stiffness optimization of non linear elastic structures this paper revisits stiffness optimization of non linear elastic structures due to the non linearity several possible stiffness measures can be identified and in this work conventional compliance i e secant stiffness designs are compared to tangent stiffness designs the optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions a well posed topology optimization problem is formulated by using restriction which is achieved via a helmholtz type filter the numerical examples provided show that for low load levels the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed

natural extensions for the rosen fractions the rosen fractions form an infinite family which generalizes the nearest integer continued fractions we find planar natural extensions for the associated interval maps this allows us to easily prove that the interval maps are weak bernoulli as well as to unify and generalize results of diophantine approximation from the literature

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

stock return distributions tests of scaling and universality from three distinct stock markets define the log return of stock price st over a time interval t rrtt log st tlog st1 analyses of returns of individual stocks 2 3 and stock indices 4 have shown that the cumulative distribution of returns is well fit by a power law asymptotic behavior with tail exponent r pr x xr 1

numerical methods for the topology optimization of structures that exhibit snap through the inclusion of non linear elastic analyses into the topology optimization problem is necessary to capture the finite deformation response e g the geometric non linear response of compliant mechanisms in previous work the non linear response is computed by standard non linear elastic finite element analysis here we incorporate a load displacement constraint method to traverse non linear equilibrium paths with limit points to design structures that exhibit snap through behaviour to accomplish this we modify the basic arc length algorithm and embed this analysis into the topology optimization problem copyright 2002 john wiley sons ltd

topology optimization of incompressible media using mixed finite elements abstract we present an alternative formulation for the topology optimization of structures made of incompressible materials a topic that cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements that are well known to be affected by the locking phenomenon a way out of the problem has recently been proposed in sigmund and clausen 2007 o sigmund p m clausen topology optimization using a mixed formulation an alternative way to solve pressure load problems comput methods appl mech engrg 196 13 16 2007 1874 1889 based on a displacement pressure finite element discretization the approach presented here consists in a truly mixed variational formulation coupled to a mixed fem discretization that uses the composite element of johnson and mercier for the discretization of the stress field by so doing the continuous and discrete inf sup conditions of the problem are automatically met even in the presence of incompressible materials a few numerical studies are presented to validate the theoretical framework for which the well known method of moving asymptotes mma is adopted for the numerical optimization of the problem different topologies in plane stress and plane strain conditions are presented with particular attention to the convergence of the last ones to pure 0 1 designs some forthcoming investigations are eventually highlighted including the solution of stress constrained topology optimization problems that find in the truly mixed setting their natural environment and the extension of the present formulation to deal with pressure load structural problems

boundary effects in a phase field approach to topology optimization a phase field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem the objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material since the interfaces between void and full material are penalized via a volume integral in the original phase field formulation there is no penalty associated with interfaces along the external boundaries in the present contribution an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization it is shown that the new boundary term enters the optimization as a robin boundary condition the method is implemented in a finite element setting and numerical simulations of typical structures are considered the results indicate that the optimal designs are influenced by the cost of interfaces to a large less

comparison theorems and orbit counting in hyperbolic geometry in this article we address an interesting problem in hyperbolic geometry this is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold e g word length displacement in the universal cover etc asymptotically our method involves a tnixture of ideas from both thermodynamic ergodic theory and the automaton associated to strongly markov groups 0 introduction in 5 cannon showed that for fundamental groups of many manifolds of negative curvature including for example compact manifolds the generating function for word length is a rational function to explain the implications of this property we recall that the growth of the quantity n n card g fe r igl n was studied by milnor in his fundamental paper 13 where he obtained estimates using comparison with the growth of volume in the universal cover cannon used purely combinatorial methods to show that the generating function is rational in particular this implies that we can find constants ybi and ci and positive integers ki i 1 n such that n n 1 1 cinkitn the key step in cannon s approach was to associate to the grol1p an automaton in this article we shall augment this with the notion of weighting this allows us to draw upon the well known theory of thermodynamic formalism to prove a number of new results which can be viewed as weighted analogues of the above results it has long been understood that this approach must havew close connections with symbolic dynamics markov partitions subshifts of finite type cf 1 20 21 and in particular the work of bourdon 4 and by extension to the whole paraphernalia of the area of dynamical systems collectively called thermodynamic formalism in this article we shall elaborate on this connection as an integral part of our analysis let teln for some n 2 denote n dimensional hyperbolic space i e the unique n dimensional simply connected complete riemannian manifold wi th all sectional received by the editors may 23 1995 1991 mathematics subject classification primary 20f32 22e40 58e40 secondary 11f72 20f10 58f20

