a nonlinear functional for general scalar hyperbolic conservation laws abstract a generalized entropy functional was introduced in t p liu t yang a new entropy functional for scalar conservation laws comm pure appl math 52 1999 1427 1442 for the scalar hyperbolic conservation laws with convex flux function this functional was crucially used in the functional approach to the l 1 stability study on the system of hyperbolic conservation laws when each characteristic field is either genuinely nonlinear or linearly degenerate however how to construct the generalized entropy functional for scalar conservation laws with general flux and then how to apply the functional approach to the l 1 study on general systems are still open in this paper we construct a new nonlinear functional which gives some partial answer to this question and we expect the analysis will shed some light on the future investigation in this direction

finite elements with increased freedom in choosing shape functions starting with a mathematical statement of the convergence requirements for an element stiffness matrix the paper discusses displacement shape functions that may be used in connection with the potential energy principle in short these functions must be force orthogonal and energy orthogonal but they need not be conforming satisfy interelement compatibility it is shown that the requirements to the displacement functions may be greatly relaxed through slight modifications of the coupling stiffness between fundamental and higher order displacement modes several alternative formulations are examined in particular a new free formulation is suggested using this form which is very simple the only requirement to the displacement patterns used is that they should contain the fundamental deformation modes and be linearly independent applications of the theory to triangular and rectangular plate bending elements are shown the simple stiffness matrix for the latter is given explicitly the numerical results compare favourably with other types of finite elements

on the application of the method of fundamental solutions for the study of the stress state of a plate subjected to elastic plastic deformation abstract the plane elastoplastic problem for the stress state of a plate with a narrowing subjected to uniaxial extension is considered the behaviour of the material that hardens with plastic deformation is characterised by the ramberg osgood stress strain relation since this relation provides a smooth continuous curve over the whole elastic and plastic deformation range the same governing equation can be used for both deformation regions the paper provides a method for solving the resulting nonlinear boundary value problem the algorithm is based on meshless methods i e the method of fundamental solutions and the method of particular solutions together with a picard iteration process the approximate solution i e the stress function obtained in each iteration step is a linear combination of fundamental and particular solutions it can thus be further used to compute the values of stresses and some effective material parameters i e the young modulus and the poisson ratio at any point of the domain

vanishing viscosity solutions of nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n system in one space dimension ut a u ux 0 assuming that the initial data have small total variation we show that the solutions of the viscous approximations ut a u ux euxx are defined globally in time and satisfy uniform bv estimates independent of e moreover they depend continuously on the initial data in the l 1 distance with a lipschitz constant independent of t e letting e 0 these viscous solutions converge to a unique limit depending lipschitz continuously on the initial data in the conservative case where a df is the jacobian

weak solutions of general systems of hyperbolic conservation laws in this paper we establish the existence theory for general system of hyperbolic conservation laws and obtain the uniform l1 boundness for the solutions the existence theory generalizes the classical glimm theory for systems for which each characteristic field is either genuinely nonlinear or linearly degenerate in the sense of lax we construct the solutions by the glimm scheme through the wave tracing method one of the key elements is a new way of measuring the potential interaction of the waves of the same characteristic family involving the angle between waves a new analysis is introduced to verify the consistency of the wave tracing procedure the entropy functional is used to study the l1 boundedness

implementation of a maximin power clustering criterion to select near replicates for regression lack of fit tests abstract in earlier work we presented a maximin power clustering criterion to partition observations into groups of near replicates specifically the criterion selects near replicate clusters for use with christensen s tests for orthogonal between and within cluster lack of fit this article further explores implementation of this clustering criterion in particular a methodology is developed to determine a collection of candidate groupings to which the maximin power criterion can be applied

the unique limit of the glimm scheme we introduce the definitions of a standard riemann semigroup and of a viscosity solution for a nonlinear hyperbolic system of conservation laws for a class including general 2 2 systems it is proved that the solutions obtained by a wavefront tracking algorithm or by the glimm scheme are precisely the semigroup trajectories in particular these solutions are unique and depend lipschitz continuously on the initial data in the l1 norm

