continuum topology optimization of buckling sensitive structures twoformulationsforcontinuum topologyoptimizationofstructurestakingbucklingconsiderationsinto account are developed implemented and compared in thee rst the structure undergoing a specie ed loading is modeled as a hyperelastic continuum at e nite deformations and is optimized to maximize the minimum critical buckling load in the second the structure under a similar loading is modeled as linear elastic and the critical buckling load is computed with linearized buckling analysis specie c issues addressed include usage of suitable mixing rules a node based design variable formulation techniques for eliminating regions devoid of structural material from the analysis problem and consistent design sensitivity analysis the performance of the formulations is demonstrated on the design of different structures when problems are solved with moderate loads and generous material usage constraints designs using compression and tension members are realized alternatively when fairly large loads together with very stringent material usage constraints are imposed structures utilizing primarily tension members result issues that arise when designing very light structures with stringent material usage constraints are discussed along with the importance of considering potential geometrical instabilities in the concept design of structural systems

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

aerodynamic shape optimization of aircraft wings using panel methods panel methods are frequently applied to aerodynamic shape optimization problems due to their fast turnaround time and ability to model arbitrary geometries despite being advantageous for design op

perturbations of kms states and noncommutative lp spaces we extend the theory of perturbations of kms states to a class of unbounded perturbations using noncommutative lp spaces we also prove certain stability of the domain of the modular operator associated with a p continuous state this allows us to define an analytic multiple time kms condition and to obtain its analyticity together with some bounds to its norm we extend the theory of perturbations of kms states to a class of unbounded perturbations using noncommutative lp spaces we also prove certain stability of the domain of the modular operator associated with a p continuous state this allows us to define an analytic multiple time kms condition and to obtain its analyticity together with some bounds to its norm

articulated mechanism design with a degree of freedom constraint this paper deals with design of articulated mechanism using a truss based ground structure representation the proposed method can accommodate extremely large displacement by considering geometric non linearity in addition it can also control the mechanical degrees of freedom dof of the resultant mechanism by using a dof equation based on maxwell s rule the optimization is based on a relaxed formulation of an original integer problem and also involves developments directed at handling the redundancy inherent in the ground structure representation one planar test example is selected as the basis for the developments so as to compare the proposed method with other alternative approaches including a graph theoretical enumeration approach which guarantees the identification of the globally optimal solution also an inverter problem is treated where a continuation method is required in order to direct the optimization algorithm towards an integer solution copyright 2004 john wiley sons ltd

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

robust topology optimization of structures with imperfect geometry based on geometric nonlinear analysis abstract topology optimization often leads to structures consisting of slender elements which are particularly sensitive to geometric imperfections such imperfections might affect the structural stability and induce large displacement effects in these slender structures this paper therefore presents a robust approach to topology optimization which accounts for geometric imperfections and their potentially detrimental influence on the structural stability geometric nonlinear effects are incorporated in the optimization by means of a total lagrangian finite element formulation in the minimization of end compliance geometric imperfections are modeled as a vector valued random field in the design domain the resulting uncertain performance of the design is taken into account by minimizing a weighted sum of the mean and standard deviation of the compliance in the robust optimization problem these stochastic moments are typically estimated by means of sampling methods such as monte carlo simulation however these methods require multiple independent nonlinear finite element analyses in each design iteration of the optimization algorithm an efficient solution algorithm which uses adjoint differentiation in a second order perturbation method is therefore developed to estimate the stochastic moments during the optimization two applications with structures that exhibit different types of structural instabilities are examined in both cases it is demonstrated by means of an extensive monte carlo simulation that the deterministic design is very sensitive to imperfections while the design obtained by means of the proposed method is much more robust

level set topology optimization with many linear buckling constraints using an efficient and robust eigensolver linear buckling c onstraints are important in structural topology optimization for obtaining designs that can support the required loads without failure during the optimization process the critical buckling eigenmode can change this poses a challenge to gradient based optimization and can require the computation of a large number of linear buckling eigenmodes this is potentially both computationally dif cult to achieve and pro hibitively expensive in this paper we motivate the need for a large number of linear buckling modes and show how several features of the block jacobi conjugate gradient bjcg eigenvalue method including opti mal shift estimates the reuse of eigenvectors adaptive eigenvector tolerances and multiple shifts can be used to ef ciently and robustly compute a large number of buckling eigenmodes this paper also introduces linear buckling constraints for level set topology optimization in our approach the velocity function is de ned as a weighted sum of the shape sensitivities for the objective and constraint functions the weights are found by solving an optimization sub problem to reduce the mass while maintaining feasibility of the buckling constraints the effectiveness of this approach in combination with the bjcg method is demonstrated using a 3d optimization problem

the hausdorff young inequality on lie groups we prove several results about the best constants in the hausdorff young inequality for noncommutative groups in particular we establish a sharp local central version for compact lie groups and extend known results for the heisenberg group in addition we prove a universal lower bound to the best constant for general lie groups