characterizing multi scale self similar behavior and non statistical properties of fluctuations in financial time series abstract we make use of wavelet transform to study the multi scale self similar behavior and deviations thereof in the stock prices of large companies belonging to different economic sectors the stock market returns exhibit multi fractal characteristics with some of the companies showing deviations at small and large scales the fact that the wavelets belonging to the daubechies db basis enables one to isolate local polynomial trends of different degrees plays the key role in isolating fluctuations at different scales one of the primary motivations of this work is to study the emergence of the k 3 behavior x gabaix p gopikrishnan v plerou h stanley a theory of power law distributions in financial market fluctuations nature 423 2003 267 270 of the fluctuations starting with high frequency fluctuations we make use of db4 and db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series the fluctuations reveal fat tail non gaussian behavior unstable periodic modulations at finer scales from which the characteristic k 3 power law behavior emerges at sufficiently large scales we further identify stable periodic behavior through the continuous morlet wavelet

topology optimization using regularized intermediate density control abstract we consider topology optimization of elastic continua the elasticity tensor is assumed to depend linearly on the design function density as in the variable thickness sheet problem in order to get black white design pictures the intermediate density values are controlled by an explicit constraint this constraint is regularized by including a compact and linear operator s to guarantee existence of solutions a proof of convergence of the finite element fe discretized optimization problem s solutions to exact ones is also given so the method is not prone to numerical anomalies such as mesh dependence or checkerboards the procedure is illustrated in some minimum compliance examples where s is chosen to be a classical convolution type operator the fe discretized optimization problems are solved by sequential convex approximations

limit theorems for functionals of mixing processes with applications to u statistics and dimension estimation in this paper we develop a general approach for investigating the asymptotic distribution of functional xn f zn k k z of absolutely regular stochastic processes zn n z such functional occur naturally as orbits of chaotic dynamical systems and thus our results can be used to study probabilistic aspects of dynamical systems we first prove some moment inequalities that are analogous to those for mixing sequences with their help several limit theorems can be proved in a rather straightforward manner we illustrate this by re proving a central limit theorem of ibragimov and linnik then we apply our techniques to u statistics matrix equation with symmetric kernel h r r r we prove a law of large numbers extending results of aaronson burton dehling gilat hill and weiss for absolutely regular processes we also prove a central limit theorem under a different set of conditions than the known results of denker and keller as our main application we establish an invariance principle for u processes un h h indexed by some class of functions we finally apply these results to study the asymptotic distribution of estimators of the fractal dimension of the attractor of a dynamical system

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

structural topology optimization based on non local shepard interpolation of density field abstract this paper presents a non local density interpolation strategy for topology optimization based on nodal design variables in this method design variable points can be positioned at any locations in the design domain and may not necessarily coincide with elemental nodes by using the shepard family of interpolants the density value of any given computational point is interpolated by design variable values within a certain circular influence domain of the point the employed interpolation scheme has an explicit form and satisfies non negative and range restricted properties required by a physically significant density interpolation since the discretizations of the density field and the displacement field are implemented on two independent sets of points the method is well suited for a topology optimization problem with a design domain containing higher order elements or non quadrilateral elements moreover it has the ability to yield mesh independent solutions if the radius of the influence domain is reasonably specified numerical examples demonstrate the validity of the proposed formulation and numerical techniques it is also confirmed that the method can successfully avoid checkerboard patterns as well as islanding phenomenon

an optimal control problem in polyconvex hyperelasticity we consider an implant shape design problem arising in the context of facial surgery the aim is to find the shape of an implant that deforms the soft tissue of the skin in a desired way assuming sufficient regularity we introduce a reformulation as an optimal control problem where the control acts as a boundary force the solution of that problem can be used to recover the implant shape from the optimal state for a simplified problem in the case where the state can be modeled as a minimizer of a polyconvex hyperelastic energy functional we show existence of optimal solutions and derive on a formal level first order optimality conditions finally preliminary numerical results are presented for the original optimal control formulation

invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions in this paper we propose a formulation of polyconvex anisotropic hyperelasticity at finite strains the main goal is the representation of the governing constitutive equations within the framework of the invariant theory which automatically fulfill the polyconvexity condition in the sense of ball in order to guarantee the existence of minimizers based on the introduction of additional argument tensors the so called structural tensors the free energies and the anisotropic stress response functions are represented by scalar valued and tensor valued isotropic tensor functions respectively in order to obtain various free energies to model specific problems which permit the matching of data stemming from experiments we assume an additive structure a variety of isotropic and anisotropic functions for transversely isotropic material behaviour are derived where each individual term fulfills a priori the polyconvexity condition the tensor generators for the stresses and moduli are evaluated in detail and some representative numerical examples are presented furthermore we propose an extension to orthotropic symmetry

some convergence results for howard s algorithm this paper deals with convergence results of howard s algorithm for the resolution of min a in mathcal a b a x c a 0 where b a is a matrix c a is a vector and mathcal a is a compact set we show a global superlinear convergence result under a monotonicity assumption on the matrices b a extensions of howard s algorithm for a max min problem of the form max b in mathcal b min a in mathcal a b a b x c a b 0 are also proposed in the particular case of an obstacle problem of the form min ax b x g 0 where a is an n times n matrix satisfying a monotonicity assumption we show the convergence of howard s algorithm in no more than n iterations instead of the usual 2 n bound still in the case of an obstacle problem we establish the equivalence between howard s algorithm and a primal dual active set algorithm m hintermuller k ito and k kunisch siam j optim 13 2002 pp 865 888 the algorithms are illustrated on the discretization of nonlinear pdes arising in the context of mathematical finance american option and merton s portfolio problem of front propagation problems and for the double obstacle problem

