the riemann problem for reversible reactive flows with metastability a hyperbolic model for dynamic phase transitions is studied the model involves three phases liquid vapor and a mixture of them metastable regions are present both in the liquid and in the vapor phase results on the behavior of traveling wave profiles of the model involving viscosity species diffusion and relaxation are obtained these behaviors are consistent with physical intuitions admissibility criteria kinetic relations that mimic the behavior of traveling wave profiles are then proposed admissible basic waves of the model are liquefaction evaporation and isobaric waves in addition to lax shock and rarefaction waves based on these waves solutions of the riemann problem for the model are constructed for general riemann initial data most of the physical phenomena are embodied in the solver for some riemann initial data solutions are expected to be nonunique which solutions actually appear depends on whether nucleation already occurred or not the model admits both solutions as it sh

an h adaptive method in the generalized finite differences abstract this paper describes an h adaptive method in generalized finite difference gfd to solve second order partial differential equations these equations representing the behaviour of many physical processes the explicit difference formulae obtained make it possible to propose an a posteriori error indicator which serves as starting point for an h adaptive method to improve the solution by selectively adding nodes to the domain this paper also analyses the influence of key parameters as the number of nodes to add in each step or the minimum distance between nodes through the analysis of the obtained solutions for different types of differential equations

ap cloud we propose a new adaptive particle in cloud ap cloud method for obtaining optimal numerical solutions to the vlasov poisson equation unlike the traditional particle in cell pic method which is commonly used for solving this problem the ap cloud adaptively selects computational nodes or particles to deliver higher accuracy and efficiency when the particle distribution is highly non uniform unlike other adaptive techniques for pic our method balances the errors in pde discretization and monte carlo integration and discretizes the differential operators using a generalized finite difference gfd method based on a weighted least square formulation as a result ap cloud is independent of the geometric shapes of computational domains and is free of artificial parameters efficient and robust implementation is achieved through an octree data structure with 2 1 balance we analyze the accuracy and convergence order of ap cloud theoretically and verify the method using an electrostatic problem of a particle beam with halo simulation results show that the ap cloud method is substantially more accurate and faster than the traditional pic and it is free of artificial forces that are typical for some adaptive pic techniques

sonic hyperbolic phase transitions and chapman jouguet detonations abstract we prove that the cauchy problem for an n n system of strictly hyperbolic conservation laws in one space dimension admits a weak global solution also in presence of sonic phase boundaries applications to chapman jouguet detonations liquid vapor transitions and elastodynamics are considered

transition to detonation in dynamic phase changes subsonically propagating phase boundaries kinks can be modelled by material discontinuities which satisfy integral conservation laws plus an additional jump condition governing the phase change kinetics the necessity of an additional jump condition distinguishes kinks from the conventional shocks which satisfy the lax criterion we study stability of kinks with respect to the breakup splitting into a sequence of waves we assume that all conventional shocks are admissible and that admissible kinks are selected by a prescribed kinetic relation as we show regardless of a particular choice of the kinetic relation sufficiently fast phase boundaries are unstable the mode of instability includes an emission of a centered riemann wave followed by a sonic shock chapman jouguet type phase boundary

