further results for enhanced strain methods with isoparametric elements abstract in this contribution the enhanced strain finite element method is investigated further with particular attention given to the analysis of the method for isoparametric elements it is shown that the results established earlier b d reddy and j c simo stability and convergence of a class of enhanced strain methods siam j numer anal 32 1995 in press for affine equivalent meshes carry over to the case of isoparametric elements that is the method is stable and convergent provided that a set of three criteria is satisfied and for plane elements at least convergence is at the same rate as in the standard method a procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress with regard to computations a new basis for enhanced strains is introduced and numerical results are presented for this basis as well as for existing bases the results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches

quadrilateral mesh revisited several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent the effect of the bi section condition on the degenerate mesh conditions is also checked

a 3d brick element based on hu washizu variational principle for mesh distortion in order to improve the accuracy of the mixed element for irregular meshes a penalty equilibrating 3d mixed element based on the hu washizu variational principle has been proposed in this paper the key idea in this work is to introduce a penalty term into the hu washizu three field functional which can enforce the stress components to satisfy the equilibrium equations in a weak form compared with the classical hybrid and mixed elements this technique can efficiently reduce the sensitivity of the element to mesh distortion the reason for the better results of this penalty technique has been investigated by considering a simple 2d problem from this investigation it has been found that the penalty parameter here plays the role of a scaling factor to reduce the influence of the parasitic strain or stress which is similar to the devised selective scaling factor proposed by sze furthermore compared with the hybrid stress element the proposed element based on the three field variational principle is more suitable for material non linear analysis numerical examples have demonstrated the improved performance of the present element especially in stress computation when fem meshes are irregular copyright 2002 john wiley sons ltd

one way communication complexity and the neciporuk lower bound on formula size in this paper the neciporuk method for proving lower bounds on the size of boolean formulas is reformulated in terms of one way communication complexity we investigate the settings of probabilistic formulas nondeterministic formulas and quantum formulas in all cases we can use results about one way communication complexity to prove lower bounds on formula size the main results regarding formula size are as follows we show a polynomial size gap between probabilistic quantum and deterministic formulas a near quadratic gap between the sizes of nondeterministic formulas with limited access to nondeterministic bits and nondeterministic formulas with access to slightly more such bits and a near quadratic lower bound on quantum formula size furthermore we give a polynomial separation between the sizes of quantum formulas with and without multiple read random inputs the lower bound methods for quantum and probabilistic formulas employ a variant of the neciporuk bound in terms of the vapnik chervonenkis dimension to establish our lower bounds we show optimal separations between one way and two way protocols for limited nondeterministic and quantum communication complexity and we show that zero error quantum one way communication complexity asymptotically equals deterministic one way communication complexity for total functions

a unified theory for formulation of hybrid stress membrane elements a theory is proposed in this paper to explain in a unified manner the three rational approaches using the incompatible displacements u in the hybrid element formulation limited to the plane stress case the theory suggests that the introduction of u is to constrain the total value of the invariant i2 x y of the assumed stresses over the element to zero in the plane stress case this is the well known condition for the stress distributions to be independent of the elastic constants of the material the theory proposed is also used to explain the closeness of the performances of the four 4 node hybrid stress membrane elements 5 i 5 ii 5 a and 5 c that have been developed previously the differences among them are shown to be of the second degree in the distortion measures of the element shape when they are compared on the basis of the non vanishing total value of i2 of their respectively adopted assumed stress field several numerical examples are used to verify and to illustrate the proposed theory

interaction in quantum communication in some scenarios there are ways of conveying information with many fewer even exponentially fewer qubits than possible classically moreover some of these methods have a very simple structure they involve only few message exchanges between the communicating parties it is therefore natural to ask whether every classical protocol may be transformed to a simpler quantum protocol one that has similar efficiency but uses fewer message exchanges we show that for any constant k there is a problem such that its k 1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity this in particular proves a round hierarchy theorem for quantum communication complexity and implies via a simple reduction an omega n1k lower bound for k message quantum protocols for set disjointness for constant k enroute we prove information theoretic lemmas and define a related measure of correlation the informational distance that we believe may be of significance in other contexts as well

new limits to classical and quantum instance compression given an instance of a hard decision problem a limited goal is to compress that instance into a smaller equivalent instance of a second problem as one example consider the problem where given

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

the space complexity of recognizing well parenthesized expressions in the streaming model the index function revisited we show an p n t lower bound for the space required by any unidirectional constanterror randomized t pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well parenthesized this proves a conjecture due to magniez mathieu and nayak 2009 and rigorously establishes the peculiar power of bi directional streams over unidirectional ones observed in the algorithms they present the lower bound is obtained by analysing the information that is necessarily revealed by the players about their respective inputs in a two party communication protocol for a variant of the index function

new stress assumption for hybrid stress elements and refined four node plane and eight node brick elements a new stress assumption for hybrid stress elements is presented generalized incompatible modes are proposed and incorporated into the constraint equations for assumed stresses the physical meaning of the resulting constraint equations is discussed the present stress assumption which can consider the mesh distortion more rigorously is based on the physical interpretation of the role of the generalized incompatible modes and substantiated with simple mesh distortion measures defined in this paper the stress assumption is adapted to the previous four node hybrid stress element 5 i and the eight node hybrid stress brick element 18 which results in a new four node plane element m5 and an new eight node brick element m18 numerical results show that the refined elements are noticeable in low sensitivity to mesh distortion and in high accuracy of stresses 1997 john wiley sons ltd

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

optimal control problem for viscous cahn hilliard equation abstract this paper is concerned with the viscous cahn hilliard equation which arises in the dynamics of viscous first order phase transitions in cooling binary solutions the optimal control under boundary condition is given and the existence of optimal solution to the equation is proved

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

optimal control for parabolic variational inequalities consider the problem of maximizing a functional that depends on a control function k x t and on the solution u x t of a parabolic variational inequality with k appearing in the data necessary conditions are obtained for the maximizers k 0 x t and the structure of k 0 is then analyzed an application to the stefan problem is given

the learnability of quantum states traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n but using ideas from computational learning theory we show that one can do exponentially better in a statistical setting in particular to predict the outcomes of most measurements drawn from an arbitrary probability distribution one needs only a number of sample measurements that grows linearly with n this theorem has the conceptual implication that quantum states despite being exponentially long vectors are nevertheless reasonable in a learning theory sense the theorem also has two applications to quantum computing first a new simulation of quantum one way communication protocols and second the use of trusted classical advice to verify untrusted quantum advice

finite rotation quadrilateral element for multi layer beams the paper presents the finite rotations beam equations derived on use of the generalized reissner hypothesis with a scalar parameter for the transverse extension the beam strain and change of curvature measures are obtained from the right stretch strain and the virtual work is given for biot type stress and couple resultants the strain energy for the first order isotropic elastic material is assumed in terms of the right stretch strain and constitutive equations for the beam stress and couple resultants are derived two finite rotation elements are developed from the derived beam equations a beam element with the transverse stretch and a quadrilateral element first the beam element with the uniformly under integrated tangent operator is developed next the formula linking the middle line variables and the interface variables of the beam is introduced consistently with the generalized reissner kinematics linearization of this formula is performed and the derived tangent operator is used to convert the two node beam element to a four node quadrilateral both the finite elements have been tested on several numerical examples some of highly non linear characteristics and their accuracy is very good it has been established that the quadrilateral element which is intended for applications to multi layer beams performs very well for high elemental aspect ratios and can therefore be applied to modelling of very thin layers copyright 1999 john wiley sons ltd

a consistent approach for mixed stress finite element formulations in linear elastodynamics abstract in this paper a mixed stress formulation for linear elastodynamic analysis based on a modified hellinger reissner functional and a consistent approach for selecting finite element approximations are presented the key idea in this new approach is to choose stress approximations by taking into account for suitable modes to equilibrate inertia forces feasibility and effectiveness of the proposed approach are numerically verified through three benchmark tests

optimal periodic control for the two phase stefan problem consider the two phase stefan problem in a domain x t x in d 0 t infty with the heat flux across a part gamma 1 of partial d being a control function k x t periodic in t of period sigma and n 1 leqq k leqq n 2 int 0 sigma int gamma 1 k x t m where n 1 n 2 m are given positive constants the solution u x t behaves asymptotically as a periodic function hat u x t we wish to maximize int 0 sigma int d p x hat u x t where p is a given positive function it is proved that any optimal control k 0 has the form k 0 x t left begin array 20 c n 2 quad text if 0 t varphi x n 1 quad text if varphi x t sigma end array right where varphi x is a smooth function

a stable affine approximate finite element method the notion of the affine figure closest to a given quadrilateral can be given a precise mathematical definition the resulting figure is referred to as the equivalent parallelogram associated with a quadrilateral equipped with such a concept it is then feasible to consider finite element approximations in which the original quadrilateral elements are replaced by their equivalent parallelograms the idea is appealing not least because of the resulting economy arising from computations performed on an element generated by an affine map furthermore numerical experiments reported recently indicate that highly efficient and accurate schemes result when such a concept is combined with the enhanced strain method or the method of incompatible modes the purpose of this work is to analyze finite element schemes resulting from approximation of quadrilaterals by their equivalent parallelograms the focus is on low order bilinear elements and the analysis is carried out in the context of linear elasticity for standard approximations as well as for those which use enhanced strains the affine approximation applies only to the element map and the primary unknown the displacement vector in the context of elasticity is approximated by conventional piecewise bilinear functions the analysis confirms convergence at the optimal rate provided that the deviations of the quadrilaterals from their equivalent parallelograms are at most o h

the cahn hilliard equation with time dependent constraint abstract we propose an abstract variational inequality formulation of the cahn hilliard equation with a time dependent constraint we introduce notions of strong and weak solutions and prove that a strong solution if it exists is a weak solution and that the existence of a unique weak solution holds under an appropriate time dependence condition on the constraint we also show that the weak solution is a strong solution under appropriate assumptions on the data our abstract results can be applied to various concrete problems

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

the gibbs thompson relation within the gradient theory of phase transitions this paper discusses the asymptotic behavior as 0 of the chemical potentials associated with solutions of variational problems within the van der waals cahn hilliard theory of phase transitions in a fluid with free energy per unit volume given by 2 2 w where is the density the main result is that is asymptotically equal to e d o with e the interfacial energy per unit surface area of the interface between phases the constant sum of principal curvatures of the interface and d the density jump across the interface this result is in agreement with a formula conjectured by m gurtin and corresponds to the gibbs thompson relation for surface tension proved by g caginalp within the context of the phase field model of free boundaries arising from phase transitions

quantum conditional mutual information and approximate markov chains a state on a tripartite quantum system a otimes b otimes c forms a markov chain if it can be reconstructed from its marginal on a otimes b by a quantum operation from b to b otimes c we show that the quantum conditional mutual information i a c b of an arbitrary state is an upper bound on its distance to the closest reconstructed state it thus quantifies how well the markov chain property is approximated

the equivalent parallelogram and parallelepiped and their application to stabilized finite elements in two and three dimensions a new class of quadrilateral and hexahedral elements four and eight noded in two and three dimensions respectively is presented these elements are obtained by combining the concept of the equivalent parallelogram for plane problems and the equivalent parallelepiped for three dimensional problems with the notion of incompatible modes a key feature of the new elements is that integration of the element stiffness matrices is carried out using one point integration the use of affine equivalent elements parallelograms and parallelepipeds permits a closed form eigenvalue analysis which includes the incompatible modes and a stabilization procedure based on the eigenvalue analysis ensures the full rank of the stiffness matrix numerical results for problems in elasticity and plasticity indicate equivalent or superior performance of the new elements when compared with various elements based on enhanced strains or incompatible modes

further discussion on four node isoparametric quadrilateral elements in plane bending the aim of the study is first to show that the finite element method for plane bending is not sensitive to the distorted geometry of isoparametric quadrilateral elements second to close out further investigations on irregular elements based on wilson incompatible functions employing ad hoc methods to force elements to pass the patch test regardless of the type of the variational formulation used for the problem a systematic review of papers dealing with finite four node plane elements with two degrees of freedom at each node is presented selected results of the benchmark example of the mesh distortion test used by all cited authors are compared suggesting that no improvement has been made in more than two decades of intensive development of new elements and methods in the field an attempt has been made to localize the pathological behaviour of irregular elements under consideration by calculating the areas of the elements after deformation for different values of the distortion parameter it made possible to observe the mass density of the whole deformed system the tip deflections at the lower and upper edge at the free end of the cantilever beam were depicted as well illustrating unexpected physical phenomena of the longitudinal fibers deviating from being parallel the horizontal displacement components at two common nodes of the adjacent elements have been compared with the analytical solution of the problem for the varying distortion parameter the resulting horizontal displacement distribution along the common side of the elements has been shown to be the source of unreal behavior of all classes of irregular elements based on wilson incompatible functions increasing the order of the interpolation functions for the displacement field i e application of subparametric elements makes the finite element method insensitive to element distortion copyright 2000 john wiley sons ltd

alternative ways for formulation of hybrid stress elements an element stiffness matrix can be derived by the conventional potential energy principle and indirectly also by generalized variational principles such as the hu washizu principle and the hellinger reissner principle the present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the hellinger reissner principle it is found that the resulting scheme is equivalent to that considered by tong 1982 for the construction of hybrid stress elements in tong s scheme the inversion of a large flexibility matrix can be avoided it is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the hellinger reissner principle and the hu washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method

extension of mitc to higher order beam models and shear locking analysis for compact thin walled and composite structures summary a class of mixed interpolated beam elements is introduced in this paper under the framework of the carrera unified formulation cuf to eliminate the detrimental effects due to shear locking the mixed interpolation of tensorial components mitc method is adopted to generate locking free displacement based beam models using general 1d finite elements an assumed distribution of the transverse shear strains is employed for the derivation of the virtual work and the full gauss legendre quadrature is used for the numerical computation of all the components of the stiffness matrix linear quadratic and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact laminated and thin walled structures a comprehensive study of how shear locking affects general beam elements when different classical integration schemes are employed is presented evidencing the outstanding capabilities of the mitc method to overcome this numerical issue refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of lagrange and legendre polynomials over the cross sectional domain allowing one to capture complex states of stress with a 3d like accuracy the numerical examples are compared to analytic numerical solutions from the literature and commercial software solutions whenever it is possible the efficiency and robustness of the proposed method is demonstrated throughout all the assessments illustrating that mitc elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations this article is protected by copyright all rights reserved

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

variational principles for non conforming finite element methods variational principles with relaxed inter element continuity requirement for non conforming element methods in linear and non linear analyses are developed based on the principles any non conforming element displacement can be used directly to derive the explicit expressions of non conforming displacement function which can ensure the passage of the patch test c for the requirement of convergence copyright 2001 john wiley sons ltd

a rational approach for choosing stress terms for hybrid finite element formulations a new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements examples using 4 node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

optimal controls of multidimensional modified swift hohenberg equation in this paper we deal with the optimal control problem governed by multidimensional modified swift hohenberg equation after showing the relationship between the control problem and its approximation we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems

extension of field consistence approach into developing plane stress elements in this research paper the possibilities for extending the field consistence approach l yunhua on shear locking in finite elements licentiate thesis stockholm 1997 l yunhua explanation and elimination of shear locking and membrane locking with field consistence approach comput methods appl mech engrg in press starting from different variational principles to plane stress elements are investigated in the extension two main difficulties are explicitly solving a set of coupled partial differential equations and satisfying inter element compatibility the first one is alleviated by constructing element interpolations from a set of quasi general solutions rather than the real general solutions to the euler lagrangian equations the second one is solved by combining the field consistence approach with the iso parametric interpolation technique the traditional assumed stress method is improved and an efficient plane stress element is obtained it seems that the relations between the three commonly used variational principles can be more reasonably established in the framework of the field consistence approach

some geometrical results and estimates for quadrilateral finite elements abstract the concept of the equivalent parallelogram associated with a quadrilateral is introduced the quadrilateral may be regarded as a perturbation of this parallelogram which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral the equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals this definition is used together with other properties to obtain in a relatively simple manner estimates in appropriate seminorms or norms of the isoparametric map and its jacobian for use in the determination of finite element interpolation error estimates

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

a uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

streaming universal distortion free entanglement concentration this paper presents a streaming sequential protocol for universal entanglement concentration at the shannon bound alice and bob begin with n identical but unknown two qubit pure states each containing e ebits of entanglement they each run a reversible algorithm on their qubits and end up with y perfect epr pairs where y ne o n our protocol is streaming so the n input systems are fed in one at a time and perfect epr pairs start popping out almost immediately it matches the optimal block protocol exactly at each stage so the average yield after n inputs is y ne o logn so somewhat surprisingly there is no tradeoff between yield and lag our protocol optimizes both in contrast the optimal n qubit block protocol achieves the same yield but since no epr pairs are produced until the entire input block is read its lag is o n finally our algorithm runs in o log n space so a lot of entanglement can be efficiently concentrated using a very small e g current or near future technology quantum processor along the way we find an optimal streaming protocol for extracting randomness from classical i i d sources and a more space efficient implementation of the schur transform

does ignorance of the whole imply ignorance of the parts large violations of noncontextuality in quantum theory a central question in our understanding of the physical world is how our knowledge of the whole relates to our knowledge of the individual parts one aspect of this question is the following to what extent does ignorance about a whole preclude knowledge of at least one of its parts relying purely on classical intuition one would certainly be inclined to conjecture that a strong ignorance of the whole cannot come without significant ignorance of at least one of its parts indeed we show that this reasoning holds in any noncontextual nc hidden variable model hv curiously however such a conjecture is false in quantum theory we provide an explicit example where a large ignorance about the whole can coexist with an almost perfect knowledge of each of its parts more specifically we provide a simple information theoretic inequality satisfied in any nc hv but which can be arbitrarily violated by quantum mechanics

dense quantum coding and quantum finite automata we consider the possibility of encoding m classical bits into many fewer n quantum bits qubits so that an arbitrary bit from the original m bits can be recovered with good probability we show that nontrivial quantum codes exist that have no classical counterparts on the other hand we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding the proof is based on an entropy coalescence principle that is obtained by viewing holevo s theorem from a new perspective in the existing implementations of quantum computing qubits are a very expensive resource moreover it is difficult to reinitialize existing bits during the computation in particular reinitialization is impossible in nmr quantum computing which is perhaps the most advanced implementation of quantum computing at the moment this motivates the study of quantum computation with restricted memory and no reinitialization that is of quantum finite automata it was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata here we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata

an incompatible element for axisymmetric structure and its modification by hybrid method this paper introduces three four node quadrilateral axisymmetric elements the first one is an incompatible element while the second one is a modification of the first element by an extended hellinger reissner principle the second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element all of the three elements are found to be invariant insensitive to nodal point numbering free of locking for nearly incompressible material able to pass the patch test and do not exhibit the false shear phenomenon numerical examples are given and satisfactory predictions are achieved

