a state space finite element for laminated composite plates this paper presents a semi analytical finite element solution for the stress analysis of cross ply laminated composite plates the method is based on a mixed variational principle that includes the variations of both displacements and stresses finite element approximation is introduced only for the in plane variations of displacements and stresses while the through thickness distributions of them are obtained by using the method of state equation numerical tests show that the results obtained approach the analytical three dimensional solutions moreover the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate compared with the traditional finite element method the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces

existence and bifurcation of solutions for an elliptic degenerate problem abstract we investigate the existence multiplicity and bifurcation of solutions of a model nonlinear degenerate elliptic differential equation x 2 u u u p 1 u in 0 1 u 0 u 1 0 this model is related to a simplified version of the nonlinear wheeler dewitt equation as it appears in quantum cosmological models we prove the existence of multiple positive solutions more precisely we show that there exists an infinite number of connected branches of solutions which bifurcate from the bottom of the essential spectrum of the corresponding linear operator nous etudions ici l existence multiplicite et proprietes de bifurcation des solutions d un probleme elliptique degenere x 2 u u u p 1 u in 0 1 u 0 u 1 0 ce probleme modele est proche d une version simplifiee et non lineaire de l equation de wheeler dewitt utilisee dans des modeles de cosmologie quantique nous prouvons l existence d une infinite de branches de solutions qui bifurquent a partir de l infimum du spectre continu de l operateur lineaire correspondant

the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

locking and boundary layer in hierarchical models for thin elastic structures in the analysis of plate and shell like structures using the finite element method we may encounter difficulties owing to locking and boundary layer effects which lead to numerical simulations with a large error there have been considerable advances in finding out the causes and remedies of locking however a posteriori detection of this phenomenon in the numerical results without comparing with other reference data is another issue with a great importance here one simple but reliable detection method is introduced on the other hand boundary layer is a non smooth singular part in the solution of the singularly perturbed boundary value problems and restricted within very thin region in the neighborhood of boundaries if this rapidly varying behavior could not have been captured enough approximated solution greatly deviates from the exact solution in this study a guideline for the optimal mesh design is provided together with mathematical analysis of this effect

a refined global local finite element analysis method a refined global local method was proposed to improve the efficiency of finite element analysis the proposed method was based on the regular finite element method in conjunction with three basic step i e the global analysis the local analysis and the refined global analysis in the first two steps a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest these local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses in the third step a new global displacement distribution based on the results of the previous two steps was assumed for the analysis from which much improved solutions for both stresses and displacements were produced numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method further this method is suitable for parallel computation

adaptive superposition of finite element meshes in elastodynamic problems an adaptive finite element procedure is developed for modelling transient phenomena in elastic solids including both wave propagation and structural dynamics although both temporal and spatial adaptivity are addressed the novel feature of the formulation is the use of mesh superposition to produce spatial refinement referred to as s adaptivity in transient problems spatial error estimation is based on superconvergent patch recovery of higher order accurate stresses and is used to guide mesh adaptivity while the temporal error estimation is based on the assumption of linearly varying third order time derivatives of the displacement field and is used to adjust the time step size for the hht variant of the newmark direct numerical integration method spatial adaptivity of the mesh is performed using a hierarchical h refinement scheme that is efficiently implemented using a structured version of finite element mesh superposition this particular spatial adaptivity scheme is extremely fast and consequently makes it feasible to repeatedly update both the mesh and the time increment as required in an adaptive transient analysis this work represents the initial effort in applying this type of spatial adaptivity to transient problems three example problems are given to demonstrate the performance characteristics of the s adaptive procedure copyright 2005 john wiley sons ltd

