some novel developments in finite element procedures for gradient dependent plasticity summary improved algorithms are proposed for a gradient plasticity theory in which the laplacian of an invariant plastic strain measure enters the yield function particular attention is given to the type of finite elements that can be used within the format of gradient dependent plasticity assuming a weak satisfaction of the yield function mixed finite elements are developed in which the invariant plastic strain measure and the displacements are discretized two families of finite elements are developed one in which the invariant plastic strain measure is interpolated using c continuous polynomials and one in which penalty enhanced c continuous interpolants are used the performance of both families of finite elements is assessed numerically in one dimensional and two dimensional boundary value problems the regularizing effect of the used gradient enhancement in computations of elastoplastic solids is demonstrated both for mesh refinement and for the directional bias of the grid lines

numerical analysis of an elasto piezoelectric problem with damage in this paper we analyze an algorithm for the quasistatic evolution of the mechanical state of an elasto piezoelectric body with damage both damage caused by the development and the growth of internal microcracks and piezoelectric effects are included in the model the mechanical problem is expressed as an elliptic system for the displacement field coupled with a non linear parabolic partial differential equation for the damage field and a linear partial differential equation for the electric potential the variational formulation leads to a coupled system composed of two linear variational equations for the displacement field and the electric potential and a non linear parabolic variational equation for the damage field the existence of a unique weak solution is stated then a fully discrete scheme is introduced by using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally some numerical simulations are performed in one two and three dimensions to demonstrate the accuracy of the scheme and the behaviour of the solution copyright 2008 john wiley sons ltd

analysis of two frictional viscoplastic contact problems with damage in this work we study two quasistatic frictional contact problems arising in viscoplasticity including the mechanical damage of the material caused by excessive stress or strain and modelled by an inclusion of parabolic type the variational formulation is provided for both problems and the existence of a unique solution is proved for each of them then a fully discrete scheme is introduced using the finite element method to approximate the spatial domain and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity assumptions the linear convergence of the algorithm is deduced finally some numerical examples are presented to show the performance of the method

elastoplastic damage modelling including the gradient of damage formulation and computational aspects a framework for continuum elastoplastic damage modelling which employs irreversible thermodynamics and internal state variables is investigated the damage part of the modelling involves the gradient of damage quantity which together with the equations of motion are issued from a new formulation of the principle of virtual power recently proposed it is shown how the plastic part of the modelling takes its standard format next we consider in detail the variational formulation and subsequent numerical implementation of the elastoplastic damage models the development of an algorithm consistent with the present formulation is given where for the plastic part it leaves the standard return mapping algorithms unchanged application is made to different classical rate independent and rate dependent plastic models with the presence of a damage mechanism the numerical implementation in the context of the finite element method is discussed in detail and a set of representative applications and numerical examples is given

gradient constitutive relations numerical aspects and application to gradient damage abstract the description of localisation and structural failure through local strain softening constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of internal variables in addition to the strain and the internal variables themselves under some assumptions it is shown that these gradient laws can be cast into a variational formulation after time discretisation the evolution of the internal variable field is characterised by a minimum principle a specific algorithm is proposed to perform the minimisation in the context of finite elements finally it is applied to a gradient brittle damage model

micromorphic approach for finite gradient elastoplasticity fully coupled with ductile damage formulation and computational aspects abstract it is well established that the use of inelastic constitutive equations accounting for induced softening leads to pathological space mesh and time discretization dependency of the numerical solution of the associated initial and boundary value problem ibvp to avoid this drawback many less or more approximate solutions have been proposed in the literature in order to regularize the ibvp and to obtain numerical solutions which are at convergence much less sensitive to the space and the time discretization the basic idea behind these regularization techniques is the formulation of nonlocal constitutive equations by introducing some effects of characteristic lengths representing the materials microstructure in this work using the framework of generalized nonlocal continua a thermodynamically consistent micromorphic formulation using appropriate micromorphic state variables and their first gradients is proposed in order to extend the classical local constitutive equations by incorporating appropriate characteristic internal lengths the isotropic damage the isotropic and the kinematic hardenings are supposed to carry the targeted micromorphic effects first the theoretical aspects of this fully coupled micromorphic formulation is presented in details and the proposed generalized balance equations as well as the fully coupled micromorphic constitutive equations deduced the associated numerical aspects in the framework of the classical galerkin based fe formulation are briefly discussed in the special case of micromorphic damage specifically the formulation of 2d finite elements with additional degrees of freedom d o f the dynamic explicit global resolution scheme as well as the local integration scheme to compute the stress tensor and the state variables at each integration point of each element are presented application is made to the typical uniaxial tension specimen under plane strain conditions in order to chow the predictive capabilities of the proposed micromorphic model particularly against its ability to give at convergence a mesh independent solution even for high values of the ductile damage i e the macroscopic cracks

