an explicit description of the global attractor of the damped and driven sine gordon equation we prove that the size of the finite dimensional attractor of the damped and driven sine gordon equation stays small as the damping and driving amplitude become small a decomposition of finite dimensional attractors in banach space is found into a part that attracts all of phase space except sets whose finitedimensional projections have lebesgue measure zero and a partc that only attracts sets whose finite dimensional projections have lebesgue measure zero we describe the components of the attractor andc which is called the hyperbolic structure for the damped and driven sine gordon equation is low dimensional but the dimension ofc which is associated with transients is much larger we verify numerically that this is a complete description of the attractor for small enough damping and driving parameters and describe the bifurcations of the attractor in this small parameter region

elliptic algebro geometric solutions of the kdv and akns hierarchies an analytic approach we provide an overview of elliptic algebro geometric solutions of the kdv and akns hierarchies with special emphasis on floquet theoretic and spectral theoretic methods our treatment includes an effective characterization of all stationary elliptic kdv and akns solutions based on a theory developed by hermite and picard

character formulas for irreducible modules of the lie superalgebras sl m n kac distinguished between typical and atypical finite dimensional irreducible representations of the lie superalgebras sl m n and provided an explicit character formula appropriate to all the typical representations here the range of validity of some character formulas for atypical representations that have been proposed are discussed several of them are of the kac weyl type but then it is proved that all formulas of this type fail to correctly give the character of one particular atypical representation of sl 3 4 having ruled out therefore all such formulas a completely new extension of the kac weyl character formula is proposed the validity of this formula in the case of all covariant tensor irreducible representations is proved and some evidence in support of the conjecture that it covers all irreducible representations of sl m n is presented

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

whittaker coinvariants for gl m n abstract let w m n be the finite w algebra attached to the principal nilpotent orbit in the general linear lie superalgebra gl m n c in this paper we study the whittaker coinvariants functor which is an exact functor from category o for gl m n c to a certain category of finite dimensional modules over w m n we show that this functor has properties similar to soergel s functor v in the setting of category o for a semisimple lie algebra we also use it to compute the center of w m n explicitly and deduce consequences for the classification of blocks of o up to morita derived equivalence

picard potentials and hill s equation on a torus hill s equation has drawn an enormous amount of consideration due to its ubiquity in applications as well as its structural richness of particular importance in the last 20 years is its connection with the kdv hierarchy and hence with integrable systems we show in this paper that regarding the independent variable as a complex variable yields a breakthrough for the problem of an efficient characterization of all elliptic finitegap potentials a major open problem in the field specifically we show that elliptic finitegap potentials of hill s equation are precisely those for which all solutions for all spectral parameters are meromorphic functions in the independent variable complementing a classical theorem of picard the intimate connection between picard s theorem and elliptic finite gap solutions of completely integrable systems is established in this paper for the first time in addition we construct the hyperelliptic riemann surface associated with a finitegap potential not necessarily elliptic i e determine its branch and singular points from a comparison of the geometric and algebraic multiplicities of eigenvalues of certain auxiliary operators associated with hill s equation these multiplicities are intimately correlated with the pole structure of the diagonal green s function of the operator h d2 dx2 q x in l2 r our construction is new in the present general complex valued periodic finite gap case before describing our approach in some detail we shall give a brief account of the history of the problem involved this theme dates back to a 1940 paper of ince 43 who studied what is presently called the lam6 ince potential

explicit feature control in structural topology optimization via level set method abstract the present paper aims to address a long standing and challenging problem in structural topology optimization explicit feature control of the optimal topology the basic idea is to resort to the level set solution framework and impose constraints on the extreme values of the signed distance level set function used for describing the topology of the structure numerical examples are also presented and discussed to illustrate the effectiveness of the proposed approach

trace formulas for non self adjoint periodic schrodinger operators and some applications abstract recently a trace formula for non self adjoint periodic schrodinger operators in l 2 r associated with dirichlet eigenvalues was proved in differential integral equations 14 2001 671 700 here we prove a corresponding trace formula associated with neumann eigenvalues in addition we investigate dirichlet and neumann eigenvalues of such operators in particular using the dirichlet and neumann trace formulas we provide detailed information on location of the dirichlet and neumann eigenvalues for the model operator with the potential k e 2 i x where k c

