three dimensional space partition based on the first laplacian eigenvalues in cells we determine a partition of three dimensional space into cells by minimization of the sum of the first laplacian eigenvalues over the cells this partitioning scheme emerges as a stationary state of a reaction diffusion process taking place in a system of n different species which mutually annihilate and simultaneously are duplicated in an autocatalytic reaction so that the number of particles is kept constant and equal for each species the system is considered in the limit of strong reactivity so that the species separate each other into cells with well defined sharp boundaries for a given n and fixed sizes of a periodic simulation box this partition minimizes the aforementioned sum of eigenvalues further minimization is done by changing n and the side ratio of the periodic box the global minimum is obtained for the structure with a15 symmetry similar to the weaire phelan foam depending on n and the side ratio there are also many local minima in particular hcp hexagonal close packed fcc face centered cubic the kelvin structure and frank kasper sigma phase

numerical implementation of multiplicative elasto plasticity into assumed strain elements with application to shells at large strains alternative formulations of isotropic large strain elasto plasticity are presented which are especially well suited for the implementation into assumed strain elements based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three distinct eigenvalue problems related to the reference intermediate and current configuration are investigated these eigenvalue problems are connected by similarity transformations which preserve the eigenvalues they play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation the developed constitutive procedures rely on the right cauchy green tensor or equivalently on the green lagrangian strain tensor rather than the deformation gradient consequently they can be applied directly to assumed strain elements specifically we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious locking effects

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

on a non linear formulation for curved timoshenko beam elements considering large displacement rotation increments summary an incremental total lagrangian formulation for curved beam elements that includes the effect of large rotation increments is developed a complete and symmetric tangent stiffness matrix is obtained and the numerical results show in general an improvement over the standard formulation where the assumption of infinitesimal rotation increments is made in the derivation of the tangent stiffness matrix

asymptotic error bounds for a class of interpolatory quadratures interpolatory quadrature formulae based on the zeros of ultraspherical polynomials of degree n are considered the corresponding asymptotic error bounds are found n to infty for the evaluation of the integrals int 1 1 1 x sigma dx and int 1 1 x x 0 sigma dx 1 x 0 1

a finite element formulation for finite strain elasto plastic analysis based on mixed interpolation of tensorial components abstract a quadrilateral finite element formulation for modelling finite strain elasto plastic deformation processes is presented the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of the associated von mises flow rule the hencky or logarithmic strain measure is used in the strain energy function the quadrilateral element is developed using displacements interpolation and interpolation of the hencky strain tensor covariant components a consistent linearization is developed obtaining a symmetric stiffness matrix

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

minimal dirichlet energy partitions for graphs motivated by a geometric problem we introduce a new nonconvex graph partitioning objective where the optimality criterion is given by the sum of the dirichlet eigenvalues of the partition components a relaxed formulation is identified and a novel rearrangement algorithm is proposed which we show is strictly decreasing and converges in a finite number of iterations to a local minimum of the relaxed objective function our method is applied to several clustering problems on graphs constructed from synthetic data mnist handwritten digits and manifold discretizations the model has a semisupervised extension and provides a natural representative for the clusters as well

a multiphase shape optimization problem for eigenvalues qualitative study and numerical results in thie paper we consider the following multiphase shape optimization problem min big sum i 1 h lambda 1 omega i alpha omega i omega i open omega i subset d omega i cap omega

numerical integration in the presence of an interior singularity abstract the convergence of sequences of integration rules applied to an improperly integrable function with an interior singularity is investigated the rules studied include the gauss jacobi rules and the interpolatory integration rules based on the zeros of 1 x 2 m p n 2m x m 0 1 for certain values of and the results are then applied to the study of the convergence of hunter s method for cauchy principal value integrals

optimal partitions for eigenvalues we introduce a new numerical method for approximating partitions of a domain minimizing the sum of dirichlet laplacian eigenvalues of any order first we prove the equivalence of the original problem and a relaxed formulation based on measures using this result we build a numerical algorithm to approximate optimal configurations we describe numerical experiments aimed at studying the asymptotic behavior of optimal partitions with large numbers of cells

asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity for functions with an interior singularity the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler euler maclaurin type formulae applying this method to certain classes of functions such as for example f x h x x u where 1 with a sufficiently smooth functionh we obtain the main term of the error expansion for quadrature rules of ultraspherical type