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

a numerical study of an ill posed boussinesq equation arising in water waves and nonlinear lattices filtering and regularization techniques1this research was supported by nsf grants no dms 9208061 and by the office of the vice president for research and associate provost for graduate studies at texas a m university 1 we consider an ill posed boussinesq equation which arises in shallow water waves and nonlinear lattices this equation has growing and decaying modes in the linear as well as nonlinear regimes and its linearized growth rate s for short waves of wavenumber k is given by s k 2 previous numerical studies have addressed numerical difficulties and construction of approximate solutions for ill posed problems with short wave instability up to s k e g kelvin helmholtz s k and rayleigh taylor s k instabilities these same issues are addressed and critically examined here for the present problem which has more severe short wave instability in order to develop numerical techniques for constructing good approximate solutions of this equation we use a finite difference scheme to investigate the effect of this short wave instability on the numerical accuracy of the exact solitary wave solution of this equation computational evidence is presented which indicates that numerical accuracy of the solutions is lost very quickly due to severe growth of numerical errors roundoff as well as truncation we use both filtering and regularization techniques to control growth of these errors and to provide better approximate solutions of this equation in the filtering technique numerical experiments with three types of spectral filters of increasing order of regularity are performed we examine the role of regularity of these filters on the accuracy of the numerical solutions numerical evidence is provided which indicates that the regularity of a filter plays an important role in improving the accuracy of the solutions in the regularization technique the ill posed equation is regularized by adding a higher order term to the equation two types of higher order terms are discussed i one that diminishes the growth rate of all modes below a cutoff wavenumber and sets the growth rate of all modes above it to zero and ii the other one diminishes the growth rate of all modes and the growth rate asymptotically approaches to zero as the wavenumber approaches infinity we have argued in favor of the first type of regularization and numerical results using a finite difference scheme are presented numerical evidence is provided which suggests that regularization in combination with the most regular c 2 here spectral filter for small values of the regularization parameter can provide good approximate solutions of the ill posed boussinesq equation for longer time than possible otherwise some of the ideas presented here can possibly be utilized for solving other ill posed problems with severe short wave instabilities and may have an important role to play in numerical studies of their solutions

the chapman jouguet closure for the riemann problem with vaporization this work is devoted to the modeling of phase transition the thermodynamic model for phase transition chosen is a model with two equations of state each of them modeling one phase of a given fluid the mixture equation of state is obtained by an entropy optimization criterion both equations of state are supposed to be convex and a necessary condition is found to ensure the convexity of the mixture equation of state then we investigate the riemann problem for the euler system with these equations of state more precisely we propose to take into account metastable states which may occur as noted in j r simoes moreira and j e shepherd j fluid mech 382 1999 pp 63 86 we check whether the chapman jouguet theory can be applied in our context and that it is consistent with the entropy growth criterion as the characteristic lax criterion does not hold for this solution an additional relation the kinetic closure is necessary the common closure i e the chapman jouguet closure is proved

stability theorem and truncation error analysis for the glimm scheme and for a front tracking method for flows with strong discontinuities typical nonlinear wave interaction problems involve strong waves moving through a background of weak disturbance previous existence theorems and error analysis for computations are usually restricted to more idealized situations such as small data or single equations we consider here the problem of a single strong discontinuity interacting with a weak background for general hyperbolic systems of conservation laws we obtain the stability consistency theorems and upper bounds of the truncation errors for the glimm scheme and for a front tracking method the major error in the glimm scheme is the error generated by the strong discontinuity this error is reduced when a front tracking method is applied to follow the location of the strong discontinuity this demonstrates an advantage of front tracking methods in one space dimension

kinetic relations and the propagation of phase boundaries in solids this paper treats the dynamics of phase transformations in elastic bars the specific issue studied is the compatibility of the field equations and jump conditions of the one dimensional theory of such bars with two additional constitutive requirements a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition a special elastic material with a piecewise linear non monotonic stress strain relation is considered and the riemann problem for this material is analyzed for a large class of initial data it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities

numerical solution of a virtual internal bond model for material fracture a virtual internal bond vib model is proposed recently in mechanical engineering literatures for simulating dynamic fracture the model is a nonlinear wave equation of mixed type hyperbolic or elliptic there is instability in the elliptic region and usual numerical methods might not work we examine the artificial viscosity method for the model and apply central type schemes directly to the corresponding viscous system to ensure appropriate numerical viscous term for such a mixed type problem we provide a formal justification of indicating convergence of the scheme despite the difficulty of the type change the exact solution of a riemann problem is used to demonstrate the numerical method for one dimensional case we then generalize the method to a two dimensional material with a triangular or hexagonal lattice structure computational results for a two dimensional example are given