the relaxation of two well energies with possibly unequal moduli the elastic energy of a multiphase solid is a function of its microstructure determining the infimum of the energy of such a solid and characterizing the associated optimal microstructures is an important problem that arises in the modeling of the shape memory effect microstructure evolution and optimal design mathematically the problem is to determine the relaxation under fixed phase fraction of a multiwell energy this paper addresses two such problems in the geometrically linear setting first in two dimensions we compute the relaxation under fixed phase fraction for a two well elastic energy with arbitrary elastic moduli and transformation strains and provide a characterization of the optimal microstructures and the associated strain second in three dimensions we compute the relaxation under fixed phase fraction for a two well elastic energy when either 1 both elastic moduli are isotropic or 2 the elastic moduli are well ordered and the smaller elastic modulus is isotropic in both cases we impose no restrictions on the transformation strains we provide a characterization of the optimal microstructures and the associated strain we also compute a lower bound that is optimal except possibly in one regime when either 1 both elastic moduli are cubic or 2 the elastic moduli are well ordered and the smaller elastic modulus is cubic for moduli with arbitrary symmetry we obtain a lower bound that is sometimes optimal in all these cases we impose no restrictions on the transformation strains and whenever the bound is optimal we provide a characterization of the optimal microstructures and the associated strain in both two and three dimensions the quasiconvex envelope of the energy can be obtained by minimizing over the phase fraction we also characterize optimal microstructures under applied stress

isophasal isopolar and isospectral schrodinger operators and elementary complex analysis we explicitly construct super exponentially decaying potentials on d so that the associated schrodinger operators are isophasal and isopolar we use similar techniques to construct isospectral schrodinger operators with periodic potentials on and isospectral schrodinger operators on

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

on hill s equation with a singular complex valued potential 1 introduction the differential equation y00 qy ey is called hill s equation if q is a realvalued periodic locally integrable function of a real variable it is very well known that the spectrum of the operator associated with this equation consists of a countably in nite number of compact intervals of the real line these intervals are called spectral bands and are generally separated by open intervals called gaps in some instances however all but a nite number of gaps are empty resulting in a spectrum consisting of a nite number of compact bands and one closed interval extending to negative in nity in this case one calls q a nite band or nite gap potential the relationship of nite band potentials with the hierarchy of korteweg de vries equations has been the reason for a heightened interest in them during the past twenty years for recent accounts see for instance the monographs by dickey 8 and belokolos et al 3 the rst non trivial example of a nite band potential was given by ince in 1940 18 consider the lame potentials q x yg g 1 x c jq q0 where g 2n and jq q0 denotes weierstrass s elliptic function with fundamental half periods q and q0 if q is real q0 is pure imaginary and c q0 then q is realvalued periodic and continuous ince s result when translated to the present language shows that q then is a nite band potential with g non empty gaps between the bands this however raises immediately the question of what happens when c 6 q0 or when the half periods are more general in these cases one encounters potentials which are complex valued but continuous as well as potentials which have singularities of the form yg g 1 x and are realor complex valued before giving an overview of the content of the paper i want to give a brief account of the history of the subject let q be a real locally integrable periodic function with period p l the differential expression d dx q and h the self adjoint operator in l r associated with l then consider the following four statements a there are precisely 2g 1 real numbers e2g e0 such that the spectrum of h is given by

modular branching rules and the mullineux map for hecke algebras of type a in a series of papers 21 22 23 kleshchev has recently proved a branching rule for modular representations of the symmetric group s r on r symbols fix a field f of arbitrary characteristic p then kleshchev s branching rule gives a precise description of the socle of the restriction of an irreducible fs r module to fs r 1 in 24 kleshchev applies this branching rule to give a purely combinatorial description of the mullineux map which describes the irreducible fs r module obtained by tensoring an arbitrary irreducible fs r module with the 1 dimensional sign representation in 13 see also 3 ford and kleshchev show with some technical combinatorics that kleshchev s description of the mullineux map is equivalent to a quite different algorithm conjectured by mullineux 27 in 1979 thus proving the so called mullineux conjecture the main purpose of this paper is to prove the quantum analogues of these results replacing the group algebra fs r with the corresponding hecke algebra h r over f at an arbitrary root of unity q f our main result is the hecke algebra analogue of kleshchev s modular branching rule it turns out that the branching rule for h r only depends on the integer where is the smallest natural number such that 1 q q 1 0 in f if q 1 is precisely the characteristic p of f and our branching rule specializes to the classical case considered by kleshchev as a consequence of this branching rule combining kleshchev s argument in 24 with the known block structure of h r from 9 we are able to deduce the quantum analogue of kleshchev s description of the corresponding mullineux map for h r the proof by ford and kleshchev in 13 that this is equivalent to mullineux s original algorithm does not depend on p being prime so our result is equivalent by 13 to a quantum version of the mullineux conjecture replacing p by we remark that there is now a quite different proof that kleshchev s algorithm gives the mullineux map using crystal bases this was first observed for fields of characteristic 0 in 25 modulo a conjecture which has now been proved 17 2 relating crystal bases for a certain affine quantum group to decomposition matrices of h r over fields of characteristic 0 the result in arbitrary characteristic can be deduced from the characteristic 0 case by an