a property of quantum relative entropy with an application to privacy in quantum communication we prove the following information theoretic property about quantum states substate theorem let and be quantum states in the same hilbert space with relative entropy s c tr log log c then for all 0 there is a state such that the trace distance tr tr 2 and 2o c 2 it states that if the relative entropy of and is small then there is a state close to i e with small trace distance tr that when scaled down by a factor 2o c sits inside or becomes a substate of this result has several applications in quantum communication complexity and cryptography using the substate theorem we derive a privacy trade off for the set membership problem in the two party quantum communication model here alice is given a subset a n bob an input i i n and they need to determine if i i a privacy trade off for set membership in any two party quantum communication protocol for the set membership problem if bob reveals only k bits of information about his input then alice must reveal at least n 2o k bits of information about her input we also discuss relationships between various information theoretic quantities that arise naturally in the context of the substate theorem

stability and stabilizability of infinite dimensional systems in this paper we are concerned with stability problems for infinite dimensional systems first we review the theory for linear systems where the dynamics are governed by strongly continuous semigro

extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids abstract this paper addresses novel extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids on one hand based upon the unified multiscale kinematics of strong discontinuities standard finite elements at the coarse scale are enriched with fine scale kinematics in which non uniform discontinuity modes are incorporated on the other hand the traction continuity condition across the discontinuity is enforced in the statically optimal form as the fine scale statics the admissible discontinuity modes satisfying a priori the traction continuity condition are derived in addition to the relative rigid body motions translations and rotations more general relative stretching modes that induce discontinuous strain stress fields in the bulk are obtained with no limit of a vanishing poisson s ratio the proposed model then particularizes to 2d quadrilateral elements the displacement jumps at the discontinuity nodes are selected as the enrichment parameters and regarded as global variables shared by neighboring elements the resulting model not only is intrinsically stress locking free for a fully softened discontinuity but also automatically guarantees global continuity of the displacement jumps another benefit is that the numerical instability suffered under the unfavorable element discontinuity configuration can be easily circumvented furthermore the vanishing displacement jumps at the discontinuity tip can be enforced trivially as conventional essential boundary conditions and those complex strategies introduced in existing models are avoided together with the failure criterion related to the element average stress and the propagation orientation based on a simplified nonlocal stress a local crack tracking algorithm is adopted to guarantee global continuity of the discontinuity path representative numerical simulations of element and structure benchmark tests are presented to verify the performance of the proposed approach in the modeling of arbitrary discontinuity propagation in solids

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

new strategy for assumed stresses for 4 node hybrid stress membrane element an oblique skew co ordinate system defined at the origin of the isoparametric co ordinates is introduced as the reference co ordinate system for assumed stresses in the formulation of a 4 node hybrid membrane element the initially uncoupled stresses in these reference co ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of pian and wu7 when suitable incompatible displacements are introduced such strategy allows the element stiffness to be formulated by using either the hellinger reissner or the complementary energy functional numerical results show that the performances of three elements constructed by using different sets of incompatible displacements in this paper are practically identical and are all of slightly higher accuracy than that of the pian sumihara element6

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

the mode amplitude technique and hierarchical stress elements a simplified and natural approach this paper reviews the derivation procedure of conventional stress based elements and then shows how the procedure can be simplified by using degrees of freedom which are amplitudes of the boundary loading modes mode amplitude technique this gives one class of element based on stress assumptions and uses only one virtual principle the natural formulation of hierarchical stress elements is shown

feedback stabilization and optimal control for the cahn hilliard equation this paper is concerned with the control problem for the cahn hilliard equation 4 the physical background is as follows suppose there is a binary solution in a container sz c ir n 5 3 and suppose the mole fraction of the a component is u then the mole fraction for the other component b is 1 u it is well known that the function u of x e sz and t 1 0 due to mass conservation satisfies the cahn hilliard equation 4 u ya2u ap u in sz x r 1 1 where y 0 is a small positive constant and typically p u u3 24 1 2 suppose u has spatial distribution uo x initially i e u x 0 u x 1 3 then the evolution of u x t is determined by 1 l 1 3 and the boundary conditions au i i aau o an x 1 4