quasistatic normal compliance contact problem of visco elastic bodies with coulomb friction implemented by qp and sgbem the quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with coulomb friction at small strains in kelvin voigt rheology is considered the discretization is made by a semi implicit formula in time and the symmetric galerkin boundary element method sgbem in space assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient the obtained recursive minimization problem formulated only on the contact boundary has a nonsmooth cost function if the normal compliance responds linearly and the 2d problems are considered then the cost function is piecewise quadratic which after a certain transformation gets the quadratic programming qp structure however it would lead to second order cone programming in 3d problems finally several computational tests are presented and analysed with an additional discussion on numerical stability and convergence of the involved approximated poincare steklov operators

large deviations of the length of the longest increasing subsequence of random permutations and random walks we study numerically the length distribution of the longest increasing subsequence lis for random permutations and one dimensional random walks using sophisticated large deviation algorithms we are able to obtain very large parts of the distribution especially also covering probabilities smaller than 10 1000 this enables us to verify for the length of the lis of random permutations the analytically known asymptotics of the rate function and even the whole tracy widom distribution we observe a rather fast convergence in the larger than typical part to this limiting distribution for the length l of lis of random walks no analytical results are known to us we test a proposed scaling law and observe convergence of the tails into a collapse for increasing system size further we obtain estimates for the leading order behavior of the rate functions in both tails

number of longest increasing subsequences we study the entropy s of longest increasing subsequences liss i e the logarithm of the number of distinct liss we consider two ensembles of sequences namely random permutations of integers and sequences drawn independent and identically distributed i i d from a limited number of distinct integers using sophisticated algorithms we are able to exactly count the number of liss for each given sequence furthermore we are not only measuring averages and variances for the considered ensembles of sequences but we sample very large parts of the probability distribution p s with very high precision especially we are able to observe the tails of extremely rare events which occur with probabilities smaller than 10 600 we show that the distribution of the entropy of the liss is approximately gaussian with deviations in the far tails which might vanish in the limit of long sequences further we propose a large deviation rate function which fits best to our observed data

large deviations for increasing sequences on the plane we prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among poisson points on the plane the rate function for lower tail deviations is derived from a 1977 result of logan and shepp about young diagrams of random permutations for the upper tail we use a coupling with hammersley s particle process and convex analytic techniques along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric hammersley s process

an elastic viscoplastic quasistatic contact problem existence and uniqueness of a weak solution in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to internal tension or compression and caused by the opening and growth of micro cracks and micro cavities is also considered the variational formulation leads to a coupled system of evolutionary equations an existence and uniqueness result is established by using approximate problems the pseudomonotone operators theory schauder fixed point theorem and a comparison result

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

financial asset returns direction of change forecasting and volatility dynamics we consider three sets of phenomena that feature prominently in the financial economics literature 1 conditional mean dependence or lack thereof in asset returns 2 dependence and hence forecastability in asset return signs and 3 dependence and hence forecastability in asset return volatilities we show that they are very much interrelated and explore the relationships in detail among other things we show that 1 volatility dependence produces sign dependence so long as expected returns are nonzero so that one should expect sign dependence given the overwhelming evidence of volatility dependence 2 it is statistically possible to have sign dependence without conditional mean dependence 3 sign dependence is not likely to be found via analysis of sign autocorrelations runs tests or traditional market timing tests because of the special nonlinear nature of sign dependence so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments 4 sign dependence is not likely to be found in very high frequency e g daily or very low frequency e g annual returns instead it is more likely to be found at intermediate return horizons and 5 the link between volatility dependence and sign dependence remains intact in conditionally non gaussian environments for example with time varying conditional skewness and or kurtosis