quantum maps from transfer operators abstract the selberg zeta function s s yields an exact relationship between the periodic orbits of a fully chaotic hamiltonian system the geodesic flow on surfaces of constant negative curvature and the corresponding quantum system the spectrum of the laplace beltrami operator on the same manifold it was found that for certain manifolds s s can be exactly ewritten as the fredholm grothendieck determinant det 1 t s where ts is a generalization of the ruelle perron frobenius transfer operator we present an alternative derivation of this result yielding a method to find not only the spectrum but also the eigenfunctions of the laplace beltrami operator in terms of eigenfunctions of ts various properties of the transfer operator are investigated both analytically and numerically for several systems

element connectivity parameterization for topology optimization of geometrically nonlinear structures in the current element density based topology optimization element stiffness is penalized to yield either solid or void or very weak materials but low density elements appear during and even after optimization iterations especially when nonlinear problems involving large deformation are considered low density finite elements cause serious numerical problems as their tangent stiffness matrices lose positive definiteness to completely eliminate the problem caused by low density elements we propose a new method all finite elements are kept solid throughout the optimization process zero length elastic links are introduced to parameterize inter element connectivity the link stiffness is penalized in this approach the design variables are defined on the links and vary from 0 and 1 corresponding to the unconnected and rigidly connected states since the finite elements used to discretize the analysis domain always remain solid typical numerical problems encountered by the standard element density based formulation disappear to implement the present method several issues such as the handling of the mass constraint and raster imaging are also investigated

the coc algorithm part ii topological geometrical and generalized shape optimization abstract after outlining analytical methods for layout optimization and illustrating them with examples the coc algorithm is applied to the simultaneous optimization of the topology and geometry of trusses with many thousand potential members the numerical results obtained are shown to be in close agreement up to twelve significant digits with analytical results finally the problem of generalized shape optimization finding the best boundary topology and shape is discussed

large strain phase field based multi material topology optimization summary a multi material topology optimization scheme is presented the formulation includes an arbitrary number of phases with different mechanical properties to ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions an obstacle potential function which introduces infinity penalty for negative densities is utilized the problem is formulated for nonlinear deformations and the objective of the optimization is the end displacement the boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method to illustrate the possibilities of the method it is applied to a simple boundary value problem where optimal designs using multiple phases are considered copyright 2015 john wiley sons ltd

fluctuations in multiplicative systems with jumps fluctuation properties of the langevin equation including a multiplicative power law noise and a quadratic potential are discussed the noise has the l evy stable distribution if this distribution is truncated the covariance can be derived in the limit of large time it falls exponentially covariance in the stable case studied for the cauchy distribution exhibits a weakly stretched exponential shape and can be approximated by the simple exponential the dependence of that function on system parameters is determined then we consider a dynamics which involves the above process and obeys the generalized langevin equation the same as for the gaussian case the resulting distributions possess power law tails which fall similarly to those for the driving noise whereas central parts can assume the gaussian shape moreover a process with the covariance 1 t at large time is constructed and the corresponding dynamical equation is solved diffusion properties of systems for both covariances are discussed

scaling properties and universality of first passage time probabilities in financial markets financial markets provide an ideal frame for the study of crossing or first passage time events of non gaussian correlated dynamics mainly because large data sets are available tick by tick data of six futures markets are herein considered resulting in fat tailed first passage time probabilities the scaling of the return with its standard deviation collapses the probabilities of all markets examined and also for different time horizons into single curves suggesting that first passage statistics is market independent at least for high frequency data on the other hand a very closely related quantity the survival probability shows away from the center and tails of the distribution a hyperbolic t ensuremath 1 2 decay typical of a markovian dynamics albeit the existence of memory in markets modifications of the weibull and student distributions are good candidates for the phenomenological description of first passage time properties under certain regimes the scaling strategies shown may be useful for risk control and algorithmic trading

boundaries of markov partitions the core of a markov partition is the nonwandering set of the map restricted to the boundary of the partition we show that the core of a markov partition is always a finitely presented system then we show that every one sided sofic system occurs as the core of a markov partition for an n fold covering map on the circle and every two sided sofic system occurs as the core of a markov partition for a hyperbolic automorphism of the two dimensional torus