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

global existence for thermomechanical processes with nonconvex free energies of ginzburg landau form abstract global existence of solutions is proved for the system of partial differential equations which governs the nonlinear thermomechanical processes in a nonviscous solid under the assumption that the corresponding free energy density is of ginzburg landau type to allow for possible solid solid phase transitions in the material the stress strain interrelation is not assumed to be monotone

a dynamical adaptive tensor method for the vlasov poisson system abstract a numerical method is proposed to solve the full eulerian time dependent vlasov poisson system the algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step this decomposition is obtained through the use of an efficient modified progressive generalized decomposition pgd method whose convergence is proved we suggest in addition a symplectic time discretization splitting scheme that preserves the hamiltonian properties of the system this scheme is naturally obtained by considering the tensor structure of the approximation the proposed approach is illustrated through time dependent 1d 1d 2d 2d and 3d 3d numerical examples

self similar fluid dynamic limits for the broadwell system this report discusses a new approach for the resolution of the fluid dynamic limit for the broadwell system of the kinetic theory of gases appropriate in the case of riemann maxwellian data since the formal limiting system is expected to have self similar solutions we are motivated to replace the knudsen number in the broadwell model so that the resulting model admits self similar solutions x t and then let go to zero the limiting procedure is justified and the resulting limit is a solution of the riemann problem for the fluid dynamic limit equations a class of riemann data for which this program can be carried out is exhibited furthermore it is shown that for the carleman model the complete program can be done successfully for arbitrary riemann data

existence of multidimensional phase transitions in a non isothermal van der waals fluid abstract in this paper we prove the existence of multidimensional subsonic phase transitions in a non isothermal van der waals fluid the argument is based on the result of the existence of travelling waves given in s y zhang existence of travelling waves in non isothermal phase dynamics j hyperbolic differ equ 4 3 2007 391 400 and the result of multidimensional stability given in s y zhang stability of multidimensional subsonic phase transition in a non isothermal van der waals fluid preprint an iteration technique a majda the existence of multi dimensional shock fronts mem amer math soc 281 1983 1 93 is applied to achieve the result

nonlinear stability of traveling wave solutions for the compressible fluid models of korteweg type abstract this paper is concerned with the existence and time asymptotic nonlinear stability of traveling wave solutions to the cauchy problem of the one dimensional compressible fluid models of korteweg type which governs the motions of the compressible fluids with internal capillarity the existence of traveling wave solutions is obtained by the phase plane analysis then the traveling wave solution is shown to be asymptotically stable by the elementary l 2 energy method

dynamical stability of phase transitions in the p system with viscosity capillarity we show for the p system with viscosity capillarity that all heteroclinic phase transitions lying sufficiently close to the maxwell line are linearly dynamically stable under localized perturbations independent of the form of the flux on the other hand we show that nearby homoclinic phase transitions involving two or more changes in phase are exponentially unstable these results together imply that stationary and slowly moving phase transitions are dynamically stable if and only if they are monotone in analogy with results obtained by carr gurtin and slemrod in the variational setting arch rational mech anal 86 1984 pp 317 351 this research is significant as the first proof of stability of a strong viscous shock wave for systems our analysis uses the technical framework developed in r gardner and k zumbrun comm pure appl math 51 1998 pp 797 855 k zumbrun and p howard indiana univ math j 47 1998 pp 741 871 together with a nonstandard energy estimate

instabilities in glimm s scheme for two systems of mixed type the behavior of glimm s scheme is examined when applied to two systems from nonlinear elasticity which change type from hyperbolic to elliptic or mixed type i e a pair of wave speeds coalesce and turn complex the hyperbolic regime is invariant for glimm s scheme but not for smooth solutions so strong convergence is not possible in general some simple exact solutions for these systems are considered which illustrate how the approximate solutions are affected by the oscillatory instabilities in these systems the approximations exhibit macroscopically random transitions to new states and nonconvergence in one example however convergence in expectation is observed and weak convergence can be observed if the courant friedrichs levy cfl number is fixed

change of type in three phase flow a simple analogue abstract we consider a system of two conservation laws in one space variable which exhibits change of type hyperbolic elliptic the characteristics are complex in a strip in phase space this example has a structure similar to model systems which appear in three phase porous medium flow for example in the saturation equations obtained employing stone s model for the relative permeabilities we solve the riemann problem analytically for initial states in and near the elliptic strip