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

convex hull of n planar brownian motions exact results and an application to ecology we compute exactly the mean perimeter and area of the convex hull of n independent planar brownian paths each of duration t both for open and closed paths we show that the mean perimeter alpha n sqrt t and the mean area beta n t for all t the prefactors alpha n and beta n computed exactly for all n increase very slowly logarithmically with increasing n this slow growth is a consequence of extreme value statistics and has interesting implications in an ecological context in estimating the home range of a herd of animals with a population size n

sampling rare events statistics of local sequence alignments a method to calculate probability distributions in regions where the events are very unlikely e g p approximately 10 40 is presented the basic idea is to map the underlying model on a physical system the system is simulated at a low temperature such that preferably configurations with originally low probabilities are generated since the distribution of such a physical system is known the original unbiased distribution can be obtained as an application local alignment of protein sequences is studied the deviation of the distribution p s of optimum scores from the extreme value distribution is quantified this deviation decreases with growing sequence length

exact scaling functions for one dimensional stationary kpz growth we determine the stationary two point correlation function of the one dimensional kpz equation through the scaling limit of a solvable microscopic model the polynuclear growth model the equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a riemann hilbert problem related to the painleve ii equation we solve these equations numerically with very high precision and compare our up to numerical rounding exact result with the prediction of colaiori and moore 1 obtained from the mode coupling approximation

empirical scaling of the length of the longest increasing subsequences of random walks we provide monte carlo estimates of the scaling of the length l n of the longest increasing subsequences of n step random walks for several different distributions of step lengths short and heavy tailed our simulations indicate that barring possible logarithmic corrections with the leading scaling exponent for the heavy tailed distributions of step lengths examined with values increasing as the distribution becomes more heavy tailed and for distributions of finite variance irrespective of the particular distribution the results are consistent with existing rigorous bounds for although in a somewhat surprising manner for random walks with step lengths of finite variance we conjecture that the correct asymptotic behavior of l n is given by and also propose the form for the subleading asymptotics the distribution of l n was found to follow a simple scaling form with scaling functions that vary with accordingly when the step lengths are of finite variance they seem to be universal the nature of this scaling remains unclear since we lack a working model microscopic or hydrodynamic for the behavior of the length of the longest increasing subsequences of random walks

investigating market efficiency through a forecasting model based on differential equations abstract a new differential equation based model for stock price trend forecast is proposed as a tool to investigate efficiency in an emerging market its predictive power showed statistically to be higher than the one of a completely random model signaling towards the presence of arbitrage opportunities conditions for accuracy to be enhanced are investigated and application of the model as part of a trading strategy is discussed

variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance friction and damage we consider a model for quasistatic frictional contact between a viscoelastic body and a foundation the material constitutive relation is assumed to be nonlinear the mechanical damage of the material caused by excessive stress or strain is described by the damage function the evolution of which is determined by a parabolic inclusion the contact is modeled with the normal compliance condition and the associated version of coulomb s law of dry friction we derive a variational formulation for the problem and prove the existence of its unique weak solution we then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions

contemporaneous asymmetry in garch processes abstract the paper introduces a new concept of asymmetry contemporaneous asymmetry in conditional heteroskedasticity models we propose an original class of models aimed to capture the leverage effect contemporaneous asymmetry as well as time varying skewness and kurtosis not only past up and down moves have different impacts on the conditional variance but also positive and negative changes are governed by different conditional variances we give conditions for the existence of a second order and strictly stationary solution the paper also provides consistency results on the quasi maximum likelihood estimation finally an empirical analysis on the french cac 40 stock index is proposed

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

le spectre de certaines mosaiques poissoniennes du plan et l enveloppe convexe du pont brownien the spectral empirical function of a homogeneous isotropic poisson mosaic process is a functional of the perimeter of the convex hull of planar brownian bridge some geometrical identities follow

the smart kinetic self avoiding walk and schramm loewner evolution the smart kinetic self avoiding walk sksaw is a random walk which never intersects itself and grows forever when run in the full plane at each time step the walk chooses the next step uniformly from among the allowable nearest neighbors of the current endpoint of the walk in the full plane a nearest neighbor is allowable if it has not been visited before and there is a path from the nearest neighbor to infinity through sites that have not been visited before it is well known that on the hexagonal lattice the sksaw in a bounded domain between two boundary points is equivalent to an interface in critical percolation and hence its scaling limit is the chordal schramm loewner evolution with kappa 6 sle 6 like sle there are variants of the sksaw depending on the domain and the initial and terminal points on the hexagonal lattice these variants have been shown to converge to the corresponding version of sle 6 it is believed that the scaling limit of all these variants on any regular lattice is the corresponding version of sle 6 we test this conjecture for the square lattice by simulating the sksaw in the full plane and find excellent agreement with the predictions of full plane sle 6