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

chaotic sets of continuous and discontinuous maps abstract this paper discusses li yorke chaotic sets of continuous and discontinuous maps with particular emphasis to shift and subshift maps scrambled sets and maximal scrambled sets are introduced to characterize li yorke chaotic sets the orbit invariant for a scrambled set is discussed some properties about maximality equivalence and uniqueness of maximal scrambled sets are also discussed it is shown that for shift maps the set of all scrambled pairs has full measure and chaotic sets of some discontinuous maps such as the gauss map interval exchange transformations and a class of planar piecewise isometries are studied finally some open problems on scrambled sets are listed and remarked

multiscale multifractal time irreversibility analysis of stock markets abstract time irreversibility is one of the most important properties of nonstationary time series complex time series often demonstrate even multiscale time irreversibility such that not only the original but also coarse grained time series are asymmetric over a wide range of scales we study the multiscale time irreversibility of time series in this paper we develop a method called multiscale multifractal time irreversibility analysis mmra which allows us to extend the description of time irreversibility to include the dependence on the segment size and statistical moments we test the effectiveness of mmra in detecting multifractality and time irreversibility of time series generated from delayed henon map and binomial multifractal model then we employ our method to the time irreversibility analysis of stock markets in different regions we find that the emerging market has higher multifractality degree and time irreversibility compared with developed markets in this sense the mmra method may provide new angles in assessing the evolution stage of stock markets

topology optimization utilizing inverse motion based form finding topology optimization at finite strain setting using the concept of inverse motion based form finding is introduced this novel procedure allows boundary conditions and shape of the structure in the operating deformed state to be prescribed the outcome of the optimization algorithm will be the shape of the undeformed structure i e the state in which the structure should be manufactured the objective of the optimization considered is to find the stiffest structure for a given amount of material the problem is regularized using a helmholtz filter which is formulated in the deformed configuration both the elastic boundary value problem and the partial differential equation associated with the helmholtz filter are solved using the finite element method the optimization problem is solved using a sequence of convex separable approximations the paper is closed by 2d as well as 3d numerical examples that clearly illustrates that the method is able to find optimal solutions for inverse motion finite strain topology optimization problems

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

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

on the third and fourth order constants of incompressible isotropic elasticity consider the constitutive law for an isotropic elastic solid with the strain energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain the stress strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit for this purpose use of the logarithmic strain tensor is of particular value it enables the limiting values of all nine fourth order elastic constants in the incompressible limit to be evaluated precisely and rigorously in particular it is explained why the three constants of fourth order incompressible elasticity and d are of the same order of magnitude several examples of application of the results follow including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation

symmetry groups of attractors for maps equivariant under the action of a finite group on n the possible symmetries of fixed points are known and correspond to the isotropy subgroups this paper investigates the possible symmetries of arbitrary possibly chaotic attractors and finds that the necessary conditions of melbourne dellnitz golubitsky 15 are sufficient at least for continuous maps

filters in topology optimization based on helmholtz type differential equations the aim of this paper is to apply a helmholtz type partial differential equation as an alternative to standard density filtering in topology optimization problems previously this approach has been successfully applied as a sensitivity filter the usual filtering techniques in topology optimization require information about the neighbor cells which is difficult to obtain for fine meshes or complex domains and geometries the complexity of the problem increases further in parallel computing when the design domain is decomposed into multiple non overlapping partitions obtaining information from the neighbor subdomains is an expensive operation the proposed filter technique requires only mesh information necessary for the finite element discretization of the problem the main idea is to define the filtered variable implicitly as a solution of a helmholtz type differential equation with homogeneous neumann boundary conditions the properties of the filter are demonstrated for various 2d and 3d topology optimization problems in linear elasticity solved on serial and parallel computers copyright 2010 john wiley sons ltd

symbolic dynamics for geodesic floes the subject of symbolic dynamics is of central importance in the modern theory of dynamical systems the use of symbolic sequences to study dynamical properties of geodesies originates in the work of koebe 21 22 and morse 24 25 and is already foreshadowed in hadamard 15 and jordan 19 the method of koebe and of morse is to code a geodesic on a surface m of negative curvature by recording the order in which it traverses a given set of labelled curves on m the treatment of morse allows variable curvature but assumes at least two boundary components whereas koebe assumes constant curvature but allows infinite connectivity and nonorientability and treats the more difficult case of a closed surface this last case is handled by recording crossings of a fixed pants decomposition anticipating the thurston parameterization of simple curves as described in 11 both koebe and morse used their codings to demonstrate the existence of countably many closed geodesies and of everywhere dense transitive geodesies morse further constructed the first nonsynthetic example of a recurrent nonperiodic discontinuous motion in modern terminology a minimal nowhere dense set later 26 morse treated the special closed surfaces of genus g associated to tesselations of the disc d by regular 4 gons each edge of a region in such a tesselation may be labelled by the isometry which glues it to another side of the same region in forming the quotient sin face m the set of isometries appearing as labels generate tti m thus any geodesic is coded as a doubly infinite sequence of generators of iri m the same method applies quite generally to tesselations associated to any fuchsian group we call the sequences thus obtained cutting sequences and refer to generating sets of this kind as geometric the difficulty of course is to determine precisely the class of sequences which occur for a surface with boundary one obtains exactly reduced sequences in the generators in generalthe problem4s gompligated1 henge the difficulties encountered in 26 see also theorem 3 below there is another method of coding geodesies using certain boundary expansions for points at infinity in the universal cover of m for the modular surface h sl 2 2 the appropriate expansions are continued fractions and for the symmetrical genus g surfaces above they are the nielsen boundary expansions of 27