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

entropic properties of d dimensional rydberg systems abstract the fundamental information theoretic measures the renyi r p and tsallis t p entropies p 0 of the highly excited rydberg quantum states of the d dimensional d 1 hydrogenic systems which include the shannon entropy p 1 and the disequilibrium p 2 are analytically determined by use of the strong asymptotics of the laguerre orthogonal polynomials which control the wavefunctions of these states we first realize that these quantities are derived from the entropic moments of the quantum mechanical probability r densities associated to the rydberg hydrogenic wavefunctions n l r which are closely connected to the l p norms of the associated laguerre polynomials then we determine the n asymptotics of these norms in terms of the basic parameters of our system the dimensionality d the nuclear charge and the hyperquantum numbers n l of the state by use of recent techniques of approximation theory finally these three entropic quantities are analytically and numerically discussed in terms of the basic parameters of the system for various particular states

the optimal centroidal voronoi tessellations and the gersho s conjecture in the three dimensional space optimal centroidal voronoi tessellations have important applications in many different areas such as vector quantization data and image processing clustering analysis and resource management in the three dimensional euclidean space they are also useful to the mesh generation and optimization in this paper we conduct extensive numerical simulations to investigate the asymptotic structures of optimal centroidal voronoi tessellations for a given domain such a problem is intimately related to the famous gersho s conjecture for which a full proof is still not available we provide abundant evidence to substantiate the claim of the conjecture the body centered cubic lattice or par6 based centroidal voronoi tessellation has the lowest cost or energy per unit volume and is the most likely congruent cell predicted by the three dimensional gersho conjecture more importantly we probe the various properties of this optimal configuration including its dual triangulations which bear significant consequences in applications to three dimensional high quality meshing

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

a co rotational quasi conforming 4 node resultant shell element for large deformation elasto plastic analysis abstract a co rotational quasi conforming formulation of a 4 node stress resultant shell element is presented for non linear analysis of plate and shell structures the tangent stiffness matrix in this quasi conforming formulation is explicitly integrated this makes the element computationally efficient in incremental non linear analysis it includes drilling degrees of freedom which improves membrane behavior and allows the modeling of stiffened plates and shells it is also free of shear locking behavior the formulation of the geometrical stiffness is derived using the full definition of green strain tensor the inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells the stresses are accurately taken at the nodal points without extrapolation the plasticity is traced by applying the von mises yield condition and prandtl reuss flow rule to discrete points through the thickness the multi layered approach is based on equally spaced stations including extreme fibers a modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part numerous tests are carried out for the non linear validation of present 4 node shell element and the results are in good agreement with references

an optimal partition problem related to nonlinear eigenvalues we extend to the case of many competing densities the results of the paper ann inst h poincare 6 2002 more precisely we are concerned with an optimal partition problem in n dimensional domains related to the method of nonlinear eigenvalues introduced by nehari acta math 105 1961 we prove existence of the minimal partition and some extremality conditions moreover in the case of two dimensional domains we give an asymptotic formula near the multiple intersection points finally we show some connections between the variational problem and the behavior of competing species systems with large interaction

product integration for the linear transport equation in slab geometry in this paper we present a product quadrature rule for the discretization of the well known linear transport equation in slab geometry in particular we give an algorithm for constructing the weights of the rule and prove that the order of convergence iso n 3 0 small as we like numerical examples are given and our formula is also compared with product simpson rules finally we examine a nystrom method based on our quadrature

