the cauchy and characteristic boundary value problems of random rigid perfectly plastic media abstract effects of spatial random fluctuations in the yield condition of rigid perfectly plastic continuous media are analysed in cases of cauchy and characteristic boundary value problems a weakly random plastic microstructure is modeled on a continuum mesoscale by an isotropic yield condition with the yield limit taken as a locally averaged random field the solution method is based on a stochastic generalization of the method of sliplines whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones containing random characteristics comparisons of response of this random medium and of a deterministic homogeneous medium with a plastic limit equal to the average of the random one are carried out numerically in several specific examples of the two boundary value problems under study an application of the method is given to the limit analysis of a cylindrical tube under internal traction the major conclusion is that weak material randomness always leads to a relatively stronger scatter in the position and field variables as well as to a larger size of the domain of dependence effects which are amplified by both presence of shear traction and inhomogeneity in the boundary data additionally it is found that there is hardly any difference between stochastic slipline fields due to either gaussian or uniform noise in the plastic limit

existence of pullback attractors for pullback asymptotically compact processes abstract this paper is concerned with the existence of pullback attractors for evolution processes our aim is to provide results that extend the following results for autonomous evolution processes semigroups i an autonomous evolution process which is bounded dissipative and asymptotically compact has a global attractor ii an autonomous evolution process which is bounded point dissipative and asymptotically compact has a global attractor the extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non autonomous evolution processes an application to damped wave problem with non autonomous damping is considered

structured least squares to improve the performance of esprit type algorithms esprit type spatial frequency estimation techniques obtain their frequency estimates from the solution of a highly structured overdetermined system of equations the so called invariance equation here the structure is defined in terms of two selection matrices applied to a matrix spanning the estimated signal subspace structured least squares sls is a new algorithm that solves the invariance equation by preserving its structure formally sls is derived as a linearized iterative solution of a nonlinear optimization problem if sls is initialized with the least squares solution of the invariance equation only one iteration i e the solution of one linear system of equations is performed to achieve a significant improvement of the estimation accuracy therefore the proposed estimation scheme that uses only one iteration of sls is not iterative in nature

scaling for orthogonality in updating algorithms where orthogonal transformations are accumulated it is important to preserve the orthogonality of the product in the presence of rounding error moonen et al ibid vol 39 p 1911 13 1991 have pointed out that simply normalizing the columns of the product tends to preserve orthogonality though not as degroat ibid vol 39 p 1913 14 1991 points out to working precision the authors discuss the previous work and give an analysis of the phenomenon

determination of rve size for random composites with local volume fraction variation abstract in this paper a novel computational procedure is proposed for the determination of the representative volume element rve size for random composites which is the basis of homogenization methods the proposed approach takes into account the local volume fraction variation by processing computer simulated images of composites with randomly scattered inclusions a variable number of microstructure models are derived directly from the images using the moving window technique each microstructure model contains different amount of inclusions measured by image analysis tools the proposed computational procedure is based on the solution of multiple boundary value problems under kinematic and static uniform boundary conditions using the extended finite element method xfem coupled with monte carlo simulation mcs in this way the statistical characteristics of the upper and lower bounds of the apparent material properties are computed the rve is attained within a prescribed tolerance by examining the convergence of these two bounds with respect to the mesoscale size the numerical results clearly demonstrate the significant effect of matrix inclusion stiffness ratio and volume fraction on the convergence rate the proposed computational procedure leads to rves which can give more realistic results when used in homogenization problems mesoscale random fields describing the spatial variation of the components of the apparent elasticity tensor are also determined using the proposed approach

urv esprit for tracking time varying signals esprit is an algorithm for determining the fixed directions of arrival of a set of narrowband signals at an array of sensors unfortunately its computational burden makes it unsuitable for real time processing of signals with time varying directions of arrival the authors develop a new implementation of esprit that has potential for real time processing it is based on a rank revealing urv decomposition rather than the eigendecomposition or singular value decomposition used in previous esprit algorithms the authors demonstrate its performance on simulated data representing both constant and time varying signals they find that the urv based esprit algorithm is effective for estimating time varying directions of arrival at considerable computational savings over the svd based algorithm