finite element formulations for hyperelastic transversely isotropic biphasic soft tissues abstract this paper presents a finite element model for the three dimensional 3 d nonlinear analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions a biphasic continuum description is used to represent the soft tissue as a two phase mixture of incompressible inviscid fluid and a hyperelastic transversely isotropic solid alternate mixed penalty and velocity pressure finite element formulations are used to solve the nonlinear biphasic governing equations including the effects of a strain dependent permeability and a hyperelastic solid phase under finite deformation the resulting first order nonlinear system of equations are discretized in time using an implicit finite difference scheme and solved using the newton raphson method a significant contribution of this work is the implementation and testing of a biphasic description with a transversely isotropic hyperelastic solid phase this description considers a helmholtz free energy function of five invariants of the cauchy green deformation tensor and the preferred direction of the material allowing for asymmetric behavior in tension and compression an exponential form is suggested and a set of material parameters is identified to represent the response of soft tissues in ranges of deformation and stress observed experimentally after demonstrating the behavior of this constitutive model in simple tension and compression a sample problem of unconfined compression is used to further validate the finite element implementation

phase field relaxation of topology optimization with local stress constraints we introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase field method in the basic formulation we have a pde constrained optimization problem where the finite element and design analysis are solved simultaneously the starting point of the relaxation is a reformulation of the material problem involving linear and 0 1 constraints only the 0 1 constraints are then relaxed and approximated by a cahn hilliard type penalty in the objective functional which yields convergence of minimizers to 0 1 designs as the penalty parameter decreases to zero a major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter the relaxation scheme yields a large scale optimization problem with a high number of linear inequality constraints we discretize the problem by finite elements and solve the arising finite dimensional programming problems by a primal dual interior point method numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness of the new approach

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

formulation of implicit finite element methods for multiplicative finite deformation plasticity some constitutive and computational aspects of finite deformation plasticity are discussed attention is restricted to multiplicative theories of plasticity in which the deformation gradients are assumed to be decomposable into elastic and plastic terms it is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non symmetric even for associated plastic flow both explicit i e no equilibrium iteration and implicit finite element formulations are considered an assumed strain formulation is used to accommodate the near incompressibility associated with fully developed isochoric plastic flow as an example of explicit integration the rate tangent modulus method is reviewed in some detail an implicit scheme is derived for which the consistent tangents resulting in quadratic convergence of the equilibrium iterations can be written out in closed form for arbitrary material models all the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method

topology optimization using a mixed formulation an alternative way to solve pressure load problems abstract a shortcoming of the traditional density based approach to topology optimization is the handling of design dependent loads that relate to boundary data such as for example pressure loads previous works have introduced spline and iso density curves or alternative parametrization schemes to determine the load surfaces in this work we suggest a new way to solve pressure load problems in topology optimization using a mixed displacement pressure formulation for the underlying finite element problem we define the void phase to be an incompressible hydrostatic fluid in this way we can transfer pressure loads through the fluid without any needs for special load surface parametrizations the method is easily implemented in the standard density approach and is demonstrated to work efficiently for both 2d and 3d problems by extending the method to a three phase solid fluid void design method we also demonstrate design of water containing dams

statistical regularities of self intersection counts for geodesics on negatively curved surfaces let s be a compact surface with constant negative curvature 1 from among all closed geodesics on of length t choose one at random and letnt be the number of its self intersections we prove that for a certain constant 0 the random variable nt t t has a limit distribution as t we conjecture that for surfaces of variable negative curvature the order of magnitude of typical variations is t rather than t we also prove analogous results for generic geodesics that is geodesics whose initial tangent vectors are chosen randomly according to normalized liouville measure date november 10 2011 1991 mathematics subject classification primary 57m05 secondary 53c22 37d40

a polyconvex framework for soft biological tissues adjustment to experimental data the main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues the advantage of our approach is that only a few parameters are necessary to approximate a variety of stress strain curves and to satisfy the condition of a stress free reference configuration a priori in the framework of polyconvexity the proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized as an example the medial layer of a human abdominal aorta is investigated modeled by some of the proposed polyconvex functions and compared with experimental data hereby the economic fitting to experimental data and hence the easy handling of the functions is shown