existence theory for hyperbolic systems of conservation laws with general flux functions to begin with we assume that the flux function f u is piecewise genuinely nonlinear in the sense that it exhibits finitely many at most p say points of lack of genuine nonlinearity along each wave curve importantly our analysis applies to arbitrary large p in the sense that the constant c restricting the total variation is independent of p second by an approximation argument we prove that the existence theory above extends to general flux functionsf u that can be approached by a sequence of piecewise genuinely nonlinear flux functions fe u

elastoplastic analysis by active macro zones with linear kinematic hardening and von mises materials in this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von mises materials under plane strain conditions is shown the proposed approach works with the symmetric galerkin boundary element method applied to multidomain problems using a mixed variables approach to obtain a more stringent solution the elastoplastic analysis is carried out as the response to the loads and the plastic strains the latter evaluated through the self equilibrium stress matrix this matrix is used both in the predictor phase for trial stress evaluation and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones i e those zones collecting bem elements where the plastic consistency condition has been violated the simultaneous use of active macro zones gives rise to a nonlocal approach which is characterized by a large decrease in the plastic iteration number although the proposed strategy requires the inversion and updating of jacobian operators generally of big dimensions a strategy developed in order to reduce the computational efforts due to the use of this matrix in a recursive process is shown

sharp convergence rate of the glimm scheme for general nonlinear hyperbolic systems consider a general strictly hyperbolic quasilinear system in one space dimesion u t a u u x 0 quad quad quad quad quad quad 1 where u mapsto a u u in omega subset mathbb r n is a smooth matrix valued map given an initial datum u 0 with small total variation let u t be the corresponding unique vanishing viscosity solution of 1 obtained as a limit of solutions to the viscous parabolic approximation u t a u u x u xx as 0 for every t 0 we prove the a priori bound left u varepsilon t cdot u t cdot right mathbb l 1 o 1 cdot sqrt varepsilon log varepsilon quad quad quad quad quad quad 1 for an approximate solution u varepsilon of 1 constructed by the glimm scheme with mesh size delta x delta t varepsilon and with a suitable choice of the sampling sequence this result provides for general hyperbolic systems the same type of error estimates valid for glimm approximate solutions of hyperbolic systems of conservation laws u t f u x 0 satisfying the classical lax or liu assumptions on the eigenvalues k u and on the eigenvectors r k u of the jacobian matrix a u df u

decay estimate for a new measure of rarefaction waves in general systems of conservation laws abstract the sharp decay estimate of rarefaction waves in terms of a partial ordering among positive measures is not only interesting in itself but also crucial in the study of convergence rate of vanishing viscosity approximations cf bressan and yang 2004 10 such an estimate is well established for genuinely nonlinear system of conservation laws cf bressan and yang 2004 9 but similar result is not available for non genuinely nonlinear system in this paper we give a new measure about the rarefaction waves in addition a sharp decay estimate of the new measure is given for the cubic nonlinear system of conservation laws

maximin clusters for near replicate regression lack of fit tests to assess the adequacy of a nonreplicated linear regression model christensen introduced the concepts of orthogonal between and within cluster lack of fit with corresponding optimal tests however the properties of these tests depend on the choice of near replicate clusters in this paper a graph theoretic framework is presented to represent candidate clusterings a clustering is then selected according to a proposed maximin power criterion from among the clusterings consistent with a specified graph on the predictor settings examples are given to illustrate the methodology

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

well posedness theory for hyperbolic conservation laws the paper presents a well posedness theory for the initial value problem for a general system of hyperbolic conservation laws we will start with the refinement of glimm s existence theory and discuss the principle of nonlinear through wave tracing our main goal is to introduce a nonlinear functional for two solutions with the property that it is equivalent to the l1 x distance between the two solutions and is time decreasing moreover the functional is constructed explicitly in terms of the wave patterns of the solutions through the nonlinear superposition it consists of a linear term measuring the l1 x distance a quadratic term measuring the coupling of waves and distance and a generalized entropy functional 1999 john wiley sons inc

the slow erosion limit in a model of granular flow we study a 2 2 system of balance laws that describes the evolution of a granular material avalanche flowing downhill the original model was proposed by hadeler and kuttler granul matter 2 9 18 1999 the cauchy problem for this system has been studied by the authors in recent papers amadori and shen in commun partial differ equ 34 1003 1040 2009 shen in j math anal appl 339 828 838 2008 in this paper we first consider an initial boundary value problem the boundary condition is given by the flow of the incoming material for this problem we prove the global existence of bv solutions for a suitable class of data with bounded but possibly large total variations we then study the slow erosion or deposition limit we show that if the thickness of the moving layer remains small then the profile of the standing layer depends only on the total mass of the avalanche flowing downhill not on the time law describing the rate at which the material slides down more precisely in the limit as the thickness of the moving layer tends to zero the slope of the mountain is provided by an entropy solution to a scalar integro differential conservation law

