a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

the equivalence in the dcp model abstract the ever increasing complexity of systems stimulates research in the area of processes equivalences in this paper processes are considered as black boxes characterized by their external interactions only and the equivalences are based on this assumption the equivalence relation induced from the partial order defined in johnston s model of discrete communicating processes is studied with the intention of finding its place within the chain of existing equivalences namely trace equivalence testing equivalence bisimulation and observational equivalence unfortunately this model does not compare easily with the others however a modification to the original model consisting in keeping more information within a process identifier namely all of its immediately performable events and explicitly writing deadlocks gives a new equivalence relation j which is finer than the original one and which has the property of being equivalent to bisimulation

computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

popular matchings in the stable marriage problem we consider the problem of computing a maximum cardinality popular matching in a bipartite graph g a b e where each vertex u a b ranks its neighbors in a strict order of preference such a graph is called an instance of the stable marriage problem with strict preferences and incomplete lists a matching m is popular if for every matching m in g the number of vertices that prefer m to m is at most the number of vertices that prefer m to m every stable matching of g is popular however a stable matching is a minimum cardinality popular matching the complexity of computing a maximum cardinality popular matching was unknown in this paper we show a simple characterization of popular matchings in g a b e we also show a sufficient condition for a popular matching to be a maximum cardinality popular matching we construct a matching that satisfies our characterization and sufficient condition in o mn 0 time where m e and n 0 min a b thus the maximum cardinality popular matching problem in g a b e can be solved in o mn 0 time

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

popular edges and dominant matchings given a bipartite graph g a cup b e with strict preference lists and given an edge e in e we ask if there exists a popular matching in g that contains e we call this the popular edge problem a matching m is popular if there is no matching m such that the vertices that prefer m to m outnumber those that prefer m to m it is known that every stable matching is popular however g may have no stable matching with the edge e in this paper we identify another natural subclass of popular matchings called dominant matchings and show that if there is a popular matching that contains the edge e then there is either a stable matching that contains e or a dominant matching that contains e this allows us to design a linear time algorithm for identifying the set of popular edges when preference lists are complete we show an o n 3 algorithm to find a popular matching containing a given set of edges or report that none exists where n a b

potential integrals associated with quadratic distributions in a triangular domain exact expressions are presented for the potentials at an arbitrary point in space due to two quadratic distributions in a triangular disc these expressions are obtained by means of extensions of the analytical techniques previously developed for evaluating the potential integrals for constant and linear distributions it is shown that the potential due to any quadratic distribution in a triangle may be obtained by using the two expressions derived here together with an expression for the potential corresponding to a linear distribution this latter expression was presented in an earlier paper 1 numerical values obtained through the use of the two expressions are compared with those which result from the numerical evaluation of the potential integrals by triangle quadratures

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

effective potentials in nonlinear polycrystals and quadrature formulae this study presents a family of estimates for effective potentials in nonlinear polycrystals noting that these potentials are given as averages several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields two of these quadrature formulae reduce to known schemes including a recent proposition ponte castaneda proc r soc lond a 471 obtained by completely different means other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments these quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials by means of a reduced order model proposed by the authors nonuniform transformation field analysis it is shown how the quadrature formulae improve on the tangent second order approximation in porous crystals at high stress triaxiality it is found that in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality a quadrature formula of higher order is required

voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials in this paper a new voronoi cell finite element model is developed for solving steady state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials the method is based on the natural discretization of a multiple phase domain into basic structural elements by dirichlet tessellation tessellation process results in a network of polygons called voronoi polygons in this paper formulations are developed for treating these polygons as elements in a finite element mesh furthermore a composite voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials effective material properties are derived for microstructures containing different distributions of second phase