a parametric method for determining the number of signals in narrow band direction finding a novel and more accurate method to determine the number of signals in the multisource direction finding problem is developed the information theoretic criteria of y yin and p krishnaiah 1988 are applied to a set of quantities which are evaluated from the log likelihood function based on proven asymptotic properties of the maximum likelihood estimation these quantities have the properties required by the criteria since the information theoretic criteria use these quantities instead of the eigenvalues of the estimated correlation matrix this approach possesses the advantage of not requiring a subjective threshold and also provides higher performance than when eigenvalues are used simulation results are presented and compared to those obtained from the nonparametric method given by h wax and t kailath 1985

asymptotically autonomous multivalued cauchy problems with spatially variable exponents abstract we study the asymptotic behavior of a non autonomous multivalued cauchy problem of the form u t t div d t u t p x 2 u t u t p x 2 u t f t u t 0 on a bounded smooth domain in r n n 1 with a homogeneous neumann boundary condition where the exponent p c satisfies p min p x 2 we prove the existence of a pullback attractor and study the asymptotic upper semicontinuity of the elements of the pullback attractor a a t t r as t for the non autonomous evolution inclusion in a hilbert space h under the assumptions amongst others that f is a measurable multifunction and d l t is bounded above and below and is monotonically nonincreasing in time the global existence of solutions is obtained through results of papageorgiou and papalini

pullback attractors for asymptotically compact non autonomous dynamical systems abstract first we introduce the concept of pullback asymptotically compact non autonomous dynamical system as an extension of the similar concept in the autonomous framework our definition is different from that of asymptotic compactness already used in the theory of random and non autonomous dynamical systems as developed by crauel flandoli kloeden schmalfuss amongst others which means the existence of a random or time dependent family of compact attracting sets next we prove a result ensuring the existence of a pullback attractor for a non autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets this attractor is minimal and in most practical applications it is unique finally we illustrate the theory with a 2d navier stokes model in an unbounded domain

continuum mechanics beyond the second law of thermodynamics the results established in contemporary statistical physics indicating that on very small space and time scales the entropy production rate may be negative motivate a generalization of continuum mechanics on account of the fluctuation theorem it is recognized that the evolution of entropy at a material point is stochastically not deterministically conditioned by the past history with an increasing trend of average entropy production hence the axiom of clausius duhem inequality is replaced by a submartingale model which by the doob decomposition theorem allows classification of thermomechanical processes into four types depending on whether they are conservative or not and or conventional continuum mechanical or not stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics with explicit models formulated for newtonian fluids with respectively parabolic or hyperbolic heat conduction several random field models of the martingale component possibly including spatial fractal and hurst effects are proposed the violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved as an example we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient

a reduced basis approach for variational problems with stochastic parameters application to heat conduction with variable robin coefficient in this work a reduced basis rb approach is used to solve a large number of boundary value problems bvps parametrized by a stochastic input expressed as a karhunen loeve expansion in order to compute outputs that are smooth functionals of the random solution fields the rb method proposed here for variational problems parametrized by stochastic coefficients bears many similarities to the rb approach developed previously for deterministic systems however the stochastic framework requires the development of new a posteriori estimates for statistical outputs such as the first two moments of integrals of the random solution fields these error bounds in turn permit efficient sampling of the input stochastic parameters and fast reliable computation of the outputs in particular in the many query context

statistical modeling of heterogeneous micro beams statistical characteristics averages and variances of heterogeneous small size beams micro beams composed of micro elements grains of randomly distributed stiffness isotropic is studied only longitudinal variations are considered element to beam size length ratio is not negligible and the use of an equivalent homogeneous structure with the classical effective material properties is not sufficient using standard statistical tools probability density and correlation functions it is shown that for indeterminate cases even average deflections obtained explicitly are load dependent and are not identical with their corresponding homogeneous case bounds for the statistical dispersion of deflections and reaction forces are found analytically for some cases of weak heterogeneity it is shown that dispersion parameters for indeterminate problems can be obtained by superposition using both averages and dispersion data of corresponding determinate cases leading to reciprocal type relations

an updating algorithm for subspace tracking in certain signal processing applications it is required to compute the null space of a matrix whose rows are samples of a signal with p components the usual tool for doing this is the singular value decomposition however the singular value decomposition has the drawback that it requires o p sup 3 operations to recompute when a new sample arrives it is shown that a different decomposition called the urv decomposition is equally effective in exhibiting the null space and can be updated in o p sup 2 time the updating technique can be run on a linear array of p processors in o p time