on large deviation properties of erdos renyi random graphs we show that large deviation properties of erdos renyi random graphs can be derived from the free energy of the q state potts model of statistical mechanics more precisely the legendre transform of the potts free energy with respect to ln q is related to the component generating function of the graph ensemble this generalizes the well known mapping between typical properties of random graphs and the q 1 limit of the potts free energy for exponentially rare graphs we explicitly calculate the number of components the size of the giant component the degree distributions inside and outside the giant component and the distribution of small component sizes we also perform numerical simulations which are in very good agreement with our analytical work finally we demonstrate how the same results can be derived by studying the evolution of random graphs under the insertion of new vertices and edges without recourse to the thermodynamics of the potts model

implicit gradient elasticity a new formulation of gradient elasticity is derived and implemented pade approximations are used to introduce an implicit relation between non local strains and displacements as a result the finite element interpolation requires only 0 continuous rather than 1 continuous shape functions the underlying energy functional is presented and it is found that the present formulation is of the mixed type whereby the non local strains act as the primary unknowns and the displacements as the auxiliary unknowns the implications on the interpolation are studied finally the influence of the additional length scale parameter on the global response is assessed copyright 2006 john wiley sons ltd

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

discontinuous bifurcation analysis of thermodynamically consistent gradient poroplastic materials abstract in this work analytical and numerical solutions of the condition for discontinuous bifurcation of thermodynamically consistent gradient based poroplastic materials are obtained and evaluated the main aim is the analysis of the potentials for localized failure modes in the form of discontinuous bifurcation in partially saturated gradient based poroplastic materials as well as the dependence of these potentials on the current hydraulic and stress conditions also the main differences with the localization conditions of the related local theory for poroplastic materials are evaluated to perfectly understand the regularization capabilities of the non local gradient based one firstly the condition for discontinuous bifurcation is formulated from wave propagation analyses in poroplastic media the material formulation employed in this work for the spectral properties evaluation of the discontinuous bifurcation condition is the thermodynamically consistent gradient based modified cam clay model for partially saturated porous media previously proposed by the authors the main and novel feature of this constitutive theory is the inclusion of a gradient internal length of the porous phase which together with the characteristic length of the solid skeleton comprehensively defined the non local characteristics of the represented porous material after presenting the fundamental equations of the thermodynamically consistent gradient based poroplastic constitutive model the analytical expressions of the critical hardening softening modulus for discontinuous bifurcation under both drained and undrained conditions are obtained as a particular case the related local constitutive model is also evaluated from the discontinuous bifurcation condition stand point then the localization analysis of the thermodynamically consistent non local and local poroplastic cam clay theories is performed the results demonstrate on the one hand and related to the local poroplastic material the decisive role of the pore pressure and of the volumetric non associativity degree on the location of the transition point between ductile and brittle failure regimes in the stress space on the other hand the results demonstrate as well the regularization capabilities of the non local gradient based poroplastic theory with exception of a particular stress condition which is also evaluated in this work finally it is also shown that due to dependence of the characteristic lengths for the pore and skeleton phases on the hydraulic and stress conditions the non local theory is able to reproduce the strong reduction of failure diffusion that takes place under both low confinement and low pore pressure of partially saturated porous materials without loosing however the ellipticity of the related differential equations

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

algorithms for gradient damage models based on a semi smooth newton method in this paper two different algorithms are applied to a model of brittle damage including the gradient of the damage variable both algorithms are based on a modified newton method in the first algorithm the newton method is applied directly to the whole system of equations while in the second algorithm the equilibrium equations and the damage evolution problem are solved uncoupled from each other in a gauss seidel scheme the algorithms are applied to two different formulations of the problem in the first formulation the thermodynamic force work conjugate to the damage variable is kept as an auxiliary variable while in the second formulation this variable is eliminated it turns out that the formulation using the extra variable is more robust in the sense that the algorithms converge even for very large load increments on the other hand the formulation where the extra variable is eliminated is more efficient for small time steps since a smaller system of equations is solved for each increment furthermore it is found that the direct approach is more efficient than the decoupled approach for this problem

a thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking a new gradient damage model is derived starting from thermodynamic statements nonstandard terms are added to the free energy potential for this purpose in contrast with existing approaches these terms are related to the kinematics of the problem and therefore come into play already in the elastic regime following the argument that the second law of thermodynamics need only be satisfied globally for a nonlocal continuum an energy balance equation is derived which must be solved together with the usual equilibrium equations numerical solutions of this coupled set of equations have been generated for a one dimensional problem in order to study the localisation behaviour of the new model in the limit where the elastic modulus related to the energy balance goes to 0 an earlier gradient damage model is retrieved this simplified model is used to study cracking of brick masonry under the influence of mechanical loading

a quasistatic contact problem for viscoelastic materials with friction and damage abstract we consider a mathematical model which describes the frictional contact between a deformable body and a foundation the process is quasistatic the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions the mechanical damage of the material is described by the damage function which is modelled by a nonlinear partial differential equation we derive the variational formulation of the problem which is a coupled system of a hemivariational inequality and a parabolic equation then we prove the existence of a unique weak solution to the model the proof is based on arguments of abstract stationary inclusion and a fixed point theorem

convex hulls of random walks in higher dimensions a large deviation study the distribution of the hypervolume v and surface v of convex hulls of multiple random walks in higher dimensions are determined numerically especially containing probabilities far smaller than p 10 1000 to estimate large deviation properties for arbitrary dimensions and large walk lengths t we suggest a scaling behavior of the distribution with the length of the walk t similar to the two dimensional case and behavior of the distributions in the tails we underpin both with numerical data in d 3 and d 4 dimensions further we confirm the analytically known means of those distributions and calculate their variances for large t

large deviations of connected components in the stochastic block model we study the stochastic block model which is often used to model community structures and study community detection algorithms we consider the case of two blocks in regard to its largest connected component and largest biconnected component respectively we are especially interested in the distributions of their sizes including the tails down to probabilities smaller than 10 ensuremath 800 for this purpose we use sophisticated markov chain monte carlo simulations to sample graphs from the stochastic block model ensemble we use these data to study the large deviation rate function and conjecture that the large deviation principle holds further we compare the distribution to the well known erd ifmmode mbox h o else h o fi s r enyi ensemble where we notice subtle differences at and above the percolation threshold

intrinsic volumes of sobolev balls with applications to brownian convex hulls a formula due to sudakov relates the first intrinsic volume of a convex set in a hilbert space to the maximum of the isonormal gaussian process over this set using this formula we compute the first intrinsic volumes of infinite dimensional convex compact sets including unit balls with respect to sobolev type seminorms and ellipsoids in the hilbert space we relate the distribution of the random one dimensional projections of these sets to the distributions s1 s2 c1 c2 studied by biane pitman yor bull ams 38 2001 we show that the k th intrinsic volume of the set of all functions on 0 1 which have lipschitz constant bounded by 1 and which vanish at 0 respectively which have vanishing integral is given by vk k 2 3 2 k 1 respectively vk k 1 2 2 3 2 k 3 2 this is related to the results of gao and vitale discrete comput geom 26 2001 elect comm probab 8 2003 who considered a similar question for functions with a restriction on the total variation instead of the lipschitz constant using the results of gao and vitale we give a new proof of the formula for the expected volume of the convex hull of the d dimensional brownian motion which is due to eldan elect j probab to appear additionally we prove an analogue of eldan s result for the brownian bridge similarly we show that the results on the intrinsic volumes of the lipschitz balls can be translated into formulae for the expected volumes of zonoids aumann integrals generated by the brownian motion and the brownian bridge also these results have discrete versions for gaussian random walks and bridges our proofs exploit sudakov s and tsirelson s theorems which establish a connection between the intrinsic volumes and the isonormal gaussian process

critical exponent for the loop erased self avoiding walk by monte carlo methods a monte carlo simulation was performed for loop erased self avoiding walks lesaw to ascertain the exponentv for the z2 and z3 lattices the estimated values were 2v 1 600 0 006 in two dimensions and 2v 1 232 0 008 in three dimensions leading to the conjecturev 4 5 for the two dimensional lesaw these results add to existing evidence that the loop erased self avoiding walks are not in the same universality class as self avoiding walks

a frictionless contact problem for elastic viscoplastic materials with normal compliance and damage abstract we study a quasistatic frictionless contact problem with normal compliance and damage for elastic viscoplastic bodies the mechanical damage of the material caused by excessive stress or strain is described by a damage function whose evolution is modelled by an inclusion of parabolic type we provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution to the model we then introduce and study a fully discrete scheme for the numerical solutions of the problem an optimal order error estimate is derived for the approximate solutions under suitable solution regularity numerical examples are presented to show the performance of the method