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

a two sided discrete concave market with possibly bounded side payments an approach by discrete convex analysis the marriage model due to gale and shapley gale d l s shapley 1962 college admissions and the stability of marriage amer math monthly69 9 15 and the assignment model due to shapley and shubik shapley l s m shubik 1972 the assignment game i the core internat j game theory1 111 130 are standard in the theory of two sided matching markets we give a common generalization of these models by utilizing discrete concave functions and considering possibly bounded side payments we show the existence of a pairwise stable outcome in our model our present model is a further natural extension of the model examined in our previous paper fujishige s a tamura a general two sided matching market with discrete concave utility functions discrete appl math 154 950 970 and the proof of the existence of a pairwise stable outcome is even simpler than the previous one

a matroid approach to stable matchings with lower quotas in 2010 huang introduced the laminar classified stable matching problem lcsm for short that is motivated by academic hiring this problem is an extension of the well known hospitals residents problem in which a hospital has laminar classes of residents and it sets lower and upper bounds on the number of residents that it can hire in each class against the intuition that variations of the stable matching problem with lower quotas are difficult in general huang proved that lcsm can be solved in polynomial time in this paper we present a matroid based approach to lcsm and we obtain the following results i we solve a generalization of lcsm in which both sides have quotas ii huang raised a question about a polyhedral description of the set of stable assignments in lcsm we give a positive answer for this question by exhibiting a polyhedral description of the set of stable assignments in a generalization of lcsm iii we prove that the set of stable assignments in a generalization of lcsm has a la

multiple scale eigendeformation based reduced order homogenization multiple scale eigendeformation based reduced order homogenization method which provides considerable computational cost saving in comparison to the direct homogenization method has been developed verified against the direct homogenization method and validated against experimental data the salient feature of the method is in the formulation of the unit cell problem in terms of residual free stresses and therefore eliminating the need for costly equilibrium calculations required by the direct homogenization method this is accomplished by introducing discretized eigendeformation fields at different scales which are collectively referred to as eigenstrains and eigenseparations and then precomputing a sequence of elasticity solutions of the unit cell problem subjected to the eigendeformation fields prior to nonlinear analysis

hierarchical model reduction at multiple scales a hierarchical model reduction approach aimed at reducing computational complexity of non linear homogenization at multiple scales is developed the method consists of the following salient features 1 formulation of non linear unit cell problems at multiple scales in terms of eigendeformation modes that a priori satisfy equilibrium equations at multiple scales and thus eliminating the need for costly solution of discretized non linear equilibrium 2 the ability to control the discretization of the eigendeformation modes at multiple scales to maintain desired accuracy and 3 hierarchical solution strategy that requires sequential solution of single scale problems a two scale formulation is verified against an one dimensional model problem for which an analytical solution can be obtained and a three scale formulation is validated against tube crash experiments copyright 2009 john wiley sons ltd

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

on the lattice structure of stable allocations in a two sided discrete concave market the stable allocation model is a many to many matching model in which each pair s partnership is represented by a nonnegative integer this paper establishes a link between two different formulations of this model the choice function model studied thoroughly by alkan and gale and the discrete concave m concave value function model introduced by eguchi fujishige and tamura we show that the choice functions induced from m concave value functions are endowed with consistency persistence and size monotonicity this implies by the result of alkan and gale that the stable allocations for m concave value functions form a distributive lattice with several significant properties such as polarity complementarity and uni size property furthermore we point out that these results can be extended for quasi m concave value functions

popular matchings with two sided preference lists and matroid constraints abstract in this paper we consider the popular matching problem with two sided preference lists and matroid constraints which is based on the variants of the popular matching problem proposed by brandl and kavitha and nasre and rawat we prove that there always exists a popular matching in our model and a popular matching can be found in polynomial time furthermore we prove that if every matroid is weakly base orderable then we can find a maximum size popular matching in polynomial time

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

observation equivalence as a testing equivalence a notion of testing is developed for transition systems with divergence the forms of testing include traces refusals copying and global testing both denotational and operational formulations of testing are given the equivalence based on this notion of testing is shown to coincide with observation equivalence

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

fully implicit formulation of elastoplastic homogenization problem for two scale analysis abstract in this study using a virtual work equation a micro macro kinematic relation and a linearized constitutive relation a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two scale analysis it is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields the computational algorithm developed is then examined by performing a two scale analysis of a holed plate with an elastoplastic micro structure subjected to tensile loading this demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method abstract this paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with voronoi cell vcfem for microstructural modeling the voronoi cell finite element model originates from dirichlet tessellation of a representative material element or a base cell in the microstructure homogenized material coefficients for a global displacement finite element model are generated by vcfem analysis using periodic boundary conditions on the base cell following the macroscopic analysis the local vcfem analysis is implemented to depict the true evolution of microstructural stresses and strains various numerical examples are executed for validating the effectiveness of vcfem macro micro modeling of elastic materials the effect of size shape orientation and distribution of heterogeneities on the local and global response are examined