uniform attractors for non autonomous p laplacian equations abstract in this paper by the galerkin method we give the existence of solutions for the non autonomous p laplacian equation u t div u p 2 u f u g t after that we explore the asymptotic behavior of the equation the existence and the structures of the l 2 l 2 uniform attractor and the l 2 l q w 0 1 p uniform attractor are proved under the conditions below the nonlinear term f is supposed to satisfy the polynomial condition of arbitrary order c 1 u q k f u u c 2 u q k and f u l where q 2 is arbitrary and the external force g t in l loc 2 r l s s 2 is translation bounded and uniformly bounded in l s with respect to t r

addressing the curse of dimensionality in ssfem using the dependence of eigenvalues in kl expansion on domain size this work is aimed at reducing the dimensionality in the spectral stochastic finite element method ssfem thus the computational cost through a domain decomposition dd method this reduction hinges on some new mathematical results on domain size dependence of the karhunen loeve kl expansion it has been reported in the literature that for few covariance kernels a lower domain size leads to a faster convergence of the kl eigenvalues this observation leads to an early truncation of the kl expansion and this reduction in stochastic dimensionality brings down the total computational cost in this work first we mathematically show the generalization of this faster convergence that is for any arbitrary covariance kernel this is achieved via developing a bound on eigenvalues as a function of the domain size then we prove that for a chosen number of terms in the kl expansion with any kernel for a one dimensional process the approximation error in the trace norm reduces with the domain size based on this domain size dependence we propose an algorithm for solving a stochastic elliptic equation in a dd framework the computational cost gain is demonstrated by a numerical study and is observed that the serial implementation of the proposed algorithm is about an order of magnitude faster compared to the existing method the cost saving increases with the stochastic dimensionality in the global domain the structure of this algorithm provides scope for parallelization which would help in efficiently solving large scale problems the sharpness of the proposed eigenvalue bounds is also tested for gaussian and exponential kernels the generalization opens avenues for developing further dd based ssfem solvers c 2016 elsevier b v all rights reserved

existence and upper semicontinuity of pullback attractors for non autonomous p laplacian parabolic problems abstract we study the asymptotic behavior of parabolic p laplacian problems of the form u t t div d t u t p 2 u t u t p 2 u t b t u t in a bounded smooth domain in r n where n 1 p 2 d l t with 0 d t x m a e in t 0 and for each 0 we have d s x d t x c s t for all x s t t for some positive constants and c moreover d d 1 in l t as 1 we prove that for each 0 the evolution process of this problem has a pullback attractor and we show that the family of pullback attractors behaves upper semicontinuously at 1

a survey of condition number estimation for triangular matrices we survey and compare a wide variety of techniques for estimating the condition number of a triangular matrix and make recommendations concerning the use of the estimates in applications each of the methods is shown to bound the condition number the bounds can broadly be categorised as upper bounds from matrix theory and lower bounds from heuristic or probabilistic algorithms for each bound we examine by how much at worst it can overestimate or underestimate the condition number numerical experiments are presented in order to illustrate and compare the practical performance of the condition estimators

memory effects for the heat conductivity of random suspensions of spheres the presence of a particulate phase defines the effective response of a suspension to changes of the average heat flux using the random point approximation we show that within the first order in the concentration one needs to solve the problem for the temperature field created by a single inclusion in a matrix subject to an unsteady temperature gradient at infinity we solve this problem by means of laplace transform and use the solution as the first order kernel in the functional expansion from this kernel we find the statistical average for the heat flux which turns out to be a memory integral of the spatially averaged time dependent temperature gradient thus we discover that the constructive relationship between the average flux and averaged temperature gradient is not local in time but rather involves a convolution integral that represents the memory due to the heterogeneity of the system this is a novel result which inter alia gives a rigorous justification to the usage of generalizations of the heat conduction law involving fractional time derivatives the decay of the kernel is very close to t 1 2 for dimensionless times lesser than one and abruptly changes to t 3 2 for larger times

shape from moments an estimation theory perspective this paper discusses the problem of recovering a planar polygon from its measured complex moments these moments correspond to an indicator function defined over the polygon s support previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given in this paper we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given similar to methods found in array processing system identification and signal processing we discuss a set of possible estimation procedures that are based on the prony and the pencil methods relate them one to the other and compare them through simulations we then present an improvement over these methods based on the direct use of the maximum likelihood estimator exploiting the above methods as initialization finally we show how regularization and thus maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon

homogenization of non periodic masonry structures a homogenization approach to assess the mechanical characteristics of masonry structures is presented in this paper in order to analyze an actual masonry the concept of periodic cell used in literature for periodic masonry is replaced with that of representative volume element this volume is found by employing a formulation based on finite size test windows the homogenized medium stiffness tensor is obtained by considering the hierarchy of estimates relative to essential and natural boundary conditions moreover an ensemble average is performed on space taking into account different test windows location on the given structure an application shows the effectiveness of the proposed approach

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

a note on p laplacian parabolic problems in rn abstract in this work we study the asymptotic behavior of parabolic p laplacian problems of the form u t div d u p 2 u a u p 2 u b u in l 2 r n where n 1 p 2 d l r n m d x 0 a e in r n 0 b l 2 r n l 2 r n is a globally lipschitz map and a r n r is a non negative continuous function we prove under suitable assumptions on a the existence of a global attractor in l 2 r n for each positive finite diffusion coefficient and we show that the family of attractors behaves upper semicontinuously with respect to positive finite diffusion parameters

generalized stochastic approach for constitutive equation in linear elasticity a random matrix model this work is concerned with the construction of stochastic models for random elasticity matrices allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely integrating the statistical dependence between the random stiffness components or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be controlled apart from the level of statistical fluctuations to this aim we first introduced a decomposition of the stochastic elasticity tensor on a deterministic tensor basis and considered the probabilistic modeling of the random components having recourse to the maxent principle strategies for random generation and estimation were further reviewed and the approach was exemplified in the case of a material that was transversely isotropic almost surely in a second stage we made use of such derivations to propose a generalized model for random elasticity matrices that took into accountconstraints on both the level of stochastic anisotropy and the level of statistical fluctuations

efficient numerically stabilized rank one eigenstructure updating signal processing rank one eigenvalue decomposition evd updating is well suited to the problem of tracking time varying subspaces previously published rank one evd updating algorithms suffer from a linear buildup of roundoff error which makes them impractical for a large number of recursive updates in the present work the authors develop a numerical stabilization technique which eliminates the error buildup problem in a computationally efficient manner and makes the rank one evd update a practical numerical tool for online computation a simplified eigenvalue iteration is also given it reduces the complexity of the algorithm somewhat as well as the computation time simulations are presented to illustrate numerical performance

growth decay and bifurcation of shock amplitudes under the type ii flux law by replacing fick s diffusion law with green and nagdhi s type ii flux law a hyperbolic counterpart to the classical fisherkpp equation is obtained in this article an analytical study of this pa

characterization of non autonomous attractors of a perturbed infinite dimensional gradient system in this paper we determine the exact structure of the pullback attractors in non autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a finite set of hyperbolic equilibria we show that the pullback attractors of the perturbed systems inherit this structure and are given as the union of the unstable manifolds of a set of hyperbolic global solutions which are the non autonomous analogues of the hyperbolic equilibria we also prove again parallel to the autonomous case that all solutions converge as t infinity to one of these hyperbolic global solutions we then show how to apply these results to systems that are asymptotically autonomous as t infinity and as t infinity and use these relatively simple test cases to illustrate a discussion of possible definitions of a forwards attractor in the non autonomous case c 2007 elsevier inc all rights reserved

on the growth and decay of acceleration waves in random media we study the effects of material spatial randomness on the growth to shock or decay of acceleration waves in the deterministic formulation such waves are governed by a bernoulli equation d d x x x 2 in which the material coefficients and represent the dissipation and elastic nonlinearity respectively in the case of a random microstructure the wavefront sees the local details it is a mesoscale window travelling through a random continuum upon a stochastic generalization of the bernoulli equation both coefficients become stationary random processes and the critical amplitude c as well as the distance to form a shock x become random variables we study the character of these variables especially as compared to the deterministic setting for various cases of the random process i one white noise ii two independent white noises iii two correlated gaussian noises and iv an ornstein uhlenbeck process situations of fully positively negatively or zero correlated noises in and are investigated in detail particular attention is given to the determination of the average critical amplitude c equations for the evolution of the moments of the probability of formation of a shock wave within a given distance x and the average distance to form a shock wave specific comparisons of these quantities are made with reference to a homogeneous medium defined by the mean values of the x process