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

a meshfree level set method for topological shape optimization of compliant multiphysics actuators abstract this paper proposes a topology optimization method for compliant multiphysics actuators of geometrically nonlinear structures using meshfree galerkin weak forms and level set methods the design boundary is implicitly represented as the zero level set of a higher dimensional level set function leading to a level set model capable of handling complex shape and topological changes with flexibilities a family of compactly supported radial basis functions csrbfs is firstly used to interpolate the level set function of lipschitz continuity and then augmented to construct the shape function for meshless approximation by satisfying basic requirements in particular the predetermined consistency and the kronecker delta function property a meshless galerkin method mgm with global weak forms is established to implement the discretization of the state equations the design of actuators is transformed into an easier size optimization from a more difficult shape and topology optimization the design boundary evolution is just a question of advancing the discrete level set function in time by updating the design variables of the size optimization compared to most conventional level set methods the proposed meshless level set method is able to implement the free moving boundary discontinuities without remeshing and unify two different numerical procedures in propagating the discrete level set function e g eulerian grid and approximating the state equation e g lagrangian mesh respectively this method can also avoid numerical difficulties in solving a series of complicate hamilton jacobi partial differential equations pdes with explicit time schemes two typical numerical examples are used to demonstrate the effectiveness of the proposed method

multiplicity and concentration results for fractional schrodinger system with steep potential wells abstract this paper is concerned with the fractional coupled schrodinger system by using the nehari manifold and fibering map we obtain the multiplicity and concentration of solutions for the given problem with steep potential wells where some new estimates will be established in particular although there exist concave convex nonlinearities in the coupled system it is not necessary to assume that the corresponding lebesgue norms of the weight functions of the convex terms need to be small enough

path generation of articulated mechanisms by shape and topology variations in non linear truss representation this paper presents studies on an optimization based method for path generation of articulated mechanisms an extended truss ground structure approach is taken in which both the shape and topology of the truss are designed using cross sectional areas and nodal positions as design variables this leads to a technique for simultaneous type and dimensional synthesis of articulated mechanisms for the analysis part it is essential to control the mechanism configuration so that the mechanism remains within a given configuration space thus stabilizing the optimization process and resulting in realistic solutions this can be achieved by using the levenberg marquardt method the design method is illustrated by a number of design cases for both closed and open input and output paths

adjoint sensitivity analysis for nonlinear dynamic thermoelastic systems an adjoint approach is presented to formulate explicit sensitivities for a general functional associated with a nonlinear dynamic thermoelastic system uncoupled thermoelastic response and small deformation behavior are assumed the formulation uses the lagrange multiplier method to define an adjoint system the convolution operator to incorporate transient effects and domain parameterization to describe shape variations variations of the functional are expressed in explicit form with respect to perturbations of the design fields structural shape material properties applied loads prescribed boundary conditions and initial conditions the functional is defined in terms of the design fields and the implicit response fields displacement temperature strain temperature gradient stress heat flux vector reaction force and reaction surface flux in an example problem the finite element method is used to evaluate the real and adjoint responses and the shape sensitivities for a tank design problem the tank is modeled as a nonlinear quasistatic uncoupled thermoelastic system

higher order multi resolution topology optimization using the finite cell method this article presents a detailed study on the potential and limitations of performing higher order multi resolution topology optimization with the finite cell method to circumvent stiffness overestimation in high contrast topologies a length scale is applied on the solution using filter methods the relations between stiffness overestimation the analysis system and the applied length scale are examined while a high resolution topology is maintained the computational cost associated with nested topology optimization is reduced significantly compared with the use of first order finite elements this reduction is caused by exploiting the decoupling of density and analysis mesh and by condensing the higher order modes out of the stiffness matrix

higher order shell elements based on a cosserat model and their use in the topology design of structures for the purpose of carrying out topology optimization of shell structures we show that it is advantageous to use shell elements based on a classical shell theory such as the cosserat theory rather than elements based on the degenerated solid approach since the shell thickness appears explicitly in the formulation thereby greatly simplifying the sensitivity analysis one of the well known shell elements based on the cosserat shell theory is the four node element presented by simo et al comput methods appl mech engrg 72 1989 267 73 1989 53 although one could use this element the use of lower order elements often results in instabilities such as the checkerboard instability in the resulting topologies this provides the motivation for developing higher order shell elements based on a classical shell theory in this work we present the formulation and implementation details for six node and seven node triangular and nine node quadrilateral shell elements which are based on the variational formulation of simo et al and show that good accuracy is obtained even with coarse meshes in fairly demanding problems we also present the topology optimization formulation and some examples of optimal topologies that are obtained using this formulation