reduced order computational continua abstract we present a new multiscale approach hereafter referred to as reduced order computational continua rc 2 that possesses computational efficiency of phenomenological models for heterogeneous media with accuracy inherent to generalized and nonlocal continua models the rc 2 approach introduces no scale separation makes no assumption about infinitesimality of the fine scale structure does not require higher order continuity introduces no new degrees of freedom is free of higher order boundary conditions and exploits a pre computed material database to effectively solve a unit cell representative volume problem it features three building blocks i the nonlocal quadrature scheme ii the coarse scale stress function and iii the residual free fields the nonlocal quadrature scheme permits nonlocal interactions to extend over finite neighborhoods and thus introduces nonlocality into the two scale integrals employed in the multiple scale asymptotic expansion methods or alternatively into the hill mandel macrohomogeneity condition the coarse scale stress function which replaces the classical notion of coarse scale stress being the average of fine scale stresses is constructed to express the governing equations in terms of coarse scale fields only finally the residual free fields are constructed to avoid costly discrete equilibrium solution of the unit cell problems which is known to be the bottleneck of multiscale computations

a context dependent equivalence between processes abstract in recent years several equivalences between nondeterministic and concurrent processes have been proposed in order to capture different notions of the extensional behaviour of a process usually the equivalences are congruences with respect to the process constructing operations in order to support hierarchic development of systems with the purpose of achieving more flexible hierarchic development methods we suggest parametrizing the equivalences with information about contexts we carry out the suggestion in full for the bisimulation equivalence which we parameterize with a special type of context information called environments as a main theorem we offer a useful characterization of the information ordering on environments also a modal characterization of the parameterized bisimulation equivalence is presented

a size popularity tradeoff in the stable marriage problem given a bipartite graph g mathcal a cup mathcal b e where each vertex ranks its neighbors in a strict order of preference the problem of computing a stable matching is classical and well studied a stable matching has size at least frac 1 2 m max where m max is a maximum size matching in g and there are simple examples where this bound is tight it is known that a stable matching is a minimum size popular matching a matching m is said to be popular if there is no matching where more vertices are better off than in m in this paper we show the first linear time algorithm for computing a maximum size popular matching in g a maximum size popular matching is guaranteed to have size at least frac 2 3 m max and this bound is tight we then consider the following problem is there a maximum size matching m that is popular within the set of maximum size matchings in g that is m m max and there is no maximum size matching that is more popular than

nonlinear microstrain theories a hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes rotation and straining of an underlying microstructure an increase in the number of degrees of freedom represents a refinement of the material description in addition to available nonlinear cosserat and micromorphic theories general formulations of elastoviscoplastic behaviour are proposed for microdilatation and microstretch continua a microstrain theory is introduced that is based on six additional degrees of freedom describing the pure straining of the microstructural element in each case balance equations and boundary conditions are derived decompositions of the finite strain measures into elastic and plastic parts are provided the formulation of finite deformation elastoviscoplastic constitutive equations relies on the introduction of the free energy and dissipation potentials thus complying with requirements of continuum thermodynamics some guidelines for the selection of a suitable higher order model for a given material close the discussion

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

finite deformation plasticity for composite structures computational models and adaptive strategies abstract we develop computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures a nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the portion of the macro domain where modeling errors are small whereas elsewhere a more detailed mathematical model based on a piecewise constant approximation of eigenstrains and elastic concentration factors is utilized the methodology is developed within the framework of statistically homogeneous composite material and local periodicity assumptions

a generalized polymatroid approach to stable matchings with lower quotas classified stable matching proposed by huang describes a matching model between academic institutes and applicants in which each institute has upper and lower quotas on classes i e subsets of applicants huang showed that the problem to decide whether there exists a stable matching or not is np hard in general on the other hand he showed that the problem is solvable if classes form a laminar family for this case fleiner and kamiyama gave a concise interpretation in terms of matroids and showed the lattice structure of stable matchings in this paper we introduce stable matchings on generalized matroids extending the model of fleiner and kamiyama we design a polynomial time algorithm which finds a stable matching or reports the nonexistence we also show that the set of stable matchings if nonempty forms a lattice with several significant properties furthermore we extend this structural result to the polyhedral framework which we call stable allocations on generalized polymatroids