on solving elliptic stochastic partial differential equations abstract a model elliptic boundary value problem of second order with stochastic coefficients described by the karhunen loeve expansion is addressed this problem is transformed into an equivalent deterministic one the perturbation method and the method of successive approximations is analyzed rigorous error estimates in the framework of sobolev spaces are given

fast recursive subspace adaptive esprit algorithms a class of fast recursive esprit algorithms for adaptive on line source localization based on subspace tracking and adaptive rank reduction is introduced these adaptive esprit algorithms can be used for on line tracking of r maneuvering sources in space using the output of an n element sensor array where n 2r the fastest of our algorithms requires only o nr o r sup 3 complex arithmetic operations to update the estimated directions of arrival doas at each time instant these highly efficient algorithms are more than only a concatenation of a subspace tracker and a conventional batch esprit algorithm a special qr reduction to standard form is the key to the fast recursive algorithms detailed computer experiments substantiate the theoretical results

pullback attractors for the norm to weak continuous process and application to the nonautonomous reaction diffusion equations abstract in this paper we introduce the concept of norm to weak continuous process in a banach space and obtain the existence of pullback attractors for this kind of process then we give a new method for proving the existence of the pullback attractors as an application we obtain the existence of pullback attractors for nonautonomous reaction diffusion equation in h 0 1 with exponential growth of the external force

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

a correlation based subspace tracking algorithm stewart 1992 proposed the urv algorithm as a less complex alternative to the svd by forming the cross product of the urv with its transpose a correlation domain decomposition is produced that involves even less computation this cross product rv crv decomposition is the basis for a new subspace tracking technique

the stochastic finite element method past present and future a powerful tool in computational stochastic mechanics is the stochastic finite element method sfem sfem is an extension of the classical deterministic fe approach to the stochastic framework i e to the solution of static and dynamic problems with stochastic mechanical geometric and or loading properties the considerable attention that sfem received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large scale problems this article aims at providing a state of the art review of past and recent developments in the sfem area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future

well posed p laplacian problems with large diffusion abstract in this work we study the asymptotic behavior of p laplacian parabolic problems of the form u t d p u u p 2 u b u in a bounded smooth domain in r n and under neumann boundary conditions when the diffusion coefficient d becomes large we prove under suitable assumptions that the family of attractors behaves lower and upper semicontinuously as the diffusion increases to infinity

asymptotic behaviour of nonlocal p laplacian reaction diffusion problems abstract in this paper we focus on studying the existence of attractors in the phase spaces l 2 and l p among others for time dependent p laplacian equations with nonlocal diffusion and nonlinearities of reaction diffusion type firstly we prove the existence of weak solutions making use of a change of variable which allows us to get rid of the nonlocal operator in the diffusion term thereupon the regularising effect of the equation is shown applying an argument of a posteriori regularity since under the assumptions made we cannot guarantee the uniqueness of weak solutions in addition this argument allows to ensure the existence of an absorbing family in w 0 1 p this leads to the existence of the minimal pullback attractors in l 2 l p and some other spaces as l p relationships between these families are also established

michell trusses in the presence of microscale material randomness limitation of optimality the classical problem of a michell optimal truss concerns a minimum weight design of a planar truss that transmits a given load to a given rigid foundation with the requirement that the axial stresses in the bars of the truss stay within an allowable range the present study considers this problem when the truss is made of a material with random microstructure that is when is a random field the trusses tending to the optimal state can be determined through a net of characteristics generalized to a stochastic setting while in the classical case of a homogeneous material this net gives the minimum weight as its spacing tends to zero the presence of a random microstructure prevents the attainment of this state basically the finer the net the stronger the scatter of characteristics which forces one to use more structural material to compensate for these fluctuations in effect there is a limitation to the attainment of the optimality of the michell truss made of a hypothetical perfectly homogeneous material