complex hill s equation and the complex periodic korteweg de vries equations on etudie la classe spectrale des operateurs differentiels l d 2 dx 2 q avec un potentiel q de periode un on traite des potentiels complexes et des operateurs auto adjoints

topology design with optimized self adaptive materials significant performance improvements can be obtained if the topology of an elastic structure is allowed to vary in shape optimization problems we study the optimal shape design of a two dimensional elastic continuum for minimum compliance subject to a constraint on the total volume of material the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology relaxation of the optimization problem via quasiconvexification or homogenization methods is required the effect of relaxation is to introduce a perforated microstructure that must be optimized simultaneously with the macroscopic distribution of material

on the composition factors of kac modules for the lie superalgebras sl m n in the classification of finite dimensional modules of lie superalgebras kac distinguished between typical and atypical modules kac introduced an induced module the so called kac module v with highest weight which was shown to be simple if is a typical highest weight if is an atypical highest weight the kac module is indecomposable and the simple module v can be identified with a quotient module of v in the present paper the problem of determining the composition factors of the kac modules for the lie superalgebra sl m n is considered an algorithm is given to determine all these composition factors and conversely an algorithm is given to determine all the kac modules containing a given simple module as a composition factor the two algorithms are presented in the form of conjectures and illustrated by means of detailed examples strong evidence in support of the conjectures is provided the combinatorial way in which the two algorithms are intertwined is both surprising and interesting and is a convincing argument in favor of the solution to the composition factor problem presented here

topology design of structures using a dual algorithm and a constraint on the perimeter dual optimization algorithms are well suited for the topology design of continuum structures in discrete variables since in these problems the number of constraints is small in comparison to the number of design variables the raw dual algorithm which was originally proposed for the minimum compliance design problem worked well when a perimeter constraint was added in addition to the volume constraint however if the perimeter constraint was gradually relaxed by increasing the upper bound on the allowable perimeter the algorithm tended to behave erratically recently a simple strategy has been suggested which modifies the raw dual algorithm to make it more robust in the absence of the perimeter constraint in particular the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated in this work we show how the perimeter constraint can be incorporated in this improved algorithm so that it not only provides a designer with a control over the topology but also generates good topologies irrespective of the value of the upper bound on the perimeter

a schauder and riesz basis criterion for non self adjoint schrodinger operators with periodic and antiperiodic boundary conditions under the assumption that v l2 0 dx we derive necessary and sufficient conditions in terms of spectral data for non self adjoint schrodinger operators d2 dx2 v in l2 0 dx with periodic and antiperiodic boundary conditions to possess a riesz basis of root vectors i e eigenvectors and generalized eigenvectors spanning the range of the riesz projection associated with the corresponding periodic and antiperiodic eigenvalues we also discuss the case of a schauder basis for periodic and antiperiodic schrodinger operators d2 dx2 v in lp 0 dx p 1

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

the center manifold and bifurcations of damped and driven sine gordon breathers abstract the generic bifurcations of breathers in the damped and driven sine gordon equation are investigated both numerically and analytically the linear stability analysis and information from periodic spectral theory suggest that three modes are relevant for the system they correspond to frequency and temporal phase changes and to the flat pendulum using these modes nonautonomous amplitude equations are derived and compared with numerical simulations of the perturbed sine gordon equation

continuous approximation of material distribution for topology optimization in this paper we propose a checkerboard free topology optimization method without introducing any additional constraint parameter this aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain that is the continuous distribution of microstructures or equivalently design variables is realized in the whole design domain in the context of the homogenization design method hdm by the discretization with finite element interpolations by virtue of this continuous fe approximation of design variables discontinuous distribution like checkerboard patterns disappear without any filtering schemes we call this proposed method the method of continuous approximation of material distribution camd to emphasize the continuity imposed on the material field two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities copyright 2004 john wiley sons ltd