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

a unified procedure for construction of theories of deformable media ii generalized continua in contrast to classical theories discussed in the accompanying paper part i the present paper deals exclusively with generalized continua a term that refers to a body embedded in a euclidean three dimensional space with each of its material points endowed with additional kinematic structure such generalized continua are conveniently identified here by cosserat or directed continua in which the additional structure is represented by independent director fields and the material domain of the body manifold is classified according to the four categories a a three dimensional volume b a two dimensional surface c a one dimensional space curve and d a point in the derivation of a thermomechanical theory for each of these categories we use the same unified procedure as in part i but now the various energies that enter the balance of energy must be modified to include additional kinetic ingredients new theories of this kind have increasingly provided over the last three decades effective means of formulating and studying new behaviour of materials in both fluid and solid mechanics that were not previously possible by the classical theories our attention is first focused in the development of the theory for the first category and this is discussed in two stages first for a cosserat continuum with a single director and then for n directors our derived results include for the first time a derivation from the balance of energy of balances of director momenta and balances of entropies in the presence of more than one independent temperature field the treatments of categories b to d are somewhat shorter since their developments are formally similar to that of category a

a fixed point approach to stable matchings and some applications we describe a fixed point based approach to the theory of bipartite stable matchings by this we provide a common framework that links together seemingly distant results like the stable marriage theorem of gale and shapley the mendelsohn dulmage theorem the kundu lawler theorem tarski s fixed point theorem the cantor bernstein theorem pym s linking theorem or the monochromatic path theorem of sands et al in this framework we formulate a matroid generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings based on the theory of lattice polyhedra and blocking polyhedra we extend results of vande vate and rothblum on the bipartite stable matching polytope

multi scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme a gradient enhanced computational homogenization procedure that allows for the modelling of microstructural size effects is proposed within a general non linear framework in this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element rve this enables us to incorporate the microstructural size and to account for non uniform macroscopic deformation fields within the microstructural cell every microstructural constituent is modelled as a classical continuum and the rve problem is formulated in terms of standard equilibrium and boundary conditions from the solution of the microstructural boundary value problem the macroscopic stress tensor and the higher order stress tensor are derived based on an extension of the hill mandel condition this automatically delivers the microstructurally based constitutive response of the higher order macro continuum and deals with the microstructural size in a natural way several examples illustrate the approach particularly the microstructural size effects

computational continua revisited summary in the recent paper fish and kuznetsov introduced the so called computational continua c2 approach which is a variant of the higher order computational homogenization that does not require higher order continuity introduces no new degrees of freedom and is free of higher order boundary conditions in a follow up paper on reduced order computational continua the c2 formulation has been enhanced with a model reduction scheme based on construction of residual free fields to yield a computationally efficient framework coined as rc2 the original c2 formulations were limited to rectangular and box elements the primary objectives of the present manuscript is to revisit the original formulation in three respects i consistent formulation of boundary conditions for unit cells subjected to higher order coarse scale fields ii effective solution of the unit cell problem for lower order approximation of eigenstrains and iii development of nonlocal quadrature schemes for general two dimensional quad and triangle and three dimensional hexahedral and tetrahedral elements copyright 2014 john wiley sons ltd

on the operational semantics of nondeterminism and divergence abstract an operational model of nondeterministic processes coupled with a novel theory of divergence is presented the operational model represents internal nondeterminism without using explicit internal transitions here the notion of internal state effectively replaces the familiar notion of internal transition giving rise to an alternative operational view of processes the weak process roughly a weak process is a collection of stable internal states together with a set of transitions each of which is defined from an internal state to another weak process internal nondeterminism arises from such refinement of processes into multiple internal states a simple extension to the basic weak process model gives rise to an elaborate operational theory of divergence according to this theory the ability of a process to undertake an infinite internal computation which is pathological or persistent is distinguished from its ability to undertake an infinite internal computation which is not although applicable to process algebraic languages with an internal action construct the resulting model is most suitable for supplying operational semantics to process algebras which express internal nondeterminism by an internal choice construct the distinction between the two forms of divergence is in particular taken into account when the hiding construct of such a process algebra is assigned a weak process semantics

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material