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity the paper presents the theory and the numerics of a thermodynamically consistent formulation of gradient plasticity at small strains starting from the classical local continuum formulation which fails to produce physically meaningful and numerically converging results within localization computations a thermodynamically motivated gradient plasticity formulation is envisioned the model is based on an assumption for the helmholtz free energy incorporating the gradient of the internal history variable a yield condition and the postulate of maximum dissipation resulting in an associated structure as a result the driving force conjugated to the hardening evolution is identified as the quasi non local drag stress which incorporates besides the strictly local drag stress essentially the divergence of a vectorial hardening flux at the numerical side besides the balance of linear momentum the algorithmic consistency condition has to be solved in weak form thereby the crucial issue is the determination of the active constraints exhibiting plastic loading which is solved by an active set search algorithm borrowed from convex non linear programming moreover different discretization techniques are proposed in order to compare the fe performance in local plasticity with the advocated gradient formulation both for hardening and softening copyright 2001 john wiley sons ltd

gradient elasticity and nonstandard boundary conditions abstract gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality the pertinent thermodynamic restrictions upon the gradient constitutive equations are derived which are shown to include besides the field differential stress strain laws a set of nonstandard boundary conditions consistently with the latter thermodynamic requirements a surface layer with membrane stresses is envisioned in the strained body which together with the above nonstandard boundary conditions make the body constitutively insulated i e no long distance energy flows out of the boundary surface due to nonlocality the total strain energy is shown to include a bulk and surface strain energy a minimum total potential energy principle is provided for the related structural boundary value problem the toupin mindlin polar type strain gradient material model is also addressed and compared with the above one their substantial differences are pointed out particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations a gradient one dimensional bar sample in tension is considered for a few applications of the proposed theory

a rational route to randomness the concept of adaptively rational equilibrium a r e is introduced agents adapt their beliefs over time by choosing from a finite set of different predictor or expectations functions each predictor is a function of past observations and has a performance or fitness measure which is publicly available agents make a rational choice concerning the predictors based upon their past performance this results in a dynamics across predictor choice which is coupled to the equilibrium dynamics of the endogenous variables as a simple but typical example we consider a cobweb type demand supply model where agents can choose between rational and naive expectations in an unstable market with small positive information costs for rational expectations a high intensity of choice to switch predictors leads to highly irregular equilibrium prices converging to a strange attractor the irregularity of the equilibrium time paths is explained by the existence of a so called homoclinic orbit and its associated complicated dynamical phenomena thus local instability and global complicated dynamics may be a feature of a fully rational notion of equilibrium

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

a two field finite element formulation for elasticity coupled to damage a two field variational formulation is proposed for continuum damage mechanics problems this formulation is applied to the numerical solution via the finite element method of initial boundary value problems arising in elasticity coupled to damage the nodal variables are the displacement and damage fields simple examples are presented to demonstrate the advantages and limitations of this formulation

an anisotropic gradient damage model for quasi brittle materials an anisotropic continuum damage model based on the microplane concept is elaborated scalar damage laws are formulated on several individual microplanes representing the planes of potential failure these uniaxial constitutive laws can be cast into a fourthorder damage formulation such that anisotropy of the overall constitutive law is introduced in a natural fashion strain gradients are incorporated in the constitutive equations in order to account for microstructural interaction consequently the underlying boundary value problem remains well posed even in the softening regime the gradient continuum enhancement results in a set of additional partial diaerential equations which are satisfied in a weak form additional nodal degrees of freedom are introduced which leads to a modified element formulation the governing equations can be linearized consistently and solved within an incremental iterative newton raphson solution procedure the capability of the present model to properly simulate the localized failure of quasi brittle materials will be demonstrated by means of several examples 2000 elsevier science s a all rights reserved

nonlocal integral elasticity 2d finite element based solutions abstract a finite element based method theorized in the context of nonlocal integral elasticity and founded on a nonlocal total potential energy principle is numerically implemented for solving 2d nonlocal elastic problems the key idea of the method known as nonlocal finite element method nl fem relies on the assumption that the postulated nonlocal elastic behaviour of the material is captured by a finite element endowed with a set of cross stiffness element s matrices able to interpret the nonlocality effects induced in the element itself by the other elements in the mesh an eringen type nonlocal elastic model is assumed with a constitutive stress strain law of convolutive type which governs the nonlocal material behaviour computational issues as the construction of the nonlocal element and global stiffness matrices are treated in detail few examples are presented and the relevant numerical findings discussed both to verify the reliability of the method and to prove its effectiveness