topology design optimization of geometrically non linear structures using meshfree method a topology optimization method using meshfree methods is developed for geometrically non linearly structures a density approach is used to optimally distribute the bulk material densities in a continuum design domain the reproducing kernel rk shape function is employed to discretize both displacement and bulk density fields thus the points can be located at any part of the design domain and be easily included in or excluded from the response analysis the well known convergence difficulty which normally occurs in the sub domain of low bulk density can be avoided by excluding the sub domain the numerical instability of bulk density solution due to the rank deficiency of system matrix is effectively prevented by properly selecting the number of independent design variables through numerous numerical examples we confirm that the developed method works very well even in the large deformation problems the sub domain exclusion scheme is found to be greatly beneficial in terms of computational costs compared with the results without the scheme

existence and asymptotic behavior of vector solutions for coupled nonlinear kirchhoff type systems abstract this paper deals with the following linearly coupled nonlinear kirchhoff type system a 1 b 1 r 3 u 2 d x u 1 u f u v in r 3 a 2 b 2 r 3 v 2 d x v 2 v g v u in r 3 u v h 1 r 3 where a i 0 b i 0 i 0 are constants for i 1 2 0 is a parameter and f g c r r under the general berestycki lions type assumptions on f and g we establish the existence of positive vector solutions and positive vector ground state solutions respectively by using variational methods we also study the asymptotic behavior of these solutions as 0

optimizing the layout of discrete objects in structures and materials a projection based topology optimization approach abstract this paper uses topology optimization to optimize the layout of discrete objects such as fixed shape void stiffening or functional inclusions in structures and periodic materials the methodology follows a material distribution approach and the heaviside projection method hpm is manipulated to ensure that the designed objects are discrete of fixed size length scale and shape and satisfy minimum spacing requirements these restrictions are achieved implicitly through projection without additional constraints or heuristics the methodology is built in the spirit of free form topology optimization and thus discrete objects are shown to appear vanish or translate across the design domain during the design evolution the technique is demonstrated on problems governed by mechanical stiffness including the design of structures and material microstructures whose elastic stiffness is to be enhanced by optimizing the location of stiff circular inclusions

an uncertainty principle for unimodular quantum groups we present a generalization of hirschman s entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups as a corollary we strengthen a well known uncertainty principle for compact groups and generalize the relation to compact quantum groups of kac type we also establish the complementarity of finite dimensional quantum group algebras in the non unimodular setting we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the haar weight as the measure of uncertainty we also show that when restricted to q traces of discrete quantum groups the relative entropy with respect to the haar weight reduces to the canonical entropy of the random walk generated by the state

voigt reuss topology optimization for structures with nonlinear material behaviors this work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization in the proposed framework alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain since two or more materials are permitted to simultaneously occupy local regions of the design domain small strain integration algorithms for general two material mixtures of solids are developed for the voigt isostrain and reuss isostress assumptions and hybrid combinations thereof structural topology optimization problems involving non linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis dsa of energy type functionals are presented the consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials elastoplastic materials and viscoelastic materials the good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures it is demonstrated through the second example that structures optimized for maximal strength can be significantly different than those optimized for minimal elastic compliance 1997 john wiley sons ltd

development of pareto topology optimization considering thermal loads abstract in this research we developed a level set based topology optimization with a topological derivative formulation considering thermal load thermo elasticity equations were utilized to obtain the sensitivity of the objective function after inserting a small hole in the domain total strain energy and the maximum stress in the design domain were taken as the objective functions after taking the thermal loading effect into account the total strain energy density function became a nonhomogeneous function of the strain in addition temperature variation changed hooke s law from a linear homogeneous to a linear nonhomogeneous expression including a zero order term we derived the sensitivity value of the selected objective functions with respect to a perturbation in the structural domain under mechanical and thermal loads while considering these changes in the governing equations we performed several numerical optimization problems to demonstrate the validity of the present level set based pareto topology optimization two types of examples compliance and stress minimization were solved based on the chosen objective functions furthermore in the stress minimization examples the derived formula was extended to consider thermal effects in the failure theories for pressure independent and dependent materials

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

a dual algorithm for the topology optimization of non linear elastic structures dual algorithms are ideally suited for the purpose of topology optimization since they work in the space of lagrange multipliers associated with the constraints to date dual algorithms have been applied only for linear structures here we extend this methodology to the case of non linear structures the perimeter constraint is used to make the topology problem well posed we show that the proposed algorithm yields a value of perimeter that is close to that specified by the user we also address the issue of manufacturability of these designs by proposing a variant of the standard dual algorithm which generates designs that are two dimensional although the loading and the geometry are three dimensional