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

dirichlet operators on loop spaces essential self adjointness and log sobolev inequality for each 0 1 and potential function v rd r we consider the dirichlet form e and the associated dirichlet operator h for the gibbs measure on the loop space e c 0 1 rd 0 1 the gibbs measure is related to the gibbs state of the quantum anharmonic oscillator with the potential v via the feynman kac formula we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the loop space e we then give an approximate criterion for the essential self adjointness of dirichlet operators associated with dirichlet forms given by probability measures on hilbert spaces under appropriate conditions on the potential we apply the approximate criterion to show that the dirichlet operator h is essentially self adjoint on the domain of smooth cylinder functions in addition if the potential satisfies a uniform convexity condition we prove that the dirichlet operator h has a gap at the lower end of spectrum we also show that the gibbs measure satisfie

adaptive superposition of finite element meshes in non linear transient solid mechanics problems an s adaptive finite element procedure is developed for the transient analysis of 2 d solid mechanics problems with material non linearity due to progressive damage the resulting adaptive method simultaneously estimates and controls both the spatial error and temporal error within user specified tolerances the spatial error is quantified by the zienkiewicz zhu error estimator and computed via superconvergent patch recovery while the estimation of temporal error is based on the assumption of a linearly varying third order time derivatives of the displacement field in conjunction with direct numerical time integration the distinguishing characteristic of the s adaptive procedure is the use of finite element mesh superposition s refinement to provide spatial adaptivity mesh superposition proves to be particularly advantageous in computationally demanding non linear transient problems since it is faster simpler and more efficient than traditional h refinement schemes numerical examples are provided to demonstrate the performance characteristics of the s adaptive method for quasi static and transient problems with material non linearity

variable kinematic modelling of laminated composite plates a displacement based variable kinematic global local finite element model is developed using hierarchical multiple assumed displacement fields at two different levels 1 at the element level and 2 at the mesh level the displacement field hierarchy contains both a conventional plate expansion 2 d and a full layerwise 3 d expansion depending on the accuracy desired the variable kinematic element can use various terms from the composite displacement field thus creating a hierarchy of different elements having a wide range of kinematic complexity and representing a number of different mathematical models the vkfe is then combined with the mesh superposition technique to further increase the computational efficiency and robustness of the computational algorithm these models are used to analyse a number of laminated composite plate problems that contain localized subregions where significant 3 d stress fields exist e g free edge effects

the fast adaptive composite grid fac method for elliptic equation the fast adaptive composite grid fag method is a systematic process for solving differential boundary value problems fac uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution it can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation this paper develops both the theoretical and practical aspects of fac as it applies to elliptic problems 1 introduction the need for local resolution in physical models occurs frequently in practice special local features of the forcing function operator coefficients boundary and boundary conditions can demand resolution in restricted regions of the domain that is much finer than the required global resolution it is important that the discretization and solution processes account for this locally that is that the local phenomena do not precipitate a dramatic increase in the overall computation unfortunately this objective of efficiently adapting to local features is often in conflict with the solution process equation solvers can degrade or even fail to apply in the presence of varying discretization scales data structures that account for irregular grids can be cumbersome the computer architecture may not be able to effectively account for grid irregularity e g vectorizability may be inhibited etc in fact even the discretization process itself may find difficulty with this objective for finite differences it is problematic to develop accurate difference formulae for irregular grids for finite elements this objective is reflected in the substantial overhead costs needed to automate the discretization the fast adaptive composite grid method fac 11 is a discretization and solution method designed to achieve efficient local resolution by constructing the

uniqueness of generalized schrodinger operators and applications abstract we prove necessary and sufficient conditions on r d r 0 a e so that the operator s 2 1 w1 n has exactly one self adjoint extension on w1 p which generates a sub markovian semigroup on w1 n these conditions are shown to be always fulfilled if d 1 and are verified for a large class of functions if d 1 we also prove an infinite dimensional analogue of this result where r d is replaced by some topological vector space e and the lebesgue measure dx by a gaussian measure the role of is taken by some ornstein uhlenbeck operator with general linear drift and dom s bounded smooth cylinder functions both results are derived as special cases from a general perturbation result we also give the corresponding probabilistic version i e we prove uniqueness for the associated martingale problem we present in some detail applications to the case where is a ground state of a hamiltonian in quantum field theory settling a problem which has been open for some time furthermore we apply our results to prove uniqueness in distribution of the diffusion first constructed by g jona lasinio and p k mitter for the stochastic quantization of f 2 field theory