an iterative method for shakedown analysis abstract shakedown analysis for elastic perfect plastic structures is discussed and a fast incremental iterative solution method is proposed suitable for the fem analyses of large structures the theoretical motivations of the proposed method are discussed in detail and an example of its implementation is described with reference to plane frame analysis some numerical results are presented showing the numerical performances of the method

on the riemann problem for non conservative hyperbolic systems we consider the construction and the properties of the riemann solver for the hyperbolic system

incremental elastoplastic analysis for active macro zones summary in this paper a strategy to perform incremental elastoplastic analysis using the symmetric galerkin boundary element method for multidomain type problems is shown the discretization of the body is performed through substructures distinguishing the bem elements characterizing the so called active macro zones where the plastic consistency condition may be violated and the macro elements having elastic behaviour only incremental analysis uses the well known concept of self equilibrium stress field here shown in a discrete form through the introduction of the influence matrix self stress matrix the nonlinear analysis does not use updating of the elastic response inside each plastic loop but at the end of the load increment only this is possible by using the self stress matrix both in the predictor phase for computing the stress caused by the stored plastic strains and in the corrector phase for solving a nonlinear global system which provides the elastoplastic solution of the active macro zones the use of active macro zones gives rise to a nonlocal and path independent approach which is characterized by a notable reduction of the number of plastic iterations the proposed strategy shows several computational advantages as shown by the results of some numerical tests reported at the end of this paper these tests were performed using the karnak sgbem code in which the present procedure was introduced as an additional module copyright 2012 john wiley sons ltd

a mixed formulation and mixed finite elements for limit analysis a mixed variational principle for the limit analysis of rigid perfectly plastic continua is discussed in which the nonlinear yield condition and the associated flow rule appear through a suitably defined penalty function a mixed finite element discrete formulation is derived and a sequential unconstrained minimization technique is devised affording a complete static and kinematic solution several results are presented in both structural and soil mechanics compared with previously available exact and numerical solutions

decay estimation in nonlinear hyperbolic system of conservation laws abstract in this paper we study some decay estimates in nonlinear hyperbolic system of conservation laws this research is not only interesting in itself but also crucial in studying the large time behavior problem by introducing a proper glimm functional we obtain some useful decay estimates which are proved helpful in obtaining decay rates of the admissible solutions to nonlinear hyperbolic conservation laws as t

the boundary riemann solver coming from the real vanishing viscosity approximation we study the limit of the hyperbolic parabolic approximation left begin array l quad l quad l v varepsilon t tilde a left v varepsilon varepsilon v varepsilon x right v varepsilon x varepsilon tilde b v varepsilon v varepsilon xx quad v varepsilon in mathbb r n cr tilde rm ss v varepsilon t 0 equiv bar g cr v varepsilon 0 x equiv bar v 0 end array right the function tilde ss is defined in such a way as to guarantee that the initial boundary value problem is well posed even if tilde b is not invertible the data bar g and bar v 0 are constant when tilde b is invertible the previous problem takes the simpler form left begin array l quad l quad l v varepsilon t tilde a left v varepsilon varepsilon v varepsilon x right v varepsilon x varepsilon tilde b v varepsilon v varepsilon xx quad v varepsilon in mathbb r n cr v varepsilon t 0 equiv bar v b cr v varepsilon 0 x equiv bar v 0 end array right again the data bar v b and bar v 0 are constant the conservative case is included in the previous formulations convergence of the v varepsilon smallness of the total variation and other technical hypotheses are assumed and a complete characterization of the limit is provided the most interesting points are the following first the boundary characteristic case is considered that is one eigenvalue of tilde a can be 0 second as pointed out before we take into account the possibility that tilde b is not invertible to deal with this case we take as hypotheses conditions that were introduced by kawashima and shizuta relying on physically meaningful examples we also introduce a new condition of block linear degeneracy we prove that if this condition is not satisfied then pathological behaviors may occur