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

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

topology and shape optimization for elastoplastic structural response abstract it is a common practice to base both material topology optimization as well as a subsequent shape optimization on linear elastic response however in order to obtain a realistic design it might be essential to base the optimization on a more realistic physical behavior i e to consider geometrically or and materially nonlinear effects in the present paper an elastoplastic von mises material model with linear isotropic hardening softening for small strains is used the objective of the design problem is to maximize the structural ductility in the elastoplastic range while the mass in the design space is prescribed with respect to the specific features of either topology or shape optimization for example the number of optimization variables or their local global influence on the structural response different methods are applied for topology optimization problems the gradient of the ductility is determined by the variational adjoint approach in shape optimization the derivatives of the state variables with respect to the optimization variables are evaluated analytically by a variational direct approach the topology optimization problem is solved by an optimality criteria oc method and the shape optimization problem by a mathematical programming mp method in topology optimization a geometrically adaptive procedure is additionally applied in order to increase the efficiency and to avoid artificial stress singularities the procedures are verified by 2d design problems under plane stress conditions

least energy solitary waves for a system of nonlinear schrodinger equations in mathbb r n in this paper we consider systems of coupled schrodinger equations which appear in nonlinear optics the problem has been considered mostly in the one dimensional case here we make a rigorous study of the existence of least energy standing waves solitons in higher dimensions we give conditions on the parameters of the system under which it possesses a solution with least energy among all multi component solutions conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie

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

uncertainty principles for locally compact quantum groups abstract in this paper we prove the donoho stark uncertainty principle for locally compact quantum groups and characterize the minimizer which are bi shifts of group like projections we also prove the hirschman beckner uncertainty principle for compact quantum groups and discrete quantum groups furthermore we show hardy s uncertainty principle for locally compact quantum groups in terms of bi shifts of group like projections

on subspaces of non commutative lp spaces abstract we study some structural aspects of the subspaces of the non commutative haagerup l p spaces associated with a general non necessarily semi finite von neumann algebra if a subspace x of l p contains uniformly the spaces l p n n 1 it contains an almost isometric almost 1 complemented copy of l p if x contains uniformly the finite dimensional schatten classes s p n it contains their l p direct sum too we obtain a version of the classical kadec pelczynski dichotomy theorem for l p spaces p 2 we also give operator space versions of these results the proofs are based on previous structural results on the ultrapowers of l p together with a careful analysis of the elements of an ultrapower l p u which are disjoint from the subspace l p these techniques permit to recover a recent result of n randrianantoanina concerning a subsequence splitting lemma for the general non commutative l p spaces various notions of p equiintegrability are studied one of which is equivalent to randrianantoanina s one and some results obtained by haagerup rosenthal and sukochev for l p spaces based on finite von neumann algebras concerning subspaces of l p containing l p are extended to the general case

canonical extension of actions of locally compact quantum groups abstract in this paper we generalize the notion of the canonical extension of automorphisms of von neumann algebras to the case of actions of locally compact quantum groups in the sense of kustermans and vaes various expected properties will be shown to hold for this new canonical extension as an application we describe the flow of weights of the crossed product of a type iii factor by some special action of a discrete kac algebra

the golden thompson trace inequality is complemented we prove a class of trace inequalities which complements the golden thompson inequality for example tr epa epb 2 p tr ea b holds for all p 0 when a and b are hermitian matrices and denotes the geometric mean we also prove related trace inequalities involving the logarithmic function namely p 1tr x log yp 2xpyp 2 tr x log x log y p 1tr x log xp 2ypxp 2 for all p 0 when x and y are nonnegative matrices these inequalities supply lower and upper bounds on the relative entropy

construction of a solution for the two component radial gross pitaevskii system with a large coupling parameter abstract we consider strongly coupled competitive elliptic systems that arise in the study of two component bose einstein condensates as the coupling parameter tends to infinity solutions that remain uniformly bounded are known to converge to a segregated limiting profile with the difference of its components satisfying a limit scalar pde in the case of radial symmetry under natural non degeneracy assumptions on a solution of the limit problem we establish by a perturbation argument its persistence as a solution to the elliptic system

topology optimization under uncertainty via non intrusive polynomial chaos expansion abstract this paper presents a systematic approach for topology optimization under uncertainty that integrates non intrusive polynomial chaos expansion with design sensitivity analysis for reliability based and robust topology optimization uncertainty is introduced in loading and in geometry to address the manufacturing variability the manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments failure probabilities and their sensitivities the number of simulations is reduced for linear structures under loading uncertainty by means of superposition efficiency of the non intrusive polynomial chaos approach is highlighted by comparison with the monte carlo method in terms of the number of simulations to demonstrate the effect of uncertainty optimized designs that consider uncertainty are compared to those that do not comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability based and worst case designs