scale effects in the optimal design of a microstructured medium against buckling abstract certain classes of problems in optimal structural design lead naturally to the introduction of periodic microstructured media as the basis material for the construction of a mechanical element the unit cell size of these microstructures cannot be arbitrarily small as suggested by the pertaining optimization analyses up to date and has to be related to the structure s overall dimensions one physically important mechanism that provides such microstructure size limitations is elastic buckling an analytically tractable model of an infinite periodic rectangular planar frame with axially compressed beams is used to study the optimal buckling loads for any given design one can find a critical stress above which buckling instability occurs in addition one can also find the region in the design space for which the optimal critical mode is a global one i e its characteristic length is much larger than the unit cell size in this region of the design space one can safely use the homogenized material properties to describe the medium for they provide all the information needed to predict a global buckling instability in addition to the detailed parametric study for the model problem investigated here implications for the optimal design against buckling of more general structures are also briefly discussed

the primitive spectrum of a basic classical lie superalgebra we prove conjecture 5 7 in coulembier and musson math j arxiv 1409 2532 describing all inclusions between primitive ideals for the general linear superalgebra in terms of the rm ext 1 quiver of simple highest weight modules for arbitrary basic classical lie superalgebras we formulate two types of kazhdan lusztig quasi orders on the dual of the cartan subalgebra where one corresponds to the above conjecture both orders can be seen as generalisations of the left kazhdan lusztig order on hecke algebras and are related to categorical braid group actions we prove that the primitive spectrum is always described by one of the orders obtaining for the first time a description of the inclusions we also prove that the two orders are identical if category mathcal o admits enough abstract kazhdan lusztig theories in particular they are identical for the general linear superalgebra concluding the proof of the conjecture

on rings of supersymmetric polynomials abstract we consider three types of rings of supersymmetric polynomials polynomial ones m n partially polynomial m n y and laurent supersymmetric rings m n for each type of rings we give their descriptions in terms of generators and relations as a corollary we get for n m an isomorphism m n y m m y 0 n m y it is also true for polynomial rings but in this case the isomorphism does not preserve the grading for each type of rings some natural basis consisting of euler supercharacters is constructed

geometry of kdv 4 abel sums jacobi variety and theta function in the scattering case the study of the general projective curve x defined by the vanishing of an irreducible polynomial p x y originated in the discovery of addition formulas for integrals v r x y dx of rational functions on such a curve

chaotic perturbations of kdv i rational solutions abstract rational pole solutions of a perturbed kdv equation describing nonlinear ion acoustic plasma waves become chaotic in time when a small perturbation is periodically driven a mcgehee transformation blows up a degenerate stationary point at infinity and the smale birkhoff homoclinic theorem adapted to submanifolds in phase permits the use of the melnikov method with pole solutions being homoclinic orbits

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

on a theorem of hochstadt in fact hochstadt gives an explicit formula for the discriminant which will be reproduced below since hochstadt s work there has been a considerable interest in finite band potentials i e potentials q such that the spectrum of the operator associated with d2 dx 2 q consists of finitely many regular analytic arcs due to their close relationship with the korteweg de vries hierarchy and hence with integrable systems however the interest is not restricted to real valued potentials for instance

vortex blob methods applied to interfacial motion we develop a boundary integral method for computing the motion of an interface separating two incompressible inviscid fluids the velocity integral is regularized so that the vortex sheet on the interface is replaced by a sum of blobs of vorticity the regularization allows control of physical instabilities we design a class of high order blob methods and analyze the errors numerical tests suggest that the blob size should be scaled with the local spacing of the interfacial markers for a vortex sheet in one fluid with a first order kernel we obtain a spiral roll up similar to krasny j comput phys 65 1986 292 but the higher order kernels lead to more detailed structure we verify the accuracy of the new method by computing a liquid gas interface with rayleigh taylor instability we then apply the method to the more difficult case of rayleigh taylor flow separating two fluids of positive density a case for which the regularization appears to be essential as found by kerr and tryggvason both j comput phys 76 1988 48 75 1988 253 we use a blob regularization in certain local terms in the evolution equations as well as in the velocity integral we find strong evidence that improved spatial resolution with fixed blob size leads to a converged regularized solution without numerical instabilities however it is not clear that there is a weak limit as the regularization is decreased