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

anisotropic elastic plastic analysis of shells at large strains a comparison of multiplicative and additive approaches to enhanced finite element design and constitutive modelling the article presents new aspects of large strain anisotropic elastoplastic analyses of shells on the side of computational shell analysis we focus on recently developed brick type mixed finite shell elements based on trilinear displacement interpolations equipped with enhanced strain modes and shell typical assumed strain modifications here we compare two classes of this shell element design based on a multiplicative and an additive definition of an enhanced strain measure respectively furthermore for both types of continuum based shell elements we outline unified interfaces to strain driven constitutive stress update algorithms of anisotropic finite plasticity on the side of computational plasticity we investigate two classes of constitutive models suitable for the description of anisotropic elastoplastic response at finite strains the first framework uses a multiplicative definition of an elastic strain measure based on a plastic map the second an additively defined elastic strain measure based on a plastic metric both constitutive frameworks use hencky type logarithmic strain measures and are specified to a model problem of orthotropic elastic plastic response of a standard material the algorithmic treatment of the two constitutive models is based on an incremental variational formulation that defines the stresses and consistent tangent moduli in terms of a function evaluation we compare the performances of the two finite element formulations and the two constitutive models by means of numerical simulations of sheet drawing processes for the range of metal plasticity at moderate strains it is shown that results obtained with the different approaches are close to each other while the additive approaches provide simpler and more efficient settings copyright 2004 john wiley sons ltd

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

a mixed shell formulation accounting for thickness strains and finite strain 3d material models a non linear quadrilateral shell element for the analysis of thin structures is presented the reissner mindlin theory with inextensible director vector is used to develop a three field variational formulation with independent displacements stress resultants and shell strains the interpolation of the independent shell strains consists of two parts the first part corresponds to the interpolation of the stress resultants within the second part independent thickness strains are considered this allows incorporation of arbitrary non linear 3d constitutive equations without further modifications the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison with other element formulations we present results for finite strain elasticity inelasticity bifurcation and post buckling problems copyright 2007 john wiley sons ltd

proof of the honeycomb asymptotics for optimal cheeger clusters abstract we prove that in the limit as k the hexagonal honeycomb solves the optimal partition problem in which the criterion is minimizing the largest among the cheeger constants of k mutually disjoint cells in a planar domain as a by product the same result holds true when the cheeger constant is replaced by the first robin eigenvalue of the laplacian

an annihilating branching particle model for the heat equation with average temperature zero we consider two species of particles performing random walks in a domain in d with reflecting boundary conditions which annihilate on contact in addition there is a conservation law so that the total number of particles of each type is preserved when the two particles of different species annihilate each other particles of each species chosen at random give birth we assume initially equal numbers of each species and show that the system has a diffusive scaling limit in which the densities of the two species are well approximated by the positive and negative parts of the solution of the heat equation normalized to have constant l1 norm in particular the higher neumann eigenfunctions appear as asymptotically stable states at the diffusive time scale

a pseudo layered elastic plastic flat shell finite element abstract a three node c0 type layered flat shell finite element is developed for the analysis of large elastic plastic deformations in plate and shell structures the system equations are derived by using virtual work principle and the updated lagrangian formulation material is assumed to be isotropic and rate insensitive obeying j2 flow rule the displacement field assumption of the min3 plate bending element is employed a layered structure is used to model through the thickness distribution of elastic and plastic zones the finite element results for three nonlinear plate bending problems are compared with experimental results to verify the accuracy of the formulation

a zador like formula for quantizers based on periodic tilings we consider zador s 1963 1966 1982 asymptotic formula for the distortion rate function for a variable rate vector quantizer in the high rate case this formula involves the differential entropy of the source the rate of the quantizer in bits per sample and a coefficient g which depends on the geometry of the quantizer but is independent of the source we give an explicit formula for g in the case when the quantizing regions form a periodic tiling of n dimensional space in terms of the volumes and second moments of the voronoi cells as an application we show extending earlier work of kashyap and neuhoff see ibid vol 47 p 2538 2383 2001 that even a variable rate three dimensional quantizer based on the a15 structure is still inferior to a quantizer based on the body centered cubic lattice we also determine the smallest covering radius of such a structure