a geometrically regularized gradient damage model with energetic equivalence abstract aiming to bridge the gap between damage and fracture mechanics for modeling localized failure in solids this paper addresses a novel geometrically regularized gradient damage model with energetic equivalence for cracking evolution with the free energy potential defined as usual in terms of the local strain and damage fields the constitutive relations are derived consistently from the standard framework of thermodynamics upon the sharp crack topology geometrically regularized by the damage localization band with a length scale the ensuing energetic equivalence naturally yields the damage evolution law of gradient type and the associated boundary condition of neumann type compared to other gradient damage models no extra assumptions like the nonlocal energy residual and insulation condition are introduced moreover the damage gradient physically accounting for microscopic nonlocal interactions is fully dissipative as expected in line with the unified phase field theory recently proposed by the author wu 2017 during failure processes the material behavior is uniquely characterized by two constitutive functions i e the degradation function defining the free energy potential of the bulk and the geometric function regularizing the sharp crack topology in particular optimal constitutive functions defining an equivalent cohesive zone model of general softening laws are postulated with the involved parameters calibrated from standard material properties the proposed model is numerically implemented into the multi field finite element method and applied to several benchmark tests of concrete under mode i and mixed mode failure it is found that the incorporated length scale can be regarded either a numerical parameter or a material property for the former considered in this work the length scale has negligible if not no effects on the global responses so long as the sharp crack topology and the damage field of high gradients within the localization band are well resolved furthermore the localization bandwidth does not exhibit spurious widening but rather it approaches to a finite value proportional to the length scale comparison between the numerical and experimental results regarding the curve of load versus displacement and crack path confirms validity of the proposed gradient damage model for characterizing localized failure in quasi brittle solids

on uniqueness of the dynamic finite step problem in gradient dependent softening plasticity the dynamic evolution of an elastoplastic softening solid is considered a material model including in the yield function the laplacian of the plastic multiplier is used to regularize the problem the dynamic finite step problem is formulated according to a generalized mid point integration scheme space discretization is carried out by a mixed finite element technique based on generalized variables a sufficient uniqueness condition of the finite step solution is proved for a one dimensional problem also a necessary and sufficient condition is presented a simple numerical test shows the regularizing properties mesh independence of the proposed model and the positive influence of the gradient term also on the time step amplitude ensuring uniqueness of solution

anisotropic ballistic deposition model with links to the ulam problem and the tracy widom distribution we compute exactly the asymptotic distribution of scaled height in a 1 1 dimensional anisotropic ballistic deposition model by mapping it to the ulam problem of finding the longest nondecreasing subsequence in a random sequence of integers using the known results for the ulam problem we show that the scaled height in our model has the tracy widom distribution appearing in the theory of random matrices near the edges of the spectrum our result supports the hypothesis that various growth models in 1 1 dimensions that belong to the kardar parisi zhang universality class perhaps all share the same universal tracy widom distribution for the suitably scaled height variables

large deviations of convex hulls of self avoiding random walks a global picture of a random particle movement is given by the convex hull of the visited points we obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of self avoiding random walks namely the classical self avoiding walk the smart kinetic self avoiding walk and the loop erased random walk to obtain a comprehensive description of the measured random quantities we applied sophisticated large deviation techniques which allowed us to obtain the distributions over a large range of support down to probabilities far smaller than p 10 ensuremath 100 we give an approximate closed form of the so called large deviation rate function mathrm ensuremath phi which generalizes above the upper critical dimension to the previously studied case of the standard random walk further we show correlations between the two observables also in the limits of atypical large or small values

post necking behaviour modelled by a gradient dependent plasticity theory abstract the delay of the onset of localization and the post necking behaviour for stretched thin sheets are determined by three dimensional effects thus a 2 d finite element analysis based on a local plasticity theory will give a physically unrealistic mesh dependent solution this in spite of the fact that the stress state is essentially two dimensional by incorporating a length scale with relation to the thickness of the sheet it is demonstrated how a 2 d finite element analysis based on a gradient dependent plasticity theory can give a good approximation of the post necking behaviour this is illustrated by numerical comparison of results from a full 3 d finite element analysis with results from a 2 d finite element model based on a finite strain version of a gradient dependent j 2 flow theory some numerical problems in the modeling will be discussed briefly

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

dimension of the loop erased random walk in three dimensions we measure the fractal dimension of loop erased random walk lerw in three dimensions and estimate that it is 1 624 00 0 000 05 lerw is closely related to the uniform spanning tree and the abelian sandpile model we simulated lerw on both the cubic and face centered cubic lattices the corrections to scaling are slightly smaller for the face centered cubic lattice

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

random convex hulls and extreme value statistics in this paper we study the statistical properties of convex hulls of n random points in a plane chosen according to a given distribution the points may be chosen independently or they may be correlated after a non exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem we present a unifying approach based on the notion of support function of a closed curve and the associated cauchy s formulae that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics as an example of correlated points we study here in detail the case when the points represent the vertices of n independent random walks in the continuum time limit this reduces to n independent planar brownian trajectories for which we compute exactly for all n the mean perimeter and the mean area of their global convex hull our results have relevant applications in ecology in estimating the home range of a herd of animals some of these results were announced recently in a short communication phys rev lett 103 140602 2009

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

temporal aggregation of volatility models in this paper we consider temporal aggregation of volatility models we introduce semiparametric volatility models termed square root stochastic autoregressive volatility sr sarv which are characterized by autoregressive dynamics of the stochastic variance our class encompasses the usual garch models and various asymmetric garch models moreover our stochastic volatility models are characterized by multiperiod conditional moment restrictions in terms of observables the sr sarv class is a natural extension of the class of weak garch models this extension has four advantages i we do not assume that fourth moments are finite ii we allow for asymmetries skewness leverage effect that are excluded from weak garch models iii we derive conditional moment restrictions and iv our framework allows us to study temporal aggregation of igarch models

existence and uniqueness of solutions for a dynamic one dimensional damage model we consider a one dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material the process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields we establish the existence of local weak solutions the existence result is derived from the a priori estimates obtained for a sequence of regularized truncated and time retarded approximations we also establish the existence of the unique weak solution of a simplified version of the model

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

an algorithm for gradient regularized plasticity coupled to damage based on a dual mixed fe formulation abstract a thermodynamically consistent theory of gradient regularized plasticity with coupling to isotropic damage was presented by svedberg and runesson 23 its main purpose was to describe the successive development of the localization zone that is pertinent to the softening regime due to excessive damage close to failure explicit constitutive relations were established for a model problem based on von mises plasticity with isotropic hardening of two types local and gradient enhanced the main purpose of this paper is to describe a new numerical algorithm for the gradient enhanced formulation using the backward euler rule leads to a gradient enhanced format of the classical closest point projection method the plastic multiplier increment is solved via a dual mixed method which is a convenient feature in the present context this leads to an unambiguous representation of the constitutive relations in the equilibrium equation moreover the classical local algebraic kuhn tucker conditions are obtained in a straightforward fashion in the limit case of local theory the developed algorithm was implemented in the educational finite element package 5 numerical results are shown for the extension of a plate in plane stress these results demonstrate the convergence characteristics with mesh refinement as well as the salient features of the adopted damage based constitutive model

convex hulls of random walks large deviation properties we study the convex hull of the set of points visited by a two dimensional random walker of t discrete time steps two natural observables that characterize the convex hull in two dimensions are its perimeter l and area a while the mean perimeter and the mean area have been studied before analytically and numerically and exact results are known for large t brownian motion limit little is known about the full distributions p a and p l in this paper we provide numerical results for these distributions we use a sophisticated large deviation approach that allows us to study the distributions over a larger range of the support where the probabilities p a and p l are as small as 10 300 we analyze open random walks as well as closed brownian bridges on the two dimensional discrete grid as well as in the two dimensional plane the resulting distributions exhibit for large t a universal scaling behavior independent of the details of the jump distributions as a function of a t and l sqrt t respectively we are also able to obtain the rate function describing rare events at the tails of these distributions via a numerical extrapolation scheme and find a linear and square dependence as a function of the rescaled perimeter and the rescaled area respectively

limiting distributions for a polynuclear growth model with external sources the purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by prahofer and spohn depending on the strength of the sources the limiting distribution functions are either the tracy widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero moreover we obtain transition functions between pairs of the above distribution functions in suitably scaled limits there are also similar results for a discrete totally asymmetric exclusion process