a high performance element for the analysis of 2d elastoplastic continua abstract the paper presents a four node element for the analysis of 2d continua described by elastic perfectly plastic von mises laws its formulation is based on the assumed stress approach which has been widely tested in the elastic field the elastoplastic formulation of the element is obtained by enriching its variational basis with the weak enforcement of the plastic loading unloading conditions in this way the elastoplastic problem is formulated with respect to the stress parameters of the element consistently with the weak statement of the compatibility condition

wave interactions and variation estimates for self similar zero viscosity limits in systems of conservation laws we consider the problem of self similar zero viscosity limits for systems ofn conservation laws first we give general conditions so that the resulting boundary value problem admits solutions the obtained existence theory covers a large class of systems in particular the class of symmetric hyperbolic systems second we show that if the system is strictly hyperbolic and the riemann data are sufficiently close then the resulting family of solutions is of uniformly bounded variation and oscillation third we construct solutions of the riemann problem via self similar zero viscosity limits and study the structure of the emerging solution and the relation of self similar zero viscosity limits and shock profiles the emerging solution consists ofn wave fans separated by constant states each wave fan is associated with one of the characteristic fields and consists of a rarefaction a shock or an alternating sequence of shocks and rarefactions so that each shock adjacent to a rarefaction on one side is a contact discontinuity on that side at shocks the solutions of the self similar zero viscosity problem have the internal structure of a traveling wave

two dimensional elastoplasticity approximation by mixed finite elements two dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non linear regime in particular four node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress plane strain axisymmetric and shear deformable plate bending problems the excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature in addition agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements

a wavefront tracking algorithm for n n nongenuinely nonlinear conservation laws we introduce a wavefront tracking algorithm for n n hyperbolic systems of conservation lawsut f u x 0 that admits characteristic fields that are neither genuinely nonlinear nor linearly degenerate in the sense of lax instead we assume that for any nongenuinely nonlinear ith characteristic family the derivative of the ith eigenvalue i u of df u in the direction of the ith right eigenvector ri u vanishes on a single n 1 dimensional hypersurface in the u space transversal to the field ri u systems that fulfill this type of assumptions are of particular interest in studying elastodynamic or rigid heat conductors at low temperature the first proof of the existence of weak solutions for nongenuinely nonlinear systems was given by t p liu mem amer math soc 30 1981 no 240 based on a glimm scheme our construction here provides an alternative method for establishing the global existence of weak solutions for such systems moreover relying on the stability analysis developed in ancona and marson preprint s i s s a i s a s 27 99 11 1999 and preprint 2000 we show that these solutions are entropy admissible in the sense of lax

a new glimm functional and convergence rate of glimm scheme for general systems of hyperbolic conservation laws in this paper we introduce a new glimm functional for general systems of hyperbolic conservation laws this new functional is consistent with the classical glimm functional for the case when each characteristic field is either genuinely nonlinear or linearly degenerate so that it can be viewed as optimal in some sense with this new functional the consistency of the glimm scheme is proved clearly for general systems moreover the convergence rate of the glimm scheme is shown to be the same as the one obtained in bressan marson arch ration mech anal 142 2 155 176 1998 for systems with each characteristic field being genuinely nonlinear or linearly degenerate

sharp decay estimates for hyperbolic balance laws abstract we consider strictly hyperbolic and genuinely nonlinear systems of hyperbolic balance laws in one space dimension sharp decay estimates are derived for the positive waves in an entropy weak solution the result is obtained by introducing a partial ordering within the family of positive radon measures using symmetric rearrangements and a comparison with a solution of burgers s equation with impulsive sources as well as lower semicontinuity properties of continuous glimm type functionals

a heterogeneous multiclass traffic flow model with creeping a heterogeneous traffic model with two vehicle classes is developed to capture overtaking and creeping in highly heterogeneous traffic flows creeping is a special case of overtaking that occurs when small vehicles continue to advance in congestion even though larger vehicles have completely stopped to motivate the new model it is shown that a two class homogeneous multiclass model is equivalent to a class of second order models originally proposed by aw rascle and zhang arz based on the properties of the arz model homogeneous models do not allow overtaking or creeping the new creeping model is a phase transition model which applies a system of conservation laws in the noncreeping phase and a system equivalent to a scalar model in the creeping phase the solution to the riemann problem is obtained by investigating the elementary waves particularly for the cases when one vehicle class is absent as well as in the presence of a phase transition based on the proposed riemann solver the solution t