computing the ground state solution of bose einstein condensates by a normalized gradient flow in this paper we present a continuous normalized gradient flow cngf and prove its energy diminishing property which provides a mathematical justification of the imaginary time method used in the physics literature to compute the ground state solution of bose einstein condensates bec we also investigate the energy diminishing property for the discretization of the cngf two numerical methods are proposed for such discretizations one is the backward euler centered finite difference befd method the other is an explicit time splitting sine spectral tssp method energy diminishing for befd and tssp for the linear case and monotonicity for befd for both linear and nonlinear cases are proven comparison between the two methods and existing methods e g crank nicolson finite difference cnfd or forward euler finite difference fefd shows that befd and tssp are much better in terms of preserving the energy diminishing property of the cngf numerical results in one two and three dimensions with magnetic trap confinement potential as well as a potential of a stirrer corresponding to a far blue detuned gaussian laser beam are reported to demonstrate the effectiveness of befd and tssp methods furthermore we observe that the cngf and its befd discretization can also be applied directly to compute the first excited state solution in bec when the initial data is chosen as an odd function

a new rotation free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries abstract this paper presents a general non linear computational formulation for rotation free thin shells based on isogeometric finite elements it is a displacement based formulation that admits general material models the formulation allows for a wide range of constitutive laws including both shell models that are extracted from existing 3d continua using numerical integration and those that are directly formulated in 2d manifold form like the koiter canham and helfrich models further a unified approach to enforce the g 1 continuity between patches fix the angle between surface folds enforce symmetry conditions and prescribe rotational dirichlet boundary conditions is presented using penalty and lagrange multiplier methods the formulation is fully described in the natural curvilinear coordinate system of the finite element description which facilitates an efficient computational implementation it contains existing isogeometric thin shell formulations as special cases several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation the presented constitutive models in particular the simple mixed koiter model that does not require any thickness integration show excellent performance even for large deformations

convergence of product integration rules for functions with interior and end point singularities over bounded and unbounded intervals the convergence of product integration rules based on gaussian quadrature points is investigated for functions with interior and endpoint singularities over bounded and unbounded intervals the investigation is based on a new convergence result for lagrangian interpolation and gaussian quadrature of singular integrands

three dimensional corotational framework for elasto plastic analysis of multilayered composite shells acontinuum basedlayerwiseshear deformablee niteelementformulationispresentedforelasto plasticanalysis oflayered compositesshells theproposed formulationiscast in a corotationalcone guration for e nitedeformation analysis the elasto plastic constitutive equations that are based on rate independent deviatoric plasticity are also written in the corotational kinematic framework issues of covariance and spatial invariance are addressed and an appropriate stress updating strategy is proposed numerical examples are presented to demonstrate the range of applicability of the proposed framework for bending dominated response of elasto plastic layered composite shells nomenclature b body force vector c e fourth order elastic modulus tensor c i n 1 tangent modului consistent with the radial return algorithm d p plastic strain rate tensor e deviatoric strain tensor e p equivalent plastic strain fn 1 incremental deformation gradient ft x deformation gradient f ae q von mises pressure insensitive yield condition a e p hardening rule for back stress i identity matrix

a diffusion generated method for computing dirichlet partitions abstract a dirichlet k partition of a closed d dimensional surface is a collection of k pairwise disjoint open subsets such that the sum of their first laplace beltrami dirichlet eigenvalues is minimal in this paper we develop a simple and efficient diffusion generated method to compute dirichlet k partitions for d dimensional flat tori and spheres for the two dimensional flat torus for most values of k 3 9 11 12 15 16 and 20 we obtain hexagonal honeycombs for the three dimensional flat torus and k 2 4 8 16 we obtain the rhombic dodecahedral honeycomb the weaire phelan honeycomb and kelvin s tessellation by truncated octahedra for the four dimensional flat torus for k 4 we obtain a constant extension of the rhombic dodecahedral honeycomb along the fourth direction and for k 8 we obtain a 24 cell honeycomb for the two dimensional sphere we also compute dirichlet partitions for k 3 7 9 10 12 14 20 our computational results agree with previous studies when a comparison is available as far as we are aware these are the first results for dirichlet partitions of the four dimensional flat torus