efficient computation of order and mode of three dimensional stress singularities in linear elasticity by the boundary finite element method the boundary finite element method bfem a novel semi analytical boundary element procedure solely relying on standard finite element formulations is employed for the investigation of the orders and modes of three dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates after a comprehensive literature review and a concise introduction to the standard three dimensional bfem formulation for the static analysis of general unbounded structures we demonstrate the application of the bfem for the computation of the orders and modes of two dimensional and three dimensional stress singularities for several classes of problems within the framework of linear elasticity special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates in all cases the bfem computations agree excellently with available reference results the required computational effort is found to be considerably lower compared to e g standard finite element method fem computations in the case of free laminate corners numerous new results on the occurring stress singularities are presented it is found that free corner problems generally seem to involve a more pronounced criticality than the corresponding free edge situations

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

hypercontractivity and spectral gap of symmetric diffusions with applications to the stochastic ising models abstract we describe some results relating the spectral gap and logarithmic sobolev constants we work initially in the context of symmetric diffusions on a finite dimensional manifold and later apply our results to the analysis of certain infinite systems of mildly interacting diffusions

gap bifurcation for nonlinear perturbations of hill s equation keywords bifurcation nonlinear hill s equation testfunctions reference ana article 1990 002view record in web of science record created on 2008 12 10 modified on 2016 08 08

on the critical fujita exponents for solutions of quasilinear parabolic inequalities abstract this work is devoted to the study of critical blow up phenomena for wide classes of quasilinear parabolic equations and inequalities the model example for this treatment is well known and comes from the theory of turbulent diffusion u t div x u m 1 u x 2 u m 1 u x u q 1 u m 1 1 we obtain the existence of critical blow up exponents for nonnegative weak solutions of inequalities of the type that belong only locally to the corresponding sobolev spaces in the half space r 1 r n n 1 we impose no conditions on the behavior of solutions on the hyperplane t 0 so that the results obtained in the paper are of liouville type the approach developed herein is directly applicable to the study of analogous problems for systems of quasilinear elliptic and parabolic equations and inequalities and its elliptic analogue has recently been developed by the authors

optimization of multilaminated structures using higher order deformation models abstract a refined shear deformation theory assuming a non linear variation for the displacement field is used to develop discrete models for the sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures the structural and sensitivity analysis formulation is developed for a family of c 0 lagrangian elements with eleven nine and seven degrees of freedom per node using a single layer formulation the design sensitivities of structural response for static free vibrations and buckling situations for objective and or constraint functions with respect to ply angles and ply thicknesses are developed these different objectives and or constraints can be generalized displacements at specified nodes hoffman s stress failure criterion elastic strain energy natural frequencies of chosen vibration modes buckling load parameter or the volume of structural material the design sensitivities are evaluated either analytically or semi analytically the accuracy and relative performance of the proposed discrete models are compared and discussed among the developed elements and with alternative models a few illustrative test designs are discussed to show the applicability of the proposed models

the s version of the finite element method for multilayer laminates summary a methodology has been developed to accurately resolve the stress field in the vicinity of free edges as well as the overall response of laminated plates without significantly affecting the computational cost this is accomplished by enriching a set of classical smooth interpolants throughout the thickness direction with co continuous displacement interpolants piecewise continuous strain field in the regions where the most critical behaviour is anticipated co continuity of the displacement field is maintained by imposing homogeneous boundary conditions on the superimposed field in the portion of the boundary which is not contained within the boundary of the problem numerical experiments for both cylindrical bending and uniform extension of cross ply laminates are presented to validate the present formulation