nonlinear hyperbolic systems nondegenerate flux inner speed variation and graph solutions we study the cauchy problem for general nonlinear strictly hyperbolic systems of partial differential equations in one space variable first we re visit the construction of the solution to the riemann problem and introduce the notion of a nondegenerate nd system this is the optimal condition guaranteeing as we show it that the riemann problem can be solved with finitely many waves only we establish that the nd condition is generic in the sense of baire for the whitney topology so that any system can be approached by a nd system second we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds third we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the cauchy problem this provides a new existence proof as well as an approximation algorithm as an application we investigate the time regularity of the graph solutions x u introduced by lefloch and propose a geometric version of our scheme in turn the spatial component x of a graph solution can be chosen to be continuous in both time and space while its component u is continuous in space and has bounded variation in time

existence of relaxation shock profiles for hyperbolic conservation laws in this paper we prove that like viscosity relaxation can also smooth weak shocks for strict hyperbolic conservation laws as equilibium systems of hyperbolic relaxation systems under some natural structural conditions these conditions were derived previously by yong from stability considerations and hence are entirely analogous to the majda pego criterion of the viscous case the proof involves a new parametrization of hugoniot curves and a delicate analysis of the algebraic structure of relaxation systems as well as construction of an appropriate center manifold

active macro zone approach for incremental elastoplastic contact analysis summary the symmetric boundary element method based on the galerkin hypotheses has found an application in the nonlinear analysis of plasticity and in contact detachment problems but both dealt with separately in this paper we want to treat these complex phenomena together as a linear complementarity problem a mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements where elastic behavior is assumed and bem elements where it is possible that plastic strains may occur elasticity equations are written for all the substructures and regularity conditions in weighted weak form on the boundary sides and in the nodes strong between contiguous substructures have to be introduced in order to attain the solving equation system governing the elastoplastic contact detachment problem the elastoplasticity is solved by incremental analysis called for active macro zones and uses the well known concept of self equilibrium stress field here shown in a discrete form through the introduction of the influence matrix self stress matrix the solution of the frictionless contact detachment problem was performed using a strategy based on the consistent formulation of the classical signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment copyright 2013 john wiley sons ltd

the semigroup generated by 2 2 conservation laws consider the cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension ie1 01 assuming that each characteristic field is either linearly degenerate or genuinely nonlinear this paper develops a new algorithm based on wave front tracking which yields a cauchy sequence of approximate solutions converging to a unique limit depending continuously on the initial data the solutions that we obtain constitute a semigroup s defined on a set ie1 02 of integrable functions with small total variation for some lipschitz constant l we have the estimate ie1 03

a mixed finite element model for plane strain elastic plastic analysis part ii application to the 4 node bilinear element in this paper the results of part i of this study are applied to the 4 node bilinear element the trial functions for different fields are defined consistently with the a priori conditions established the rate problem is generalized to cover finite loading steps and the solution strategy is presented computations referred to some discriminating examples from the literature demonstrate that the proposed model is actually capable of predicting the perfectly plastic collapse load for pathological plane strain problems exhibits excellent performances with coarse meshes and is rather insensitive to mesh distortion

decay rates for nonconvex systems of conservation laws we study decay of solutions for hyperbolic systems of conservation laws which are not genuinely nonlinear for a generic class of such systems we determine sharp algebraic rates of decay in the total variation of the wave speed for solutions with compact initial support our analysis involves generalized characteristic arguments and the random choice difference scheme of glimm 1993 john wiley sons inc