a highly accurate 1st and 2nd order differentiation scheme for hyperelastic material models based on hyper dual numbers abstract in this paper we propose a numerical scheme for the calculation of stresses and corresponding consistent tangent moduli for hyperelastic material models which are derived in terms of the first and second derivatives of a strain energy function this numerical scheme provides a compact model independent framework which means that once the framework is implemented any other hyperelastic material model can be incorporated by solely modifying the energy function the method is based on the numerical calculation of strain energy derivatives using hyper dual numbers and thus referred to as hyper dual step derivative hdsd the hdsd does neither suffer from roundoff errors nor from truncation errors and is thereby a highly accurate method with high stability being insensitive to perturbation values furthermore it enables the calculation of derivatives of arbitrary order this is a great advantage compared to other numerical approaches as e g the finite difference approximation which is highly sensitive with respect to the perturbation value and which thus only yields accurate approximations for a small regime of perturbation values another alternative the complex step derivative approximation enables highly accurate derivatives for a wide range of small perturbation values but it only provides first derivatives and is thus not able to calculate stresses and moduli at once in this paper representative numerical examples using an anisotropic model are provided showing the performance of the proposed method in detail an introductory example shows the insensitivity with respect to the perturbation values and the higher accuracy compared to the finite difference scheme furthermore examples demonstrate the robustness and simple implementation of the hdsd scheme in finite element software it turns out that the higher accuracy compared with other approaches can still be achieved in reasonable computing time

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

metrical diophantine approximation for continued fraction like maps of the interval we study the metrical properties of a class of continued fraction like mappings of the unit interval each of which is defined as the fractional part of a mobius transformation taking the endpoints of the interval to zero and infinity

a variational approach for materially stable anisotropic hyperelasticity abstract in this work we propose an anisotropic stored energy function which satisfies a priori the legendre hadamard condition which is strongly related to the material stability of the constitutive equations in the linearized case this condition implies positive wave speeds the legendre hadamard condition plays also an important role for the local existence of solutions in the neighborhood of stationary points we apply the proposed hyperelastic energies to soft tissues and compare the formulation with existing models which have been used for the calculation of medial collateral ligament and arterial walls in our numerical and analytical investigations we discuss the distribution of wave speeds for a sequence of deformation states containing some essential stress strain characteristics of the compared models

implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers abstract in this paper novel implementation schemes for the automatic calculation of internal variables stresses and consistent tangent moduli for incremental variational formulations ivfs describing inelastic material behavior are proposed ivfs recast inelasticity theory as an equivalent optimization problem where the incremental stress potential within a discrete time interval is minimized in order to obtain the values of internal variables in the so called multilevel newton raphson method for the inelasticity theory this minimization problem is typically solved by using second derivatives with respect to the internal variables in addition to that to calculate the stresses and moduli further second derivatives with respect to deformation tensors are required compared with classical formulations such as the return mapping method the ivfs are relatively new and their implementation is much less documented furthermore higher order derivatives are required in the algorithms demanding increased implementation efforts therefore even though ivfs are mathematically and physically elegant their application is not standard here novel approaches for the implementation of ivfs using hdns of second and higher order are presented to arrive at a fully automatic and robust scheme with computer accuracy the proposed formulations are quite general and can be applied to a broad range of different constitutive models which means that once the proposed schemes are implemented as a framework any other dissipative material model can be implemented in a straightforward way by solely modifying the constitutive functions these include the helmholtz free energy function the dissipation potential function and additional side constraints such as e g the yield function in the case of plasticity its uncomplicated implementation for associative finite strain elasto plasticity and performance is illustrated by some representative numerical examples

almost sure invariance principle for sequential and non stationary dynamical systems we establish almost sure invariance principles a strong form of approximation by brownian motion for non stationary time series arising as observations on dynamical systems our examples include observations on sequential expanding maps perturbed dynamical systems non stationary sequences of functions on hyperbolic systems as well as applications to the shrinking target problem in expanding systems

howard s algorithm in a phase field topology optimization approach abstract in undetermined the topology optimization problem is formulated in a phase field approach the solution procedure is based on the allan cahn diffusion model where the conservation of volume is enforced by a global constraint the functional defining the minimization problem is selected such that no penalization is imposed for full and void materials upper and lower bounds of the density function are enforced by infinite penalty at the bounds a gradient term that introduces cost for boundaries and thereby regularizing the problem is also included in the objective functional conditions for stationarity of the functional are derived and it is shown that the problem can be stated as a variational inequality or a max min problem both defining a double obstacle problem the numerical examples used to demonstrate the method are solved using the fem whereas the double obstacle problem is solved using howard s algorithm less

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

polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility abstract in this article we investigate several models contained in the literature in the case of near incompressibility based on invariants in terms of polyconvexity and coerciveness inequality which are sufficient to guarantee the existence of a solution these models are due to rivlin and saunders namely the generalized polynomial type elasticity and arruda and boyce the extension to near incompressibility is usually carried out by an additive decomposition of the strain energy into a volume changing and a volume preserving part where the volume changing part depends on the determinant of the deformation gradient and the volume preserving part on the invariants of the unimodular right cauchy green tensor it will be shown that the arruda boyce model satisfies the polyconvexity condition whereas the polynomial type elasticity does not therefore we propose a new class of strain energy functions depending on invariants moreover we focus our attention on the structure of further isotropic strain energy functions

a new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization the main goal of this paper is to provide simple parameter identification process for most of hyperelastic constitutive laws in biomechanics of soft tissues the advantage of our approach lies on its rapidity and effectiveness by reducing analytically the number of parameters to identify in the model during the identification procedure with the use of genetic algorithms the search for an adequate initial guess point is avoided and the space solution of the objective function is reduced to meet only parameters that cannot be calculated analytically as an example we focus on models that predict arterial wall behaviour such as laws based on fung s type energy function holzapfel 2006 14 and holzapfel et al 2000 model 15 our approach is applied on uniaxial extension tests and the results are compared with available data in the literature