the riemann problem for thermoelastic materials with phase change abstract we consider the riemann problem for a system of conservation laws related to a phase transition problem the system is nonisentropic and we treat the case where the latent heat is not zero we study the cases where the initial data are given in the same phase and in the different phases the role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion we confine our attention to the case where the speeds of phase boundaries are close to zero this is one interesting case in physics we discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the riemann problem

fast relaxation solvers for hyperbolic elliptic phase transition problems phase transition problems in compressible media can be modelled by mixed hyperbolic elliptic systems of conservation laws within this approach phase boundaries are understood as shock waves that satisfy additional constraints sometimes called kinetic relations for numerical approximation tracking type algorithms have been suggested the core piece of these algorithms is the usage of exact riemann solvers incorporating the kinetic relation however exact riemann solvers are computationally expensive or even not available in this paper we present a class of approximate riemann solvers for hyperbolic elliptic models that relies on a generalized relaxation procedure it preserves in particular the kinetic relation for phase boundaries exactly and gives for isolated phase transitions the correct solutions in combination with a novel subiteration procedure the approximate riemann solvers are used in the tracking algorithms the efficiency of the approach is validated on a barotropic system with linear kin

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

kinetic stabilization of a nonlinear sonic phase boundary we consider a system arising in the study of phase transitions in elastodynamics a system of two conservation laws in a single space dimension the system has two hyperbolic regions with an elliptic zone in between a phase boundary is a strong discontinuity in a solution with left and right states belonging to different hyperbolic regions we call such a solution a phase wave

admissible riemann solvers for genuinely nonlinear p systems of mixed type abstract we consider in this paper the riemann problem for p systems of mixed type that define two hyperbolic phases with a stress function satisfying general genuinely nonlinear hypotheses we describe here all the global riemann solvers that are continuous for the l 1 distance with respect to initial data while conserving the natural symmetry properties of the p system and coinciding with the lax solution when defined these riemann solvers can be described entirely by a kinetic function used to select a manifold of subsonic phase transitions and a corresponding set of supersonic phase transitions

global classical solutions to the one dimensional compressible fluid models of korteweg type with large initial data abstract this paper is concerned with the global existence of classical solutions with large initial data away from vacuum to the cauchy problem of the one dimensional isothermal compressible fluid models of korteweg type with density dependent viscosity coefficient and capillarity coefficient the case when the viscosity coefficient and the capillarity coefficient for some parameters r is considered under some conditions on we first show the global existence of large solutions around constant states if the far fields of the initial data are the same while if the far fields of the initial data are different we prove the global stability of rarefaction waves with large strength here global stability means the initial perturbation can be arbitrarily large our analysis is based on the elementary energy method and the technique developed by y kanel 29

global solutions of a high dimensional system for korteweg materials the global existence of solutions to a high dimensional system of korteweg materials is established when the initial data are small the complete model was proposed by dunn and serrin and the local existence of the solution was obtained in an earlier paper by the authors

l1 well posedness of euler equations with dynamic phase boundaries abstract we discuss the well posedness of the initial value problem to euler equations related to phase transition the solution contains two phase boundaries moving in opposite directions entropy condition and kinetic relation are used as the main admissibility criteria to select the physically relevant solution we show the existence of the entropy solution under a suitable finiteness condition and a stability condition guarantees the stability of the problem in l 1 bv and the existence of a lipschitz semigroup of solutions we also discuss the well posedness of the problem given that the wave speeds do not differ significantly between different phases

propagating phase boundaries formulation of the problem and existence via the glimm method this paper treats the hyperbolic elliptic system of two conservation laws which describes the dynamics of an elastic material having a non monotone strain stress function followingabeyaratne knowles we propose a notion of admissible weak solution for this system in the class of functions of bounded variation the formulation includes an entropy inequality a kinetic relation imposed along any subsonic phase boundary and an initiation criterion for the appearance of new phase boundaries we prove thel1 continuous dependence of the solution to the riemann problem our main result yields the existence and the stability of propagating phase boundaries the proofs are based onglimm s scheme and in particular on the techniques ofglimm andlax in order to deal with the kinetic relation we prove a result of pointwise convergence of the phase boundary

