of measures has a certain rectangularity property all of the main results for finite and infinite horizon dp extend to natural robust counterparts we discuss techniques from nilim and el ghaoui 17 for constructing suitable sets of conditional measures that allow one to efficiently solve for the optimal robust policy we also show that robust dp is equivalent to stochastic zero sum games with perfect information

approximation and numerical realization of 2d contact problems with coulomb friction and a solution dependent coefficient of friction the paper analyzes discrete contact problems with the coulomb law of friction which involves a solution dependent coefficient of friction f solutions to these problems are defined as fixed points of an auxiliary mapping it is shown that there exists at least one solution provided that f is bounded and continuous in r 1 further conditions guaranteeing uniqueness of the solution are studied the paper is completed by numerical results of several model examples

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

approximation and numerical realization of 3d contact problems with coulomb friction and a solution dependent coefficient of friction this paper analyzes 3d discrete contact problems with coulomb friction and a coefficient of friction depending on the solution the formulation of this problem is based on a fixed point approach existence of at least one discrete solution is guaranteed for any continuous non negative and bounded function the uniqueness result is established for small enough and lipschitz continuous with a sufficiently small modulus of lipschitz continuity results of several numerical experiments are shown copyright 2009 john wiley sons ltd

combined symmetric bem and semi smooth newton method for the contact problems in linear elasticity of yukawa type the semi smooth newton method and the boundary element method are developed and analyzed for the solution of 2 d signorini contact problems in linear elasticity of yukawa type first we consider the contact problem with tresca friction this leads to a constrained non differentiable minimization problem where the solvability is in general problematic but by utilizing the fenchel duality theory the dual formulation in terms of contact stresses turns out to be a quadratic optimization problem with a smooth functional the regularization of the dual problem motivated by the augmented lagrangian is suitable for the application of the generalized newton method applying the boundary integral equation method the problem is reduced to the boundary curve the corresponding boundary integral equations are approximated by using a galerkin method with the help of b splines on the boundary curve bem this yields an algebraic system of linear equations with dense stiffness matrix but which is symmetric the symmetry property of the stiffness matrix enables the application of efficient iterative solution strategies for the linear systems at each newton step second the methods are carried over to the coulomb friction problem by means of a fixed point approach in particular the analysis of the algorithm is presented and some numerical examples which show a remarkable efficiency and reliability of the semi smooth newton method are given

shape optimization in contact problems with coulomb friction and a solution dependent friction coefficient the present paper deals with shape optimization in discretized two dimensional 2d contact problems with coulomb friction where the coefficient of friction is assumed to depend on the unknown solution discretization of the continuous state problem leads to a system of finite dimensional implicit variational inequalities parametrized by the so called design variable that determines the shape of the underlying domain it is shown that if the coefficient of friction is lipschitz and sufficiently small in the c 0 1 norm then the discrete state problems are uniquely solvable for all admissible values of the design variable the admissible set is assumed to be compact and the state variables are lipschitzian functions of the design variable this facilitates the numerical solution of the discretized shape optimization problem by the so called implicit programming approach our main results concern sensitivity analysis which is based on the well developed generalized differential calculus of b mord

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

finite element approximation of a problem with a nonlinear newton boundary condition the paper is concerned with the study of an elliptic boundary value problem with a nonlinear newton boundary condition the existence and uniqueness of the solution of the continuous problem is established with the aid of the monotone operator theory the main attention is paid to the investigation of the finite element approximation using numerical integration for the computation of nonlinear boundary integrals the solvability of the discrete finite element problem is proved and the convergence of the approximate solutions to the exact one is analysed

evolutionary policy iteration for solving markov decision processes we propose a novel algorithm called evolutionary policy iteration epi for solving infinite horizon discounted reward markov decision processes epi inherits the spirit of policy iteration but eliminates the need to maximize over the entire action space in the policy improvement step so it should be most effective for problems with very large action spaces epi iteratively generates a population or a set of policies such that the performance of the elite policy for a population monotonically improves with respect to a defined fitness function epi converges with probability one to a population whose elite policy is an optimal policy epi is naturally parallelizable and along this discussion a distributed variant of pi is also studied

qualitative analysis of 3d elastostatic contact problems with orthotropic coulomb friction and solution dependent coefficients of friction this paper analyzes a discrete form of 3d contact problems with local orthotropic coulomb friction and coefficients of friction which may depend on the solution itself the analysis is based on the fixed point reformulation of the original problem conditions guaranteeing the existence and uniqueness of discrete solutions are established finally numerical results of a model example are presented

markov decision processes with imprecise transition probabilities we present new numerical algorithms and bounds for the infinite horizon discrete stage finite state and action markov decision process with imprecise transition probabilities we assume that the transition probability mass vector for each state and action is described by a finite number of linear inequalities this model of imprecision appears to be well suited for describing statistically determined confidence limits and or natural language statements of likelihood the numerical procedures for calculating an optimal max min strategy are based on successive approximations reward revision and modified policy iteration the bounds that are determined are at least as tight as currently available bounds for the case where the transition probabilities are precise

bounded parameter markov decision process in this paper we introduce the notion of a em bounded parameter markov decision process as a generalization of the traditional em exact mdp a bounded parameter mdp is a set of exact mdps specified by giving upper and lower bounds on transition probabilities and rewards all the mdps in the set share the same state and action space bounded parameter mdps can be used to represent variation or uncertainty concerning the parameters of sequential decision problems bounded parameter mdps can also be used in aggregation schemes to represent the variation in the transition probabilities for different base states aggregated together in the same aggregate state we introduce em interval value functions as a natural extension of traditional value functions an interval value function assigns a closed real interval to each state representing the assertion that the value of that state falls within that interval an interval value function can be used to bound the performance of a policy over the set of exact mdps associated with a given bounded parameter mdp we describe an iterative dynamic programming algorithm called em interval policy evaluation which computes an interval value function for a given bounded parameter mdp and specified policy interval policy evaluation on a policy policy computes the most restrictive interval value function that is sound i e that bounds the value function for policy in every exact mdp in the set defined by the bounded parameter mdp a simple modification of interval policy evaluation results in a variant of value iteration bellman57 that we call em interval value iteration which computes a policy for an bounded parameter mdp that is optimal in a well defined sense

solving controlled markov set chains with discounting via multipolicy improvement we consider markov decision processes mdps where the state transition probability distributions are not uniquely known but are known to belong to some intervals so called controlled markov set chains with infinite horizon discounted reward criteria we present formal methods to improve multiple policies for solving such controlled markov set chains our multipolicy improvement methods follow the spirit of parallel rollout and policy switching for solving mdps in particular these methods are useful for online control of markov set chains and for designing policy iteration pi type algorithms we develop a pi type algorithm and prove that it converges to an optimal policy

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

clustering coding switching hierarchical ordering and control in a network of chaotic elements abstract a network of chaotic elements is investigated with the use of globally coupled maps a simple coding of many attractors with clustering is shown through the coding the attractors are organized so that their change exhibits bifurcation like phenomena a precision dependent tree is constructed which leads to the similarity of our attractor with those of spin glasses hierarchical dynamics is constructed on the tree which leads to the dynamical change of trees and the temporal change of effective degrees of freedom by a simple input on a site we can switch among attractors and tune the strength of chaos a threshold on a cluster size is found beyond which a peculiar posi nega switch occurs possible application to biological information processing is discussed with the emphasis on the fuzzy switch chaotic search and hierarchical code categorization

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other