shape and topology optimization of compliant mechanisms using a parameterization level set method in this paper a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms the structural shape boundary is implicitly embedded into a higher dimensional scalar function as its zero level set resultantly establishing the level set model by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function the temporal and spatial hamilton jacobi equation from the conventional level set method is then discretized into a series of algebraic equations accordingly the original shape and topology optimization is now fully transformed into a parameterization problem namely size optimization with the expansion coefficients of interpolants as a limited number of design variables design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints the structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method it is highlighted that the present method can not only inherit the merits of the implicit boundary representation but also avoid some unfavorable features of the conventional discrete level set method such as the cfl condition restriction the re initialization procedure and the velocity extension algorithm finally an extensively investigated example is presented to demonstrate the benefits and advantages of the present method especially its capability of creating new holes inside the design domain

algebraic tensor products and internal homs of noncommutative lp spaces abstract we prove that the multiplication map is an isometric isomorphism of quasi banach m m bimodules here is the noncommutative l p space of an arbitrary von neumann algebra m and m denotes the algebraic tensor product over m equipped with the quasi projective tensor norm but without any kind of completion similarly the left multiplication map is an isometric isomorphism of quasi banach m m bimodules where hom m denotes the algebraic internal hom in particular we establish an automatic continuity result for such maps applications of these results include establishing explicit algebraic equivalences between the categories of modules of junge and sherman for all p 0 as well as identifying subspaces of the space of bilinear forms on spaces this paper is also available at arxiv 1309 7856v2

the walsh basis in the lp spaces of hyperfinite iiiλ factors 0 λ 1 abstract we introduce a non commutative walsh system and prove that it forms a schauder basis in the l p spaces 1 p associated with the hyperfinite iii factors 0 1

a consistent relaxation of optimal design problems for coupling shape and topological derivatives in this article we introduce and analyze a general procedure for approximating a black and white shape and topology optimization problem with a density optimization problem allowing for the presence of grayscale regions our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem and on an interpolation scheme which endows the intermediate density regions with fictitious material properties under mild hypotheses on the smoothing operator and on the interpolation scheme we prove that the features of the approximate density optimization problem material properties objective function etc converge to their exact counterparts as the smoothing parameter vanishes in particular the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact objective these results shed new light on the connections between these two different notions of sensitivities for functions of the domain and they give rise to different numerical algorithms which are illustrated by several experiments

optimal design for polymer extrusion part i sensitivity analysis for nonlinear steady state systems we present a general framework to obtain analytical design sensitivities for steady state nonlinear systems where special emphasis is given to design variables that define prescribed boundary conditions the sensitivities are derived for a general response functional using both the direct and adjoint methods and are compared to show that the two sensitivity analysis methods yield identical expressions both adjoint and direct sensitivities for the generalized hele shaw system which models the flow of purely viscous non newtonian fluids through thin cavities are obtained using weak formulations and then discretized for the finite element analysis these sensitivities are used with numerical optimization to design polymer sheeting dies with minimum pressure drop and reduced velocity variation across the die exit

the non commutative flow of weights on a von neumann algebra abstract the flow of weights of connes and takesaki is a canonical functor from the category of separable factors to the category of ergodic flows the non commutative flow of weights is another canonical functor from the category of separable factors to the category of covariant systems of semi finite von neumann algebras equipped with trace scaling one parameter automorphism groups with conjugations as morphisms the constructions of these two functors are very similar the flow of weights functor is obtained by looking at all semi finite normal weights on a factor with the murray von neumann equivalence relation the non commutative flow of weights functor is obtained by relating an arbitrary pair of faithful semi finite normal weights by the connes cocycle not only does this construction put a period to the search for a canonical construction of the core of a factor of type iii but it also allows us to put the characteristic square of a factor obtained by katayama sutherland and takesaki in a new perspective the power of this new approach is seen in an ultimate solution to a long standing question of extending the extended modular automorphism of a dominant weight to an arbitrary weight which has been left open ever since the introduction of extended modular automorphisms by connes and takesaki over 20 years ago the construction of the functor ties together the theory of l p spaces of haagerup kosaki hilsum terp and izumi to the structure theory of a factor of type iii in fact the non commutative flow of weights is obtained by the analytic continuation of l p spaces to a pure imaginary value of p

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

interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems abstract the focus of this paper is on interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements numerical instability in the finite element simulations can often be observed due to excessive distortion in low stiffness regions a new energy interpolation scheme is proposed in order to stabilize the numerical simulations the elastic energy density in the solid and void regions is interpolated using the elastic energy densities for large and small deformation theory respectively the performance of the proposed method is demonstrated for a challenging test geometry as well as for topology optimization of minimum compliance and compliant mechanisms the effect of combining the proposed interpolation scheme with different hyperelastic material models is investigated as well numerical results show that the proposed approach alleviates the problems in the low stiffness regions and for the simulated cases results in stable topology optimization of structures undergoing large displacements