stability of finite element models for distributed parameter optimization and topology design abstract we address a problem of numerical instability that is often encountered in finite element solutions of distributed parameter optimization and variable topology shape design problems we show that the cause of this problem is numerical rather than physical in nature we consider a two field distributed parameter optimization problem involving a design field and a response field and show that the optimization problem corresponds to a mixed variational problem an improper selection of the discrete function spaces for these two fields leads to grid scale anomalies in the numerical solutions to optimization problems similar to those that are sometimes encountered in mixed formulations of the stokes problem we present a theoretical framework to explain the cause of these anomalies and present stability conditions for discrete models the general theoretical framework is specialized to analyze the stability of specific optimization problems and stability results for various mixed finite element models are presented we propose patch tests that are useful in identifying unstable elements

topological design for vibrating structures the topological optimization technique using micro scale voids with the homogenization method for stress analysis of perforated structures has been applied to solve stiffness maximization problem with success here the homogenization design technique is extended to design problems concerning vibrating structures an extended optimization algorithm is also derived to maximize a set of eigenvalues as well as to identify the topology design for specified eigenvalues to characterize forced vibration of a structure

a robust dual algorithm for topology design of structures in discrete variables dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since in topology design problems the number of constraints is small in comparison to the number of design variables good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint however when the perimeter constraint is relaxed the dual algorithm tends to give bad results even with the use of higher order finite element models as we demonstrate in this work since a priori one does not know what a good value of the perimeter to be specified is it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint we show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint in particular we show that the problem of checkerboarding which is frequently observed with the use of lower order finite elements is eliminated

some new extragradient iterative methods for variational inequalities abstract in this paper we suggest and analyze some new extragradient iterative methods for finding the common element of the fixed points of a nonexpansive mapping and the solution set of the variational inequality for an inverse strongly monotone mapping in a hilbert space we also consider the strong convergence of the proposed method under some mild conditions several special cases are also discussed results proved in this paper may be viewed as improvement and refinement of the previously known results

character formulae for ortho symplectic lie superalgebras osp n 2 abstract the characters of finite dimensional irreducible modules of the lie superalgebra osp n 2 are completely determined in terms of those of generalized verma modules as a by product the irreducible decomposition of the tensor of any finite dimensional irreducible module with the natural module is obtained

coupled deformations of elastic curves and surfaces an equilibrium theory for the coupled finite deformations of elastic curves and surfaces is described possible wrinkling of the curve or surface is taken into account by using a relaxed version of the theory obtained from minimum energy considerations the relaxed theory admits a dual formulation leading to extremum principles and uniqueness of the equilibrium stress distribution a number of examples are treated using spatial finite differences together with a dynamic relaxation method in which equilibrium configurations are obtained in the long time limit of a damped dynamical problem

singularities of the complex korteweg de vries flows on etudie le probleme isospectral de l equation de hill complexe etant donne 2g 1 valeurs propres simples dans le plan complexe trouver la classe spectrale correspondante q on considere la caracterisation de la classe isospectrale et ses sections singulieres on construit q a l aide des flots non lineaires de korteweg de vries dans c 1 les fonctions regulieres de periode 1

distributed parameter optimization and topology design for non linear thermoelasticity abstract topology optimization has been the focus of considerable attention in the shape optimization community in recent years since significant performance improvements can be obtained if the topology is allowed to vary in shape optimization problems attention has mainly focussed on the topology design of an elastic continuum for minimum compliance subject to a volume constraint the macroscopic version of this problem is not well posed if no restrictions are placed on the structure topology the most widely used method for making the problem has been the so called homogenization method which introduces microstructure to the design space though there are a number of advantages to this method it also suffers from some drawbacks optimal designs generated using an optimal microstructure are difficult to manufacture while using sub optimal microstructures reverts the problem back to the original ill posed problem in addition extension of the homogenization method to problems involving non linear material behavior is quite difficult to address some of these issues a new method for making the compliance optimization problem well posed has recently been proposed this method introduces an additional constraint on the perimeter of the solid regions in the design to make the problem well posed since microstructure is not introduced the designs are easily manufacturable preliminary results for topology design using the perimeter method for problems where the material behavior is linear elastic have already been reported in the literature we show that the perimeter method can be used even when the material behavior involves material and geometric non linearities we formulate the distributed parameter optimization and topology design problems using the perimeter method for non linear thermoelasticity finite element optimization procedures based on this formulation are developed and numerical solutions for the distributed parameter optimization problem are presented though we use the compliance as the objective function one could optimize any objective function by making minor modifications in the method outlined here

hook young diagrams with applications to combinatorics and to representations of lie superalgebras definition et etude des tableaux k l semi standards applications a la combinatoire et aux representations des superalgebres de lie des diagrammes de young a crochets