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

a locally quadratic glimm functional and sharp convergence rate of the glimm scheme for nonlinear hyperbolic systems consider the cauchy problem for a strictly hyperbolic n n quasilinear system in one space dimension u t a u u x 0 qquad u 0 x bar u x quad quad quad quad 1 where u mapsto a u is a smooth matrix valued map and the initial data overline u is assumed to have small total variation we investigate the rate of convergence of approximate solutions of 1 constructed by the glimm scheme under the assumption that letting k u rk u denote the k th eigenvalue and a corresponding eigenvector of a u respectively for each k th characteristic family the linearly degenerate manifold mathcal m k doteq left u in omega nabla lambda k u cdot r k u 0 right is either the whole space or it is empty or it consists of a finite number of smooth n 1 dimensional connected manifolds that are transversal to the characteristic vector field rk we introduce a glimm type functional which is the sum of the cubic interaction potential defined in bianchini discrete contin dyn syst 9 133 166 2003 and of a quadratic term that takes into account interactions of waves of the same family with strength smaller than some fixed threshold parameter relying on an adapted wave tracing method and on the decrease amount of such a functional we obtain the same type of error estimates valid for glimm approximate solutions of hyperbolic systems satisfying the classical lax assumptions of genuine nonlinearity or linear degeneracy of the characteristic families

optimal discriminating designs for several competing regression models the problem of constructing optimal designs for a class of regression models is considered we investigate a version of the tp optimality criterion as introduced by atkinson and fedorov 1975b and demonstrate that optimal designs with respect to this type of criteria can be obtained by solving nonlinear vector valued approximation problems we provide a characterization of the best approximations in this context and use these results to develop an efficient algorithm for the determination of the optimal discriminating designs the results are illustrated by fnumerical examples

existence theory by front tracking for general nonlinear hyperbolic systems we consider the cauchy problem for a strictly hyperbolic n n quasilinear system in one space dimension u t a u u x 0 qquad u 0 x bar u x 1 where u u t x u 1 t x dots u n t x u mapsto a u is a smooth matrix valued map and the initial data overline u is assumed to have small total variation we present a front tracking algorithm that generates piecewise constant approximate solutions converging in mathbb l loc 1 to the vanishing viscosity solution of 1 which by the results in 6 is the unique limit of solutions to the artificial viscous parabolic approximation u t a u u x mu u xx qquad u 0 x bar u x as mu to 0 in the conservative case where a u is the jacobian matrix of some flux function f u with values in mathbb r n the limit of front tracking approximations provides a weak solution of the system of conservation laws ut f u x 0 satisfying the liu admissibility conditions

uniqueness for multidimensional hyperbolic systems with commuting jacobians we consider nonlinear hyperbolic systems of conservation laws in several space dimensions with jacobian matrices that commute and more generally systems that need not be conservative generalizing a theorem by bressan and lefloch for one dimensional systems we establish that the cauchy problem admits at most one entropy solution depending continuously upon its initial data the uniqueness result is proven within the class introduced here of locally regular bv functions with locally controlled oscillation these regularity conditions are modeled on well known properties in the one dimensional case our uniqueness theorem also improves upon the known results for one dimensional systems

a new nonlinear functional for general scalar conservation laws abstract the approach based on the construction of some nonlinear functionals was proved to be robust in the study of the well posedness theories of hyperbolic conservation laws especially in one space dimensional case in particular a generalized entropy functional was constructed in t p liu t yang a new entropy functional for scalar conservation laws comm pure appl math 52 1999 1427 1442 for the l 1 stability of weak solutions however this generalized functional is so far only defined for scalar equations with convex flux function in this paper we introduce a new nonlinear functional which is motivated by the new glimm functional introduced in j l hua z h jiang t yang a new glimm functional and convergence rate of glimm scheme for general systems of hyperbolic conservation laws preprint for general scalar conservation laws this functional improves the one given in h x liu t yang a nonlinear functional for general scalar hyperbolic conservation laws j differential equations 235 2 2007 658 667 and it can be viewed as a better attempt for the generalized entropy functional for general equations

an improved convergence rate of glimm scheme for general systems of hyperbolic conservation laws we study the convergence rate of glimm scheme for general systems of hyperbolic conservation laws without the assumption that each characteristic field is either genuinely nonlinear or linearly degenerate we first give a sharper estimate of the error arising from the wave tracing argument by a careful analysis of the interaction between small waves with this key estimate the convergence rate is shown to be o 1 s13 lns 1 which is sharper compared to o 1 s14 lns given in t yang convergence rate of glimm scheme for general systems of hyperbolic conservation laws taiwanese j math 7 2 2003 195 205 however it is still slower than o 1 s12 lns given in a bressan a marson error bounds for a deterministic version of the glimm scheme arch ration mech anal 142 2 1998 155 176 for systems with each characteristic field being genuinely nonlinear or linearly degenerate here s is the mesh size and is any positive constant

optimal discrimination designs we consider the problem of constructing optimal designs for model discrimination between competing regression models various new properties of optimal designs with respect to the popular t optimality criterion are derived which in many circumstances allow an explicit determination of t optimal designs it is also demonstrated that in nested linear models the number of support points of t optimal designs is usually too small to estimate all parameters in the extended model in many cases t optimal designs are usually not unique and we give a characterization of all t optimal designs finally t optimal designs are compared with optimal discriminating designs with respect to alternative criteria by means of a small simulation study

stable viscosity matrices for systems of conservation laws abstract a natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension u 1 f u x 0 u r m is studied these matrices are admissible in the sense that small amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system u t f u x v du x x as ifv 0 if d is in this class the class is determined by a linearized stability requirement the cauchy problem for the equation u 1 f u 0 u x vdu xx should be well posed in l 2 uniformly in v as v 0 previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion

an efficient design for model discrimination and parameter estimation in linear models summary we consider experimental designs in a regression set up where the unknown regression function belongs to a known family of nested linear models the objective of our design is to select the correct model from the family of nested models as well as to estimate efficiently the parameters associated with that model we show that our proposed design is able to choose the true model with probability tending to one as the number of trials grows to infinity we also establish that our selected design converges to the optimal design distribution for the true linear model ensuring asymptotic efficiency of least squares estimators of model parameters

a unified approach for variationally consistent finite elements in elastoplasticity abstract a general variationally consistent approach for elastoplastic finite element analysis is presented a weak formulation of the finite step i e in terms of finite increments elastoplastic boundary value problem is obtained by enforcing the stationarity of a mixed functional of hu washizu type a peculiarity of the present formulation is that the constitutive equations are expressed in weak form also all fields are then independently discretized in terms of so called generalized variables the result is a set of non linear algebraic equations a subset of which can be interpreted as the backward difference time integrated constitutive law of the finite element an iterative procedure where all calculations are at the element and not at the gauss point level resting on newton raphson scheme is proposed for the solution of the governing equations it is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation

a comparison of sequential and non sequential designs for discrimination between nested regression models summary classical regression analysis is usually performed in two steps in a first step an appro priate model is identified to describe the data generating process and in a second step statistical inference is performed in the identified model in this paper we investigate a sequential and a non sequential design strategy which take into account these different goals of the analysis for a class of nested models it is demonstrated that non sequential designs usually identify the correct model with a higher probability than sequential methods although non sequential designs can never be guaranteed to achieve the best possible efficiency in the correct model it is demonstrated by means of a simulation study that for realistic sample sizes the efficiencies of the non sequential designs for the estimation of the parameters in the correct model are at least as high as the corresponding efficiencies of the sequential methods

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

robust optimal extrapolation designs summary we study robustness properties of optimal extrapolation designs at a single point under various model assumptions a curious result is the efficiency of the optimal extrapolation design for a polynomial of degree m is the same whether the true underlying model is a polynomial of degree k or m k k 1 2 m 1 in addition the loss in efficiency of the optimal extrapolation designs is between 40 50 when we overestimate the degree of the polynomial model and the extrapolated point is far from the design space we propose a new class of optimality criteria for extrapolation the new optimal extrapolation designs are shown to be more efficient and robust to the regression functions they enjoy good power for discriminating among polynomial models and if the extrapolated point is sufficiently far from the design space they coincide with the optimal discrimination designs studied in dette 1994

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

bv solutions of the semidiscrete upwind scheme consider the strictly hyperbolic system of conservation laws u t f u x 0 1 where u n f n n smooth the system is said to be strictly hyperbolic provided that the jacobian matrix a u df u has n distinct eigenvalues 1 u n u

robust t optimal discriminating designs this paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the t optimality criterion introduced by atkinson and fedorov 1975a t optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification as a solution of this problem we propose a bayesian and standardized maximin approach to construct robust and efficient discriminating designs on the basis of the t optimality criterion it is shown that the corresponding bayesian and standardized maximin optimality criteria are closely related to linear optimality criteria for the problem of discriminating between two polynomial regression models which differ in the degree by two the robust t optimal discriminating designs can be found explicitly the results are illustrated in several examples ams subject classification 62k05