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

weil petersson metrics manhattan curves and hausdorff dimension in this note we want to relate the weil petersson metric on teichm uller space to the boundary correspondence between the actions on the boundary of fuchsian groups consider the space of riemann metrics g on a compact surface v with negative euler characteristic this can be endowed with a number of natural riemannian metrics of particular interest is the weil petersson metric whose definition was proposed by weil in 1958 based on earlier work of petersson cf 18 there is a particularly intuitive equivalent definition of the weil petersson metric using the second derivative of lengths of typical closed geodesics due to thurston and wolpert 19

topology optimization of energy absorbing structures with maximum damage constraint summary a novel density based topology optimization framework for plastic energy absorbing structural designs with maximum damage constraint is proposed this framework enables topologies to absorb large amount of energy via plastic work before failure occurs to account for the plasticity and damage during the energy absorption a coupled elastoplastic ductile damage model is incorporated with topology optimization appropriate material interpolation schemes are proposed to relax the damage in the low density regions while still ensuring the convergence of newton raphson solution process in the nonlinear finite element analyses an effective method for obtaining path dependent sensitivities of the plastic work and maximum damage via adjoint method is presented and the sensitivities are verified by the central difference method the effectiveness of the proposed methodology is demonstrated through a series of numerical examples copyright 2017 john wiley sons ltd

universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices the investigations of financial markets from a complex network perspective have unveiled many phenomenological properties in which the majority of these studies map the financial markets into one complex network in this work we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph a universal allometric scaling law is uncovered in the minimal spanning trees whose scaling exponent is independent of the stock market and the length of the stock index in contrast the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors there are marked discrepancies in the allometric scaling behaviors between the stock indices and the brownian motions using surrogate time series we find that these discrepancies are caused by the fat tailedness of the return distribution and the nonlinear long term correlation

the dynamics of pythagorean triples we construct a piecewise onto 3 to 1 dynamical system on the positive quadrant of the unit circle such that for rational points which correspond to normalized primitive pythagorean triples the associated ternary expansion is finite and is equal to the address of the ppt on barning s 1963 ternary tree of ppts while irrational points have infinite expansions the dynamical system is conjugate to a modified euclidean algorithm the invariant measure is identified and the system is shown to be conservative and ergodic we also show based on a result of aaronson and denker 1999 that the dynamical system can be obtained as a factor map of a cross section of the geodesic flow on a quotient space of the hyperbolic plane by the group 2 a free subgroup of the modular group with two generators

correlations for pairs of closed geodesics in this article we consider natural counting problems for closed geodesics on negatively curved surfaces we present asymptotic estimates for pairs of closed geodesics the differences of whose lengths lie in a prescribed family of shrinking intervals related pair correlation problems have been studied in both quantum chaos and number theory

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

symbolic dynamics for the modular surface and beyond in this expository article we describe the two main methods of representing geodesics on surfaces of constant negative curvature by symbolic sequences and their development a geometric method stems from a 1898 work of j hadamard and was developed by m morse in the 1920s it consists of recording the successive sides of a given fundamental region cut by the geodesic and may be applied to all finitely generated fuchsian groups another method of arithmetic nature uses continued fraction expansions of the end points of the geodesic at infinity and is even older it comes from the gauss reduction theory introduced to dynamics by e artin in a 1924 paper this method was used to exhibit dense geodesics on the modular surface for 80 years these classical works have provided inspiration for mathematicians and a testing ground for new methods in dynamics geometry and combinatorial group theory we present some of the ideas results old and recent and interpretations that illustrate the multiple facets of the subject

on lyapunov exponent and sensitivity sensitive dependence on initial conditions is widely understood as being the central idea of chaos for a large class of transformations of the interval we prove that positiveness of the lyapunov exponent implies the sensitivity property we also provide bounds for the sensitivity constant

generalized continued fractions1research supported by garc src kosef 1 the invariant measures for the transformations x f x on the unit interval are studied where i f c 2 ii f or p p 0 0 241485

correlations of length spectra for negatively curved manifolds in this paper we obtain asymptotic estimates for pairs of closed geodesics on negatively curved manifolds the differences of whose lengths lie in a prescribed family of shrinking intervals where the geodesics are ordered with respect to a discrete length in certain cases this discrete length can be taken to be the word length with respect to a set of generators for the fundamental group

shape and topology optimization based on the phase field method and sensitivity analysis this paper discusses a structural optimization method that optimizes shape and topology based on the phase field method the proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions the advantage of the method is the simplicity of computation since extra operations such as re initialization of functions are not required structural shapes are represented by the phase field function defined in the design domain and optimization of this function is performed by solving a time dependent reaction diffusion equation the artificial double well potential function used in the equation is derived from sensitivity analysis the proposed method is applied to two dimensional linear elastic and vibration optimization problems such as the minimum compliance problem a compliant mechanism design problem and the eigenfrequency maximization problem the numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations

eigenvalue based optimization of incompressible media using mixed finite elements with application to isolation devices abstract an alternative formulation for the eigenvalue optimization of structures made of incompressible material is presented the proposed methodology is based on the adoption of a truly mixed variational formulation that descends from the principle of hellinger reissner and passes the inf sup condition f brezzi m fortin mixed and hybrid finite element methods springer verlag new york 1991 even for incompressible materials this therefore allows to avoid the locking phenomenon that is a difficulty often found handling rubber material by means of commonly used displacement based finite elements the approach implemented in the work consists in the adoption of the discretized form of the truly mixed formulation that uses the composite element of johnson and mercier c johnson b mercier some equilibrium finite elements methods for two dimensional elasticity problems numer math 30 1978 103 116 to address eigenvalue based optimization problems for rubber like materials firstly classical eigenvalue designs for in plane vibrating bidimensional structures are studied relying on mma k svamberg method of moving asymptotes a new method for structural optimization int j numer methods engrg 24 3 1987 359 373 as minimization algorithm peculiar attention is paid to numerical troubles that may arise managing such kind of problems as the appearance of localized modes preventing an adequate convergence pattern and the difficulties in getting pure 0 1 designs typical of plane strain conditions suitable mass and stiffness interpolations are presented and tested to overcome these problems afterwards the proposed framework is used to approach the design of rubber like materials in a minimum compliance setting with the imposition of an upper limit on the first eigenvalue a bi phase stiffness interpolation is moreover implemented to deal with steel rubber design of aseismic bearing devices in civil engineering some forthcoming investigations are eventually highlighted including the implementation of stress constraints to improve the presented designs for manufacturing

free energy as a geometric invariant the free energy plays a fundamental role in statistical and condensed matter physics a related notion of free energy plays an important role in the study of hyperbolic dynamical systems in this paper we introduce and study a natural notion of free energy for surfaces with variable negative curvature this geometric free energy encodes a new type of marked length spectrum of closed geodesics which lies between the well known marked length spectrum marked by the corresponding element of the fundamental group and the unmarked length spectrum we prove that the free energy parametrizes the boundary of the domain of convergence of a poincare series which also encodes this spectrum we also show that this new length spectrum or equivalently the geometric free energy is not an isometry invariant in the final section we use tools from multifractal analysis to effect a fine asymptotic comparison of word length and geodesic length of closed geodesics we hope that our geometric understanding of free energy will provide new insight into this fundamental physical and dynamical quantity

materials with prescribed constitutive parameters an inverse homogenization problem abstract this paper deals with the construction of materials with arbitrary prescribed positive semi definite constitutive tensors the construction problem can be called an inverse problem of finding a material with given homogenized coefficients the inverse problem is formulated as a topology optimization problem i e finding the interior topology of a base cell such that cost is minimized and the constraints are defined by the prescribed constitutive parameters numerical values of the constitutive parameters of a given material are found using a numerical homogenization method expressed in terms of element mutual energies numerical results show that arbitrary materials including materials with poisson s ratio 1 0 and other extreme materials can be obtained by modelling the base cell as a truss structure furthermore a wide spectrum of materials can be constructed from base cells modelled as continuous discs of varying thickness only the two dimensional case is considered in this paper but formulation and numerical procedures can easily be extended to the three dimensional case

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

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

a multifractal detrended fluctuation analysis of trading behavior of individual and institutional traders in tehran stock market abstract employing the multifractal detrended fluctuation analysis mf dfa the multifractal properties of trading behavior of individual and institutional traders in the tehran stock exchange tse are numerically investigated using daily trading volume time series of these two categories of traders the scaling exponents generalized hurst exponents generalized fractal dimensions and singularity spectrum are derived furthermore two main sources of multifractality i e temporal correlations and fat tailed probability distributions are also examined we also compare our results with data of s p 500 results of this paper suggest that for both classes of investors in tse multifractality is mainly due to long range correlation while for s p 500 the fat tailed probability distribution is the main source of multifractality

statistical properties of trading volume of chinese stocks abstract the cumulative distribution of trading volume is investigated for chinese stocks different from the power law scaling of mature markets the distribution is well fitted by a stretched exponential function f x e x with the autocorrelation function and the detrended fluctuation analysis the long range autocorrelation of trading volume is revealed the conditional dependence of volume on volatility and the volume volatility cross correlation are studied and a positive long range correlation between volume and volatility is observed