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

coupled mode equations and gap solitons for the 2d gross pitaevskii equation with a non separable periodic potential abstract gap solitons near a band edge of a spatially periodic nonlinear pde can be formally approximated by solutions of coupled mode equations cmes here we study this approximation for the case of the 2d periodic nonlinear schrodinger gross pitaevskii equation with a non separable potential of finite contrast we show that unlike in the case of separable potentials t dohnal d pelinovsky g schneider coupled mode equations and gap solitons in a two dimensional nonlinear elliptic problem with a separable periodic potential j nonlinear sci 19 2009 95 131 the cme derivation has to be carried out in bloch rather than physical coordinates using the lyapunov schmidt reduction we then give a rigorous justification of the cmes as an asymptotic model for reversible non degenerate gap solitons and provide h s estimates for this approximation the results are confirmed by numerical examples including some new families of cmes and gap solitons absent for separable potentials

stress based topology optimization of continuum structures under uncertainties abstract this work addresses the use of the topology optimization approach to the design of continuum structures with failure constraints under the hypothesis of uncertainties in the spatial distribution of young s modulus to this end the first order perturbation approach is used to model the response of the structure and the midpoint discretization technique is used to represent the random field the objective is the minimization of the amount of material used in the design subjected to local stress constraints under uncertainties the probability of failure is bounded by the one sided chebychev inequality since the exact probability distribution function of the stress constraints is not known in advance the effective probability of failure of the obtained optimal designs is validated with the use of the monte carlo simulation approach indicating that the probability of failures of the topologies obtained with the stochastic approach is within the bounds provided by the one sided chebychev inequality the optimization problem is solved by means of the augmented lagrangian method in order to address the large number of constraints associated to this kind of formulation it is shown that the correlation length and the number of standard deviations considered in the formulation play an important role in both the obtained topology and effective probability of failure

minimal energy solutions for repulsive nonlinear schrodinger systems abstract in this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear schrodinger system u u u 2 q 2 u b u q 2 u v q in r n v 2 v v 2 q 2 v b u q v q 2 v in r n we consider the repulsive case b 0 and assume that the exponent q satisfies 1 q n n 2 in case n 3 and 1 q in case n 1 or n 2 for space dimensions n 2 and arbitrary b 0 we prove the existence of fully nontrivial nonnegative solutions which converge to a solution of some optimal partition problem as b in case n 1 we prove that minimal energy solutions exist provided the coupling parameter b has small absolute value whereas fully nontrivial solutions do not exist if 1 q 2 and b has large absolute value

minimal coexistence configurations for multispecies systems abstract we deal with strongly competing multispecies systems of lotka volterra type with homogeneous neumann boundary conditions in dumbbell like domains under suitable non degeneracy assumptions we show that as the competition rate grows indefinitely the system reaches a state of coexistence of all the species in spatial segregation furthermore the limit configuration is a local minimizer for the associated free energy

sensitivity analysis of bifurcation load of finite dimensional symmetric systems three methods are presented for sensitivity analysis of bifurcation load factor of finite dimensional conservative symmetric systems subjected to a set of symmetric proportional loads in the first method a conventional method with diagonalization is utilized to derive an explicit formula of sensitivity coefficients corresponding to a minor imperfection next a new concept is introduced to find the sensitivity coefficients of the load factor displacements and the eigenmodes under fixed lowest eigenvalue of the tangent stiffness matrix based on this concept a method is presented for finding approximate sensitivity coefficients of the buckling load factor finally a direct method is presented to find the accurate sensitivity coefficients of the bifurcation load factor displacements at buckling and the buckling mode of a symmetric system note that different formula should be used for sensitivity analysis of a limit point load factor in the examples the proposed three methods are compared in view of accuracy of the results and simplicity in coding

an algorithm for the topology optimization of geometrically nonlinear structures summary most papers on topology optimization consider that there is a linear relation between the strains and displacements of the structure implicitly assuming that the displacements of the structure are small however when the external loads applied to the structure are large the displacements also become large so it is necessary to suppose that there is a nonlinear relation between strains and displacements in this case we say that the structure is geometrically nonlinear in practice this means that the linear system that needs to be solved each time the objective function of the problem is evaluated is replaced by an ill conditioned nonlinear system of equations moreover the stiffness matrix and the derivatives of the problem also become harder to compute the objective of this work is to solve topology optimization problems under large displacements through a new optimization algorithm named sequential piecewise linear programming this method relies on the solution of convex piecewise linear programming subproblems that include second order information about the objective function to speed up the algorithm these subproblems are converted into linear programming ones the new algorithm is not only globally convergent to stationary points but our numerical experiments also show that it is efficient and robust copyright 2014 john wiley sons ltd