solving second order non linear hyperbolic pdes using generalized finite difference method gfdm abstract the generalized finite difference method gfdm has been proved to be a good meshless method to solve several linear partial differential equations pdes wave propagation advection diffusion plates beams etc the gfdm allows us to use irregular clouds of nodes that can be of interest for modelling non linear parabolic pdes this paper illustrates that the gfd explicit formulae developed to obtain the different derivatives of the pde s are based in the existence of a positive definite matrix that it is obtained using moving least squares approximation and taylor series development criteria for convergence of fully explicit method using gfdm for different non linear parabolic pdes are given this paper shows the application of the gfdm to solving different non linear problems including applications to heat transfer acoustics and problems of mass transfer

asymptotic stability of monotone increasing traveling wave solutions for viscous compressible fluid equations with capillarity term abstract asymptotic stability of monotone increasing traveling wave solutions is investigated for a class of viscous compressible fluid equations with capillarity term by using the theory of planar dynamical systems the existence has been proved for the monotone increasing traveling wave solution moreover through building uniformly a priori energy estimate for the perturbation of the traveling wave solution we prove that the monotone increasing traveling wave solution is asymptotically stable in h 2 h 1

relative entropy in multi phase models of 1d elastodynamics convergence of a non local to a local model abstract in this paper we study a local and a non local regularization of the system of nonlinear elastodynamics with a non convex energy we show that solutions of the non local model converge to those of the local model in a certain regime the arguments are based on the relative entropy framework and provide an example of how local and non local regularizations may compensate for non convexity of the energy and enable the use of the relative entropy stability theory even if the energy is not quasi or poly convex

spectral stability of ideal gas shock layers extending recent results in the isentropic case we use a combination of asymptotic ode estimates and numerical evans function computations to examine the spectral stability of shock wave solutions of the compressible navier stokes equations with ideal gas equation of state our main results are that in appropriately rescaled coordinates the evans function associated with the linearized operator about the wave i converges in the large amplitude limit to the evans function for a limiting shock profile of the same equations for which internal energy vanishes at one end state and ii has no unstable positive real part zeros outside a uniform ball thus the rescaled eigenvalue ode for the set of all shock waves augmented with the nonphysical limiting case form a compact family of boundary value problems that can be conveniently investigated numerically an extensive numerical evans function study yields one dimensional spectral stability independent of amplitude for gas constant in 1 2 3 and ratio of heat conduction to viscosity coefficient within 0 2 5 1 4 1 47 for air other values may be treated similarly but were not considered the method of analysis extends also to the multi dimensional case a direction that we shall pursue in a future work

the uniqueness and stability of the solution of the riemann problem of a system of conservation laws of mixed type we establish the uniqueness and stability of the similarity solution of the riemann problem for a 2 2 system of conservation laws of mixed type with initial data separated by the elliptic region which satisfies the viscosity capillarity travelling wave admissibility criterion

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

stability of periodic solutions of conservation laws with viscosity analysis of the evans function nonclassical conservation laws with viscosity arising in multiphase fluid and solid mechanics exhibit a rich variety of traveling wave phenomena including homoclinic pulse type and periodic solutions along with the standard heteroclinic shock or front type solutions here we investigate stability of periodic traveling waves within the abstract evans function framework established by r a gardner our main result is to derive a useful stability index analogous to that developed by gardner and zumbrun in the traveling front or pulse context giving necessary conditions for stability with respect to initial perturbations that are periodic on the same period t as the traveling wave moreover we show that the periodic stability index has an interpretation analogous to that of the traveling front or pulse index in terms of well posedness of an associated riemann problem for an inviscid medium now to be interpreted as allowing a wider class of measure valued solutions or alternatively in terms of existence and nonsingularity of a local mass map from perturbation mass to potential time asymptotic t periodic states a closely related calculation yields also a complementary long wave stability criterion necessary for stability with respect to periodic perturbations of arbitrarily large period nt n we augment these analytical results with numerical investigations analogous to those carried out by brin in the traveling front or pulse case approximating the spectrum of the linearized operator about the wave