domain decomposition methods to evaluate effective elastic properties of random fibre composites in the framework of the double scale homogenization abstract the paper deals with the evaluation of the effective elastic properties in the framework of domain decomposition the field of random fibre composites for which the network of heterogeneities is complex and leads to several numerical shortcomings is considered 2d representative volume elements rves of the composite are generated and some elastic properties are estimated with the help of the double scale homogenization such methodology is reliable but turns out to be potentially inefficient due to the required size of rves two adaptations of domain decomposition methods in the framework of double scale homogenization are proposed to drastically reduce the calculation costs a schur complement method and a mixed schur complement and feti 1 method several numerical tests are performed which highlight reliability and efficiency of the first one in the present context

a note on efficient numerically stabilized rank one eigenstructure updating and reply in the above named paper r d degroat and r a roberts see ibid vol 38 no 2 p 301 16 feb 1990 developed a reorthogonalization scheme for stabilizing eigenstructure updating algorithms the commenters show that only part of this scheme namely the renormalization is essential for the stability so that a cheaper scheme with roughly half as many computations can perform equally well degroat addresses two points raised by the commenters work

cost reduction of stochastic galerkin method by adaptive identification of significant polynomial chaos bases for elliptic equations abstract one widely used and computationally efficient method for uncertainty quantification using spectral stochastic finite element is the stochastic galerkin method here the solution is represented in polynomial chaos expansion and the residual of the discretized governing equation is projected on the polynomial chaos bases this results in a system of deterministic algebraic equations with the polynomials chaos coefficients as unknown however one impediment for its large scale applications is the curse of dimensionality that is the exponential growth of the number of polynomial chaos bases with the stochastic dimensionality and degree of expansion here for a stochastic elliptic problem an adaptive selection of polynomial chaos bases is proposed accordingly during the first few iterations in the preconditioned conjugate gradient method for solving the system of linear algebraic equations the chaos bases with maximal contribution in an appropriately defined metric to the solution are first identified subsequently only these bases are retained for further iterations until convergence is achieved using numerical studies a three times cost saving over the existing method is observed furthermore for enhancing the computational cost gain the stochastic galerkin method is reformulated as a generalized sylvester equation this step allowed efficient usage of the sparsity of moments of product of polynomial chaos bases through numerical studies on problems with large stochastic dimensionality an additional cost saving of up to one order of magnitude twenty times is observed this amounts to sixty times speedup over the existing method when adaptive selection and generalized sylvester equation formulation are used together the proposed methodology can be easily incorporated in an existing standard stochastic galerkin method solver for elliptic problems

a complete characterization of nonlinear absorption for the evolution p laplacian equations to have positive or extinctive solutions this paper is concerned with long time behaviors of solutions to the initial boundary value problem of the evolution p laplacian equations with nonlinear absorption a long time behavior of solutions to these equations has been studied so far for particular types of nonlinear absorption term the purpose of this paper is to give a complete characterization of the nonlinear absorption term according to the parameter p in p laplacian operator and the growth of the nonlinear absorption term near the origin in order to determine whether the solution to the equations is extinctive or positive in addition we also give upper bounds for extinction times of solutions

an inverse micro mechanical analysis toward the stochastic homogenization of nonlinear random composites abstract an inverse mean field homogenization mfh process is developed to improve the computational efficiency of non linear stochastic multiscale analyzes by relying on a micro mechanics model first full field simulations of composite stochastic volume element sve realizations are performed to characterize the homogenized stochastic behavior the uncertainties observed in the non linear homogenized response which result from the uncertainties of their micro structures are then translated to an incremental secant mfh formulation by defining the mfh input parameters as random effective properties these effective input parameters which correspond to the micro structure geometrical information and to the material phases model parameters are identified by conducting an inverse analysis from the full field homogenized responses compared to the direct finite element analyzes on sves the resulting stochastic mfh process reduces not only the computational cost but also the order of uncertain parameters in the composite micro structures leading to a stochastic mean field reduced order model mf rom a data driven stochastic model is then built in order to generate the random effective properties under the form of a random field used as entry for the stochastic mf rom embedded in a stochastic finite element method sfem the two cases of elastic unidirectional ud fibers embedded in an elasto plastic matrix and of elastic ud fibers embedded in a damage enhanced elasto plastic matrix are successively considered in order to illustrate the capabilities of the method the stochastic response of a ply is studied under transverse loading condition