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

minimization of the renyi entropy production in the stationary states of the brownian process with matched death and birth rates we analyze the fleming viot process the system is confined in a box whose boundaries act as a sink of brownian particles the death rate at the boundaries is matched by the branching birth rate in the system and thus the number of particles is kept constant we show that such a process is described by the renyi entropy whose production is minimized in the stationary state the entropy production in this process is a monotonically decreasing function of time irrespective of the initial conditions the first laplacian eigenvalue is shown to be equal to the renyi entropy production in the stationary state as an example we simulate the process in a two dimensional box

on quantization with the weaire phelan partition until recently the solution to the kelvin problem of finding a partition of r sup 3 into equal volume cells with the least surface area was believed to be tessellation by the truncated octahedron in 1994 d weaire and r phelan described a partition that outperformed the truncated octahedron partition in this respect this raises the question of whether the weaire phelan wp partition can outperform the truncated octahedron partition in terms of normalized moment of inertia nmi thus providing a counterexample to gersho s conjecture that the truncated octahedron partition has the least nmi among all partitions of r sup 3 in this correspondence we show that the effective nmi of the wp partition is larger than that of the truncated octahedron partition we also show that if the wp partition is used as the partition of a three dimensional 3 d vector quantizer vq with the corresponding codebook consisting of the centroids of the cells then the resulting quantization error is white we then show that the effective nmi of the wp partition cannot he reduced by passing it through an invertible linear transformation another contribution of this correspondence is a proof of the fact that the quantization error corresponding to an optimal periodic partition is white which generalizes a result of zamir and feder 1996

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

threshold dynamics for networks with arbitrary surface tensions we present and study a new algorithm for simulating the n phase mean curvature motion for an arbitrary set of isotropic surface tensions the departure point is the threshold dynamics algorithm of merriman bence and osher for the two phase case a new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of n phases for arbitrary surface tensions and arbitrary isotropic mobilities for a large class of surface tensions the algorithm is shown to be consistent in the sense that at every time step it decreases an energy functional that is an approximation in the sense of gamma convergence of the interfacial energy a broad range of numerical tests shows good convergence properties an important application is the motion of grain boundaries in polycrystalline materials it is also established that the above mentioned large class of surface tensions contains the read shockley surface tensions both in the two dimensional and three dimensional settings 2015 wiley periodicals inc

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

minimization of the renyi entropy production in the space partitioning process the spontaneous division of space in fleming viot processes is studied in terms of non extensive thermodynamics we analyze a system of n different types of brownian particles confined in a box particles of different types annihilate each other when they come into close contact each process of annihilation is accompanied by a simultaneous nucleation of a particle of the same type so that the number of particles of each component remains constant the system eventually reaches a stationary state in which the available space is divided into n separate subregions each occupied by particles of one type within each subregion the particle density distribution minimizes the renyi entropy production we show that the sum of these entropy productions in the stationary state is also minimized i e the resulting boundaries between different components adopt a configuration which minimizes the total entropy production the evolution of the system leads to decreasing of the total entropy production monotonically in time irrespective of the initial conditions in some circumstances the stationary state is not unique the entropy production may have several local minima for different configurations in the case of a rectangular box the existence and stability of different stationary states are studied as a function of the aspect ratio of the rectangle

analysis of thin shells using anisotropic polyconvex energy densities in this contribution the numerical framework for the simulation of anisotropic thin shells is presented on the basis of polyconvex strain energy functions the nonlinear shell theory is based on the reissner mindlin kinematic along with inextensible director vectors for the variational framework we consider a three field variational functional taking into account independent displacements enhanced strains and stress resultants where the latter field is eliminated by the evaluation of some orthogonality conditions the iterative enforcement of the zero normal stress condition at the integration points allows consideration of arbitrary three dimensional constitutive equations due to the fact that we are interested in fiber reinforced materials we consider an additive structure of the energy decoupled in an isotropic part for the matrix and a superposition of transversely isotropic parts for the fiber families for the representation of the anisotropy we use the concept of structural tensors and formulate the strain energy function in terms of principal and mixed invariants of the right cauchy green tensor and the structural tensor in order to guarantee the existence of minimizers we focus on polyconvex strain energy functions the anisotropy effect is documented in several representative examples

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation