landau de gennes theory of isotropic nematic smectic liquid crystal transitions we propose a landau de gennes variational theory fit to simultaneously describe isotropic nematic smectic a and smectic c phases of a liquid crystal the unified description allows us to deal with systems in which one or all of the order parameters develop because of the influence of defects external fields and or boundary conditions we derive the complete phase diagram of the system that is we characterize how the homogeneous minimizers depend on the value of the constitutive parameters the coupling between the nematic order tensor and the complex smectic order parameter generates an elastic potential which is a nonconvex function of the gradient of the smectic order parameter this lack of convexity yields in turn a loss of regularity of the free energy minimizers we then consider the effect on an infinitesimal second order regularization term in the free energy functional which fixes the optimal number of defects in the singular configurations

on minima of a functional of the gradient necessary conditions in this paper we propose a new method for texture segmentation based on the use of texture feature detectors derived from a decorrelation procedure of a modified version of a pseudo wigner distribution pwd the decorrelation procedure is accomplished by a cascade recursive least squared crls principal component pc neural network the goal is to obtain a more eacient analysis of images by combining the advantages of using a high resolution joint representation given by the pwd with an eaective adaptive principal component analysis pca through the use of feedforward neural networks 1999 elsevier science b v all rights reserved

a version of olech s lemma in a problem of the calculus of variations this paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions a necessary and sufficient condition based on the facial structure of the epigraph of the integrand is provided for the continuous dependence of the solutions on boundary data

two dimensional prony modeling and parameter estimation a new method for estimating the two dimensional 2d exponential modes and amplitude coefficients in a prony model is presented this method involves two parts each utilizing a 1d singular value decomposition based technique and is capable of locating frequencies anywhere in the 2d frequency plane simulations are shown which demonstrate the performance of the algorithm

a fast elastostatic solver based on fast fourier transform on multipoles fftm in this paper we present a fast algorithm to solve elasticity problems governed by the navier equation using the boundary element method bem this fast algorithm is based on the fast fourier transform on multipoles fftm method that has been developed for the laplace equation the fftm method uses multipole moments and their kernel functions together with the fast fourier transform fft to accelerate the far field computation the memory requirement of the original fftm tends to be high especially when the method is extended to the navier equation that involves vector quantities in this paper we used a compact representation of the translation matrices for the navier equation based on solid harmonics this reduces the memory usage significantly allowing large elasticity problems to be solved efficiently the improved fftm is compared with the commonly used fmm revealing that the fftm requires shorter computational time but more memory than the fmm to achieve comparable accuracy finally the method is applied to calculate the effective young s modulus of a material containing numerous voids of various shapes sizes and orientations copyright 2008 john wiley sons ltd

a relaxation theorem and its application to the equilibrium of gases keywords relaxed problem lower convex envelope gas equilibrium van der waal s equation reference caa article 1981 001doi 10 1007 bf00280643view record in web of science record created on 2008 11 25 modified on 2017 05 12

optimal design and relaxation of variational problems iii abstract this paper has attempted a synthesis of three subjects that have developed separately optimal design homogenization and relaxation in the calculus of variations the underlying theme is that of oscillations they occur with certain definite patterns in minimizing sequences for the variational problem the same patterns recur in nearly optimal designs and in the coefficients of the equation being homogenized each problem is resolved by determining the structure of those oscillations and above all their macroscopic averages it is those averages that solve the relaxed problem they also determine the optimal design and the solution of the homogenized equation we emphasize also the role of optimization the homogenized equations and composite materials of interest here come not from arbitrary mixtures but from those that are extremal since they correspond to minimizing sequences for the variational problem the effective properties of these composites attain the optimal bounds for given materials in fixed proportions

minimizers for a double well problem with affine boundary conditions this paper is concerned with the existence of minimizers for functionals having a double well integrand with affine boundary conditions such functionals are related to the so called kohn strang functional which arises in optimal shape design problems in electrostatics or elasticity they are known to be not quasi convex and therefore existence of minimizers is in general guaranteed only for their quasi convex envelopes we generalize previous results in 1 and give necessary and sufficient conditions on the affine boundary conditions for existence of minimizers our method relies on the computation of the quasiconvexification of these functionals by using homogenization theory we also prove by a general argument that their rank one convexifications coincide with their quasi convexifications