a stochastic computational multiscale approach application to mems resonators abstract the aim of this work is to develop a stochastic multiscale model for polycrystalline materials which accounts for the uncertainties in the micro structure at the finest scale we model the micro structure using a random voronoi tessellation each grain being assigned a random orientation then we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the meso scale a random field of the meso scale elasticity tensor can thus be generated based on the information obtained from the sve simulations finally using a stochastic finite element method these meso scale uncertainties are propagated to the coarser scale as an illustration we study the resonance frequencies of mems micro beams made of poly silicon materials and we show that the stochastic multiscale approach predicts results in agreement with a monte carlo analysis applied directly on the fine finite element model i e with an explicit discretization of the grains

faster computation of the karhunen loeve expansion using its domain independence property the goal of this work is to reduce the cost of computing the coefficients in the karhunen loeve kl expansion the kl expansion serves as a useful and efficient tool for discretizing second order stochastic processes with known covariance function its applications in engineering mechanics include discretizing random field models for elastic moduli fluid properties and structural response the main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel mathematically this is a homogeneous fredholm equation of second type one widely used method for solving this integral eigenvalue problem is to use finite element fe bases for discretizing the eigenfunctions followed by a galerkin projection this method is computationally expensive in the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using kl expansion although the individual kl terms are affected based on this domain independence property a numerical integration based scheme accompanied by a modification of the domain is proposed in addition to presenting mathematical arguments to establish the domain independence numerical studies are also conducted to demonstrate and test the proposed method numerically it is demonstrated that compared to the galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example and of one to two orders of magnitude for a three dimensional example while retaining the same level of accuracy it is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved both normal and lognormal fields are considered in the numerical studies c 2014 elsevier b v all rights reserved

asymptotic behavior of a class of non autonomous degenerate parabolic equations abstract we investigate the asymptotic behavior of solutions of a class of non autonomous degenerate parabolic equations on r n with unbounded external forcing terms the existence of a pullback global attractor is proved in l 2 r n l p r n w 1 r r n for any p r 2

stochastic finite element analysis of composite structures based on mesoscale random fields of material properties abstract the linking of microstructure uncertainty with the random variation of material properties at higher scales is of paramount importance in the framework of the stochastic finite element method sfem an efficient computational scheme has been recently proposed by the authors for the determination of mesoscale random fields for the apparent properties and of the rve size of particle reinforced composites based on computer simulated images of their microstructure the proposed approach exploits the excellent synergy of the extended finite element method xfem and monte carlo simulation in order to analyze the microstructure models and obtain statistical information probability distribution correlation structure for the apparent properties of the composite in each mesoscale size in this paper sample functions of the statistically homogeneous mesoscale random fields are generated using the spectral representation method in conjunction with translation field theory moreover micro mechanically consistent lower and upper bounds on the macroscopic response of composite structures are computed in the framework of sfem useful conclusions are derived regarding the effect of particle matrix stiffness ratio on the probabilistic characteristics of the mesoscale random fields as well as the influence of mesoscale size on the response variability

random field models of heterogeneous materials abstract one of the main challenges in solid mechanics lies in the passage from a heterogeneous microstructure to an approximating continuum model in many cases e g stochastic finite elements statistical fracture mechanics the interest lies in resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale this may be accomplished with the help of a meso scale window which becomes the classical representative volume element rve in the infinite limit it turns out that the material properties at such a mesoscale cannot be uniquely approximated by a random field of stiffness compliance with locally isotropic realizations but rather two random continuum fields with locally anisotropic realizations corresponding respectively to essential and natural boundary conditions on the meso scale need to be introduced to bound the material response from above and from below we study the first and second order characteristics of these two meso scale random fields for anti plane elastic response of random matrix inclusion composites over a wide range of contrasts and aspect ratios special attention is given to the convergence of effective responses obtained from the essential and natural boundary conditions which sheds light on the minimum size of an rve additionally the spatial correlation structure of the crack density tensor with the meso scale moduli is studied

asymptotically autonomous dynamics for parabolic equations abstract given an asymptotically autonomous system it is shown that the components of the pullback attractor converge to the global attractor if and only if the pullback attractor is forward compact this result reduces two uniformness conditions in the theoretical result given by kloeden and simsen j math anal appl 2015 2017 some constructions from the forward limit set of a pullback attractor are established some applications are given for two classes of non autonomous quasi linear parabolic equations one has a parabolic operator with spatially variable exponents and another has a weakly dissipative nonlinearity for two equations it is shown that the pullback attractor is forward compact and upper semi continuous to the global attractor moreover there is an inclusion between the global attractor and the forward limit set of pullback attractors

a block qr algorithm and the singular value decomposition abstract in this note we consider an iterative algorithm for moving a triangular matrix toward diagonality the algorithm is related to algorithms for refining rank revealing triangular decompositions and in a variant form to the qr algorithm it is shown to converge if there is a sufficient gap in the singular values of the matrix and the analysis provides a new approximation theorem for singular values and singular subspaces

stochastic finite elements as a bridge between random material microstructure and global response this paper presents a finite element method aimed at the introduction of microstructural material randomness below the level of a single finite element a consideration of dependence of effective moduli on scale and on the defining boundary conditions leads to an identification of a finite element as a mesoscale window or a mesoscale finite element in a stochastic finite element method sfe an estimation of the global response can be obtained through bounds stemming from minimum potential energy and complementary energy principles which involve dirichlet and neumann boundary conditions on all the mesoscale finite elements respectively while in the classical case of a homogeneous material these two bounds converge to each other as the finite element mesh becomes sufficiently fine an optimal mesoscale with respect to the difference between both bounds may exist in the case of a heterogeneous material the proposed sfe method is illustrated with a numerical example of a sample two phase voronoi composite with some 26 000 grains where a reference solution taking into account the entire microstructure without any smearing out is shown to fall between both energy bounds a generalization to an ensemble response is straightforward

robust recursive least squares learning algorithm for principal component analysis a learning algorithm for the principal component analysis pca is developed based on the least square minimization the dual learning rate parameters are adjusted adaptively to make the proposed algorithm capable of fast convergence and high accuracy for extracting all principal components the proposed algorithm is robust to the error accumulation existing in the sequential pca algorithm we show that all information needed for pca can he completely represented by the unnormalized weight vector which is updated based only on the corresponding neuron input output product the updating of the normalized weight vector can be referred to as a leaky hebb s rule the convergence of the proposed algorithm is briefly analyzed we also establish the relation between oja s rule and the least squares learning rule finally the simulation results are given to illustrate the effectiveness of this algorithm for pca and tracking time varying directions of arrival

on the continuity of pullback attractors for evolution processes in this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes we then revisit results of d li p e kloeden equi attraction and the continuous dependence of pullback attractors on parameters stoch dyn 4 3 2004 373 384 which show that under certain conditions continuity is equivalent to uniformity of attraction over a range of parameters equi attraction we are able to simplify their proofs and weaken the conditions required for this equivalence to hold generalizing a classical autonomous result a v babin m i vishik attractors of evolution equations north holland amsterdam 1992 we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting to apply these results in a more concrete situation we show that a non autonomous regular perturbation of a gradient like system produces a family of pullback attractors that are uniformly exponentially attracting these attractors are therefore continuous and we can give an explicit bound on the distance between members of this family c 2009 elsevier ltd all rights reserved

compactness results with applications for nonautonomous coupled inclusions abstract in this work we provide compactness results which are generalizations of baras theorem for the case when the main operator is time dependent and we give applications for nonautonomous coupled inclusions proving that these multivalued problems define exact generalized processes

a multiscale stochastic finite element method on elliptic problems involving uncertainties in this study a multiscale stochastic finite element method mssfem is developed to resolve scale coupling stochastic elliptic problems based on formulations of a stochastic variational approach and scale bridging multiscale shape functions by employing polynomial chaos expansions and lagrange polynomials stochastic galerkin method and stochastic collocation method are introduced and combined with deterministic multiscale methods i e variational multiscale method and multiscale finite element method the resulting spectral and pseudo spectral stochastic finite element methods are incorporated into the fine and coarse mesh computation of the mssfem a benchmark multiscale model and the numerical experiment based on the formulated mssfem are provided for illustration it is expected that the proposed mssfem can act as a paradigm for solving of general stochastic partial differential equations involving multiscale stochastic data

existence and upper semi continuity of pullback attractors of a p laplacian equation with delay in this paper we study the dynamics of a non autonomous p laplacian equation with delay we first prove the existence and uniqueness of solutions for this equation by using the galerkin approximations then applying the sobolev compactness theorem ascoli azerla theorem and energy method we show the existence of pullback attractors for the associated process in space c h 0 lp as well as in space c h 0 l2 the upper semi continuity result of the pullback attractors is also established here