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

uniqueness of generalized schrodinger operators part ii abstract we prove that for h 1 2 loc r d dx 0 dx a e the generalized schrodinger operator s 2 1 dom s c 0 r d has exactly one self adjoint extension on l 2 r d 2 dx which generates a sub markovian semigroup on l 2 r d 2 dx this is based on our previous work where a necessary and sufficient condition on for this to hold was proved but which was only verified to always hold if d 1 we also prove a corresponding result where r d is replaced by an infinite dimensional space and the lebesgue measure by some gaussian measure whose covariance operator has a discrete spectrum

systems of semilinear higher order evolution inequalities on the heisenberg group abstract this paper is devoted to nonexistence results for solutions to the problem skm k u i t k h a i u i h i 1 u i 1 p i 1 h n t 0 1 i m u m 1 u 1 where h is the laplacian on the 2n 1 dimensional heisenberg group h n h is the distance from in h to the origin m 2 k 1 pm 1 p1 m 1 1 and a i l h n 0 1 i m these nonexistence results hold for q 2n 2 less than critical exponents which depend on k pi and i 1 i m for k 1 and 2 we retrieve the results obtained by el hamidi and kirane manuscripta math submitted corresponding respectively to the parabolic and hyperbolic systems in order to show that the obtained exponents are also valid for m 1 we study the scalar case ik k u t k h au h u p where p 1 are real parameters and a l h n 0

multiscale enrichment based on partition of unity a new multiscale enrichment method based on the partition of unity mepu method is presented it is a synthesis of mathematical homogenization theory and the partition of unity method its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible mepu is perfectly suited for enriching the coarse scale continuum descriptions pdes with fine scale features and the quasi continuum formulations with relevant atomistic data numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi continuum formulations copyright 2005 john wiley sons ltd

fast and reliable analysis of free edge stress fields in a thermally loaded composite strip by a layerwise laminate theory a layerwise theory for the analysis of free edge effects in thermally loaded symmetric laminates with arbitrary layups is developed the laminate under investigation is decomposed into an arbitrary number of mathematical layers through the thickness the theory approach employs displacement terms according to classical laminate plate theory which are upgraded by layerwise displacement functions the additional layerwise displacement functions consist of unknown inplane functions and linear thickness terms the principle of minimum potential energy yields the governing euler lagrange equations which allow for a closed form analytical solution for the inplane functions thus characterizing this method as a semi analytical one the underlying boundary conditions of traction free edges are fulfilled in an integral sense the present results are in excellent agreement with accompanying finite element computations copyright 2006 john wiley sons ltd

the quantizing effect of potentials on the critical number of reaction diffusion equations we give an almost complete characterization of the relation between the critical fujita number of the equation u vu up ut 0 and the potentials v behaving like a 1 d x b here a 0 and b is any real number the only type of v not covered is when v x a 1 d x b with b 2 and a is not small it is interesting to note that when v a 1 d x 2 we are at a border line case where the critical exponent depending on a can vary from 1 to for all other v except the ones the theorem does not cover the critical fujita number takes only three discrete values 1 and 1 2n in the euclidean case we also obtain global estimates of schrodinger heat kernels and a liouville theorem for a semilinear elliptic equation

the equivalence of the logarithmic sobolev inequality and the dobrushin shlosman mixing condition given a finite range lattice gas with a compact continuous spin space it is shown cf theorem 1 2 that a uniform logarithmic sobolev inequality cf 1 4 holds if and only if the dobrushin shlosman mixing condition cf 1 5 holds as a consequence of our considerations we also show cf theorems 3 2 and 3 6 that these conditions are equivalent to a statement about the uniform rate at which the associated glauber dynamics tends to equilibrium in this same direction we show cf theorem 3 19 that these ideas lead to a surprisingly strong large deviation principle for the occupation time distribution of the glauber dynamics

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

existence and nonexistence results for higher order semilinear evolution inequalities with critical potential we prove nonexistence results for higher order semilinear evolution equations and inequalities of the form ku tk u x 2u u qin rn 0 where n 22 2 this problem can be seen as a higher order evolution version of the nonlinear wheeler de witt equation which appears in the theory of quantum cosmology in order to show that our result is sharp in the parabolic case we establish the existence of positive solutions to the semilinear equation u t u x 2u uqin rn 0 for 0 the nonexistence results are based on the test function method developed by mitidieri pohozaev tesei and veron the existence result is established by the construction of an explicit global solution of the semilinear parabolic inequality