on the nested refinement of quadrilateral and hexahedral finite elements and the affine approximation it is shown in this paper that the optimal approximation property of bilinear or trilinear finite elements would be retained when the affine mapping is used to replace the q1 mapping on each element if the grids are refined nestedly the new method truncates the quadratic and cubic terms in reference mappings and produces constant jacobians and jacobian matrices this would avoid a shortcoming of the quadrilateral and hexahedral elements where the integrals of rational functions have to be computed or approximated numerical tests verify the analysis

a unified analysis for stress strain hybrid methods of high performance abstract several methods have been developed in the literatures of computational mechanics to improve the performance of the conventional lower order displacement finite elements which yield poor results for problems with bending and for nearly incompressible medium this paper is devoted to a unified analysis of convergence for pian sumihara s chen cheung s and piltner taylor s enhanced stress strain schemes by virtue of the energy compatibility and the rank condition error estimates for these typical finite elements of high performance are obtained in a unified framework and especially weakly locking free error estimates with respect to the poisson s ratio in energy norms are obtained uniformly for 1 ch 2 as h 0 where c is a constant independent of and the mesh size h very much the same about the three methods is pointed out

stress analysis around holes or notches by special finite elements in this paper three special elements for stress concentration analysis around holes or notches are presented one is based on a variational principle involving displacements unsymmetric stresses and rotations as independent variables the other two on the classical hellinger reissner principle the new elements are designed to be used in a single layer along the cavity rim where enhanced properties are needed to get a satisfactory level of accuracy special properties are obtained by enforcing the stress approximation to satisfy a priori the traction free boundary condition on the element side positioned along the cavity rim and by properly enriching the displacement interpolation the proposed elements are applicable to geometries of arbitrary shape easy to use low cost and readily implementable into existing finite element codes copyright 2005 john wiley sons ltd

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

improved four node hellinger reissner elements based on skew coordinates mixed four node elements based on the hellinger reissner hr functional are developed for stress representations in various coordinates including the skew natural and cartesian ones the two field hr functional is used in the classical form and in the incremental form suitable for non linear materials we argue that the skew coordinates not the natural ones should be associated with the natural basis at the element s center if 5 and 7 parameter stress representations are assumed in these coordinates then for a linear elastic case the homogenous equilibrium equations and the stress form of compatibility equation are satisfied point wise two mixed four node elements are developed and tested 1 an assumed stress element hr5 s is developed from the non enhanced hr functional for a 5 parameter representation of stresses formally identical as the one used for example in pian and sumihara int j numer meth engng 1984 20 1685 1695 but in terms of skew coordinates this element is very simple and uses a smaller number of parameters but is equally accurate as the elements by yuan et al int j numer meth engng 1993 36 1747 1763 and by piltner and taylor int j numer meth engng 1995 38 1783 1808 2 an assumed stress enhanced strain element hr9 is developed from the enhanced hr functional for a 7 parameter representation of stress and a 2 parameter enhanced assumed displacement gradient or enhanced assumed strain enhancement various forms of 7 parameter representations appearing in the literature are reviewed and we prove that they are linked by a linear onto transformation the choice of coordinates for the stress and the enhancement turns out to be the crucial factor and four combinations of coordinates for which the element performs the best are identified both elements are based on the green strain and several numerical tests show their good accuracy in particular their robustness to shape distortions for coarse meshes two update schemes for the multipliers of modes and the incremental constitutive procedure accounting for the plane stress condition for non linear materials are tested for large deformation problems copyright 2008 john wiley sons ltd

relations between incompatible displacement model and hybrid stress model an examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by irons in 1972 but the basic differences between the two are also identified for 8 node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by irons purely from his physical insight