positive solutions for schrodinger system with asymptotically periodic potentials abstract this paper is concerned with the following class of elliptic equations u x u f u v 2 u in r n v x v g v u 2 v in r n where u v h 1 r n n 3 0 are coupling constants x and x are asymptotically periodic functions f and g are continuous functions with subcritical growth this type of system arises in particular in models in bose einstein condensates theory we prove the existence of positive solution for this weakly coupled system with 0 sufficiently large furthermore we obtain some sufficient conditions for the nonexistence of positive solutions

ground state of n coupled nonlinear schrodinger equations in mathbb r n n leq 3 we establish some general theorems for the existence and nonexistence of ground state solutions of steady state n coupled nonlinear schrodinger equations the sign of coupling constants ij s is crucial for the existence of ground state solutions when all ij s are positive and the matrix is positively definite there exists a ground state solution which is radially symmetric however if all ij s are negative or one of ij s is negative and the matrix is positively definite there is no ground state solution furthermore we find a bound state solution which is non radially symmetric when n 3

schur and fourier multipliers of an amenable group acting on non commutative l p spaces consider a completely bounded fourier multiplierof a locally compact group g and take 1 p one can associate toa schur multiplier on the schatten classes sp l 2 g as well as a fourier multiplier on l p lg the non commutative l p space of the group von neumann algebra of g we prove that the completely bounded norm of the schur multiplier is not greater than the completely bounded norm of the l p fourier multiplier when g is amenable we show that equality holds extending a result by neuwirth and ricard to non discrete groups for a discrete group g and in the special case when p 6 2 is an even integer we show the following if there exists a map between l p lg and an ultraproduct of l p m sp l 2 g that intertwines the fourier multiplier with the schur multiplier then g must be amenable this is an obstruction to extend the neuwirth ricard result to non amenable groups

a reduction method for noncommutative l_p spaces and applications we consider the reduction of problems on general noncommutative l p spaces to the corresponding ones on those associated with finite von neumann algebras the main tool is an unpublished result of the first named author which approximates any noncommutative l p space by tracial ones we show that under some natural conditions a map between two von neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative l p spaces we present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale ergodic inequalities to those in the tracial case

nuclear maps and modular structures i general properties abstract we establish a correspondence between the split property of inclusions a b of von neumann algebras and nuclearity properties of the natural embeddings p l a lp b p 1 2 given by the modular theory

a gradient based parameter free approach to shape optimization in shape optimization the independent node movement approach wherein finite element node coordinates are used directly as design variables allows the most freedom for shape change and avoids the time consuming parameterization preprocess however this approach lacks a length scale control that is necessary to ensure a well posed shape optimization problem and avoid numerical instability motivated by the success of filtering techniques that impose minimum length scales in topology optimization we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

quantum f divergences in von neumann algebras i standard f divergences we make a systematic study of standard f divergences in general von neumann algebras an important ingredient of our study is to extend kosaki s variational expression of the relative entropy to an arbitrary standard f divergence from which most of the important properties of standard f divergences follow immediately in a similar manner we give a comprehensive exposition on the renyi divergence in von neumann algebras some results on relative hamiltonians formerly studied by araki and donald are improved as a by product we make a systematic study of standard f divergences in general von neumann algebras an important ingredient of our study is to extend kosaki s variational expression of the relative entropy to an arbitrary standard f divergence from which most of the important properties of standard f divergences follow immediately in a similar manner we give a comprehensive exposition on the renyi divergence in von neumann algebras some results on relative hamiltonians formerly studied by araki and donald are improved as a by product

a density gradient approach to topology optimization under design dependent boundary loading abstract the paper proposes a density gradient based approach to topology optimization under design dependent boundary loading since there is no explicit boundary representation in density based topology optimization the design dependent boundary loads are implicitly imposed through a domain integration of spatial gradient of the density field the density gradient based loading is formally derived and justified based on the smoothed boundary method for numerical solution of pde the heaviside projection density filtering and local refinement are combined to efficiently control the thickness of the loading interface and the number of elements within it for problems with both loading and non loading boundary an auxiliary density field is introduced to keep track of the loading boundary both 2d and 3d heat conduction problems linear elasticity problems and coupled thermoelastic problems under design dependent boundary loading are presented to illustrate the effectiveness and efficiency of the method

an immersed boundary element method for level set based topology optimization summary in this paper we propose a new bem for level set based topology optimization in the proposed bem the nodal coordinates of the boundary element are replaced with the nodal level set function and the nodal coordinates of the eulerian mesh that maintains the level set function because this replacement causes the nodal coordinates of the boundary element to disappear the boundary element mesh appears to be immersed in the eulerian mesh therefore we call the proposed bem an immersed bem the relationship between the nodal coordinates of the boundary element and the nodal level set function of the eulerian mesh is clearly represented and therefore the sensitivities with respect to the nodal level set function are strictly derived in the immersed bem furthermore the immersed bem completely eliminates grayscale elements that are known to cause numerical difficulties in topology optimization by using the immersed bem we construct a concrete topology optimization method for solving the minimum compliance problem we provide some numerical examples and discuss the usefulness of the constructed optimization method on the basis of the obtained results copyright 2012 john wiley sons ltd

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

canonical operator space structures on non commutative lp spaces we analyze canonical operator space structures on the non commutative lp spaces lp m constructed by interpolation a la stein weiss based on two normal semifinite faithful weights on a w algebra m we show that there is only one canonical i e arising by interpolation operator space structure on lp m when m and p are kept fixed namely for any n s f weights on m and 0 1 the spaces lp m are all completely isomorphic when they are canonically considered as operator spaces finally we also describe the norms on all matrix spaces mn lp m which determine such a canonical quantized structure

megapixel topology optimization on a graphics processing unit we show how the computational power and programmability of modern graphics processing units gpus can be used to efficiently solve large scale pixel based material distribution problems using a gradient based optimality criterion method to illustrate the principle a so called topology optimization problem that results in a constrained nonlinear programming problem with over 4 million decision variables is solved on a commodity gpu

adaptive continuation solid isotropic material with penalization for volume constrained compliance minimization abstract in this paper the traditional decreasing tolerance continuation solid isotropic material with penalization csimp was extended by providing a way to adapt the penalty step between subproblems decreasing the number of subproblems solved four linearly elastic volume constrained compliance minimization problems were used to test the efficacy of the penalty adaptation for different parameter settings three of the problems are common 2d test problems and one is 3d the main factors affecting the efficacy of the penalty adaptation were identified experimental results confirmed that the penalty adaptation successfully reduces the number of finite element analysis fea simulations needed to converge to the optimal solution when using the decreasing tolerance csimp dec tol csimp with exponentially decaying tolerance in particular the number of fea simulations required by dec tol csimp was cut down by an average of 28 8 with no more than 4 1 increase in the objective value in the worst case finally a mathematical and experimental treatment of the effect of x m i n on the convergence of the simp algorithm was given with recommendations for choosing a suitable value for x m i n

short note shape and topology optimization for electrothermomechanical microactuators using level set methods in this short note a shape and topology optimization method is presented for multiphysics actuators including geometrically nonlinear modeling based on an implicit free boundary parameterization method a level set model is established to describe structural design boundary by embedding it into the zero level set of a higher dimensional level set function the compactly supported radial basis functions csrbf are introduced to parameterize the implicit level set surface with a high level of accuracy and smoothness the original more difficult shape and topology optimization driven by the hamilton jacobi partial differential equation pde is transferred into a relatively easier parametric size optimization to which many well founded optimization algorithms can be applied thus the structural optimization is transformed to a numerical process that describes the design as a sequence of motions of the design boundaries by updating the expansion coefficients of the size optimization two widely studied examples are chosen to demonstrate the effectiveness of the proposed method

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

voigt reuss topology optimization for structures with linear elastic material behaviours the desired results of variable topology material layout computations are stable and discrete material distributions that optimize the performance of structural systems to achieve such material layout designs a continuous topology design framework based on hybrid combinations of classical reuss compliant and voigt sti mixing rules is investigated to avoid checkerboarding instabilities the continuous topology optimization formulation is coupled with a novel spatial ltering procedure the issue of obtaining globally optimal discrete layout designs with the proposed formulation is investigated using a continuation method which gradually transitions from the sti voigt formulation to the compliant reuss formulation the very good performance of the proposed methods is demonstrated on four structural topology design optimization problems from the literature 1997 by john wiley sons ltd

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

improving the efficiency of large scale topology optimization through on the fly reduced order model construction summarytopology optimization of large scale structures is computationally expensive notably because of the cost of solving the equilibrium equations at each iteration reduced order models by projection also known as reduced basis models have been proposed in the past for alleviating this cost we propose here a new method for coupling reduced basis models with topology optimization to improve the efficiency of topology optimization of large scale structures the novel approach is based on constructing the reduced basis on the fly using previously calculated solutions of the equilibrium equations the reduced basis is thus adaptively constructed and enriched based on the convergence behavior of the topology optimization a direct approach and an approach with adjusted sensitivities are described and their algorithms provided the approaches are tested and compared on various 2d and 3d minimum compliance topology optimization benchmark problems computational cost savings by up to a factor of 12 are demonstrated using the proposed methods copyright textcopyright 2014 john wiley sons ltd