solutions of vectorial hamilton jacobi equations and minimizers of nonquasiconvex functionals abstract we provide a unified approach to prove existence results for the dirichlet problem for hamilton jacobi equations and for the minimum problem for nonquasiconvex functionals of the calculus of variations with affine boundary data the idea relies on the definition of integro extremal solutions introduced in the study of nonconvex scalar variational problem

existence of minimizers for non quasiconvex integrals keywords quasiconvexity existence of minimizers reference caa article 1995 002doi 10 1007 bf00380915 record created on 2008 11 25 modified on 2017 05 12

a fast algorithm for three dimensional electrostatics analysis fast fourier transform on multipoles fftm in this paper we propose a new fast algorithm for solving large problems using the boundary element method bem like the fast multipole method fmm the speed up in the solution of the bem arises from the rapid evaluations of the dense matrix vector products required in iterative solution methods this fast algorithm which we refer to as fast fourier transform on multipoles fftm uses the fast fourier transform fft to rapidly evaluate the discrete convolutions in potential calculations via multipole expansions it is demonstrated that fftm is an accurate method and is generally more accurate than fmm for a given order of multipole expansion up to the second order it is also shown that the algorithm has approximately linear growth in the computational complexity implying that fftm is as efficient as fmm copyright 2004 john wiley sons ltd

an example of a quasiconvex function that is not polyconvex in two dimensions we study the different notions of convexity for the function f 2 2 2 det where e 2 2 introduced by dacorogna marcellini we show that f is convex polyconvex quasiconvex rank one convex if and only if 2 3 2 1 1 for some 0 2 3 respectively

the gradient theory of phase transitions for systems with two potential wells on generalise la theorie du gradient des transitions de phase au cas a valeur vectoriel on considere la famille des perturbations e e u w u dx e 2 u 2 dx de la fonctionnelle non convexe e 0 u w u dx ou w r n r supporte deux phases et n 1

new version fast multipole method accelerated electrostatic calculations in biomolecular systems in this paper we present an efficient and accurate numerical algorithm for calculating the electrostatic interactions in biomolecular systems in our scheme a boundary integral equation bie approach is applied to discretize the linearized poisson boltzmann pb equation the resulting integral formulas are well conditioned for single molecule cases as well as for systems with more than one macromolecule and are solved efficiently using krylov subspace based iterative methods such as generalized minimal residual gmres or biconjugate gradient stabilized bicgstab methods in each iteration the convolution type matrix vector multiplications are accelerated by a new version of the fast multipole method fmm the implemented algorithm is asymptotically optimal o n both in cpu time and memory usage with optimized prefactors our approach enhances the present computational ability to treat electrostatics of large scale systems in protein protein interactions and nano particle assembly processes applications including calculating the electrostatics of the nicotinic acetylcholine receptor nachr and interactions between protein sso7d and dna are presented

nonconvex problems of the calculus of variations on etudie le probleme de dirichlet pour des fonctionnelles non convexes du calcul des variations dans lequel l integrand depend seulement de x et on demontre des theoremes d existence

restrictions on microstructure we consider the following question given a set of matrices with no rank one connections does it support a nontrivial young measure limit of gradients our main results are these a a young measure can be supported on four incompatible matrices b in two space dimensions a young measure cannot be supported on finitely many incompatible elastic wells c in three or more space dimensions a young measure can be supported on three incompatible elastic wells and d if supports a nontrivial young measure with mean value 0 then the linear span of must contain a matrix of rank one

an existence result in a problem of the vectorial case of the calculus of variations we prove that the problem hbox minimize int omega g phi nabla t x dx quad t in t b w 0 1 infty omega rn admits at least one solution for any lower semicontinuous extended valued function g for any quasiaffine real valued function phi and for any piecewise affine boundary datum t b such that phi nabla t b is constant