compactness and the maximal gibbs state for random gibbs fields on a lattice we prove for a general class of gibbsian random field on that the set of tempered gibbs states is compact this class contains the euclidean random fields moreover if the interaction is attractive there is a unique minimal and maximal gibbs state and are unique translation invariant ant and have the global markov property we also prove that uniqueness of the tempered gibbs state is equivalent to the magnetizationsm qx being equal which is true if the pressure is differentiable

large time behavior of reaction diffusion equations with bessel generators abstract we investigate explosion in finite time of one dimensional semilinear equations of the form u t t x 1 2 2 u t x 2 x x x u t x x a x 2 u t x u t 1 x with initial value 0 where c 2 r is positive and a 0 0 are constants in the free case a 0 we provide conditions on under which any positive nontrivial solution is non global in the case a 0 and x x 1 2 r which includes in the special case 1 2 the equation u t t x 1 2 2 u t x 2 x a x 2 u t x u t 1 x we use the feynman kac formula for bessel processes to give conditions on the equation parameters ensuring finite time blowup and existence of nontrivial positive global solutions

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

finite element analysis of inelastic laminated plates using a global local formulation with delamination abstract this work represents the initial step toward the development of an efficient computational framework that can be used to study the response and or failure of laminated composite plates under a variety of loading conditions including complex severe static and dynamic loads the proposed finite element formulation is based on the global local laminated plate theory of williams t o williams a generalized multilength scale non linear composite plate theory with delamination int j solids struct 36 20 1999 3015 3050 which is founded on a generalized superposition of displacement fields associated with different length scales the global field which spans the thickness of the plate and a set of local fields consistent with the layering thickness this global local strategy allows the local layerwise fields to be activated only in regions of critical interest within the computational domain to obtain accurate results in those regions without compromising overall computational efficiency in the present work attention is restricted to the geometrically linear case however the formulation allows treatment of problems involving non linear constitutive behavior and facilitates the incorporation of delamination kinematics several numerical examples are presented to examine the performance characteristics of the proposed global local plate element

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

dobrushin s uniqueness for quantum lattice systems with nonlocal interaction based on dobrushin s fundamental criterion we prove uniqueness of euclidean gibbs states for a certain class of quantum lattice systems with unbounded spins nonharmonic pair potentials and infinite radius of interaction the necessary estimates on dobrushin s coefficients are obtained from the log sobolev inequality which holds for the one point conditional distributions on the infinite dimensional single spin loop spaces

uniqueness and clustering properties of gibbs states for classical and quantum unbounded spin systems we consider quantum unbounded spin systems lattice boson systems in dimensional lattice space z under appropriate conditions on the interactions we prove that in a region of high temperatures the gibbs state is unique is translationally invariant and has clustering properties the main methods we use are the wiener integral representation the cluster expansions for zero boundary conditions and for general gibbs state and explicitly dependent probability estimates for one dimensional systems we show the uniqueness of gibbs states for any value of temperature by using the method of perturbed states we also consider classical unbounded spin systems we derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems

the essential self adjointness of generalized schrodinger operators a necessary and sufficient condition is given for the generalized schrodinger operator a 12 i 1n di di to be essentially self adjoint in l2 dx under general assumptions on and for arbitrary domains in rn in particular if is strictly positive and locally lipschitz continuous on rn then a is essentially self adjoint examples of non essential self adjointness and a complete discussion of the one dimensional case are also given these results have applications to the problem of the essential self adjointness of quantum hamiltonians and to the uniqueness problem of markov processes

dirichlet forms and dirichlet operators for infinite particle systems essential self adjointness we study the dirichlet forms and the associated dirichlet operators for gibbs measures on infinite particle configuration space the dirichlet forms are defined to be gradient type forms by introducing a measurable field of rigged hilbert spaces on the configuration space under mild conditions on the interaction including singular potentials we show that the pre dirichlet operator is symmetric and that the closure of the pre dirichlet form satisfies the markovian property when the interaction is three times differentiable and decreasing sub exponentially we show that the dirichlet operator is essentially self adjoint on a domain consisting of bounded smooth local functions