global continuous riemann solver for nonlinear elasticity we consider in this paper an isothermal model of nonlinear elasticity this model is described by two conservation laws that define a problem of mixed type both elliptic and hyperbolic we restrict ourselves to the linearly degenerate case and consider riemann data that lies in the hyperbolic regions the lack of uniqueness of the riemann problem is solved by the introduction of a so called kinetic relation used to narrow the set of admissible subsonic phase transitions in this situation we consider the riemann problem for any data lying in the hyperbolic region using either explicit computations or geometric arguments this construction allows us to give sufficient conditions on the kinetic relation in order that the generated riemann solver possesses properties of uniqueness globality and continuous dependence on the initial data in the l 1 distance

the riemann problem for a van der waals fluid with entropy rate admissibility criterion nonisothermal case where a and b are the characteristic constants of the fluid thus when the temperature is sufficiently low p v is positive and thus the system i 1 is elliptic on a certain interval c fl while p v is negative on b liquid phase as well as on oo vapor phase on which 1 1 is hyperbolic the riemann problem for i 1 is a special initial value problem in which the initial data are of the form

stability of undercompressive shock profiles abstract using a simplified pointwise iteration scheme we establish nonlinear phase asymptotic orbital stability of large amplitude lax undercompressive overcompressive and mixed under overcompressive type shock profiles of strictly parabolic systems of conservation laws with respect to initial perturbations u 0 x e 0 1 x 3 2 in c 0 e 0 sufficiently small under the necessary conditions of spectral and hyperbolic stability together with transversality of the connecting profile this completes the program initiated by zumbrun and howard in k zumbrun p howard pointwise semigroup methods and stability of viscous shock waves indiana univ math j 47 4 1998 741 871 extending to the general undercompressive case results obtained for lax and overcompressive shock profiles in a szepessy z xin nonlinear stability of viscous shock waves arch ration mech anal 122 1993 53 103 t p liu pointwise convergence to shock waves for viscous conservation laws comm pure appl math 50 11 1997 1113 1182 k zumbrun p howard pointwise semigroup methods and stability of viscous shock waves indiana univ math j 47 4 1998 741 871 k zumbrun refined wave tracking and nonlinear stability of viscous lax shocks methods appl anal 7 2000 747 768 m r raoofi l 1 asymptotic behavior of perturbed viscous shock profiles thesis indiana univ 2004 c mascia k zumbrun pointwise green s function bounds and stability of relaxation shocks indiana univ math j 51 4 2002 773 904 c mascia k zumbrun stability of small amplitude shock profiles of symmetric hyperbolic parabolic systems comm pure appl math 57 7 2004 841 876 c mascia k zumbrun pointwise green s function bounds for shock profiles with degenerate viscosity arch ration mech anal 169 3 2003 177 263 c mascia k zumbrun stability of large amplitude shock profiles of hyperbolic parabolic systems arch ration mech anal 172 1 2004 93 131 c mascia k zumbrun stability of large amplitude shock profiles of general relaxation systems siam j math anal in press and for special weakly coupled respectively scalar diffusive dispersive undercompressive profiles in t p liu k zumbrun nonlinear stability of an undercompressive shock for complex burgers equation comm math phys 168 1 1995 163 186 t p liu k zumbrun on nonlinear stability of general undercompressive viscous shock waves comm math phys 174 2 1995 319 345 respectively p howard k zumbrun pointwise estimates for dispersive diffusive shock waves arch ration mech anal 155 2000 85 169 in particular together with spectral results of k zumbrun dynamical stability of phase transitions in the p system with viscosity capillarity siam j appl math 60 2000 1913 1924 our results yield nonlinear stability of large amplitude undercompressive phase transitional profiles near equilibrium of slemrod s model m slemrod admissibility criteria for propagating phase boundaries in a van der waals fluid arch ration mech anal 81 4 1983 301 315 for van der waal gas dynamics or elasticity with viscosity capillarity

short note controlling self force errors at refinement boundaries for amr pic we analyze the source of the self force errors in the node centered adaptive mesh refinement particle in cell amr pic algorithm and propose a method for reducing those self forces our approach is based on a method of charge deposition due to mayo a mayo the fast solution of poisson s and the biharmonic equations on irregular regions siam journal of numerical analysis 21 2 1984 285 299 that can reduce the self force error to any specified degree of accuracy

density weighted nystrom method for computing large kernel eigensystems the nystrom method is a well known sampling based technique for approximating the eigensystem of large kernel matrices however the chosen samples in the nystrom method are all assumed to be of equal importance which deviates from the integral equation that defines the kernel eigenfunctions motivated by this observation we extend the nystrom method to a more general density weighted version we show that by introducing the probability density function as a natural weighting scheme the approximation of the eigensystem can be greatly improved an efficient algorithm is proposed to enforce such weighting in practice which has the same complexity as the original nystrom method and hence is notably cheaper than several other alternatives experiments on kernel principal component analysis spectral clustering and image segmentation demonstrate the encouraging performance of our algorithm

asymptotic behavior of solutions to a system of viscous conservation laws related to a phase transition problem we study the asymptotic behavior of solutions for a system of viscous conservation laws with discontinuous initial data we discuss mainly the case where the system without the viscosity term is of hyperbolic elliptic mixed type this problem is related to a phase transition problem we study the initial value problem and show the decay rates of solutions to piecewise constant states where two phases coexist the modification necessary for the hyperbolic case is also discussed

the interaction of nonlinear hyperbolic waves nonlinearities in wave equations lead to focusing and defocusing of solutions focusing causes sharply defined wave fronts the interaction of such sharply defined wave fronts and more generally of nonlinear hyperbolic waves is of fundamental importance and includes such phenomena as mach triple point formation shock wave diffraction patterns and the study of riemann problems in one and higher dimensions recent progress in the study of nonlinear hyperbolic wave interactions has revealed a surprising range of new mathematical phenomena and structures this mathematical theory should be useful in the design of improved computational algorithms and in part was motivated by such considerations it is also of considerable interest for its own sake as new mathematical phenomena as well as in terms of the direct insight it provides into physical phenomena within the subject matter and point of view adopted here we have attempted to present a broad and we hope a representative account of recent progress

a vanishing viscosity approach on the dynamics of phase transitions in van der waals fluids abstract the existence of solutions for the riemann problem of a mixed type system is established by a vanishing similarity viscosity approach the solutions that we construct are also admissible by the travelling wave criterion derived from the most common form of viscosity the assumption needed includes the constitutive function of van der waals fluids

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

weak asymptotic decay via a relaxed invariance principle for a wave equation with nonlinear non monotone damping this paper considers the problem of asymptotic decay as t of solutions of the wave equation u tt u a x u t u t x a bounded open connected set in n n 1 with smooth boundary u 0 on the nonlinear function is not assumed to be globally lipschitz continuous 0 y 2 y n 1 0 y 1 y 1 y n 1 0 for all y n 1 is not assumed to be monotone in y 1 under additional restrictions on the kernel of conditions are given which imply that u u t converges to 0 0 weakly in h h 1 0 l 2 as t the work generalises earlier results of dafermos and haraux where strong decay in h as t was obtained in the case y 1 y n 1 q y 1 q monotone on

exploitation of the entropy principle proof of liu theorem if the gradients of the governing equations are considered as constraints the exploitation of the entropy principle in thermodynamics with lagrange multipliers the so called liu procedure is based on the celebrated liu theorem in some recent papers where either rigid heat conductors or korteweg fluids have been considered the liu procedure has been generalized by using the gradients of the governing equations as additional constraints here a rigorous proof of the validity of the extended procedure to arbitrary first order nonlocal continua is provided thus explicitly generalizing the liu theorem as an application heat conducting first order korteweg type fluids with a scalar internal variable are analyzed the thermodynamic restrictions are determined by the extended liu procedure moreover a comparison with the thermodynamic analysis obtained by the application of an extended coleman noll procedure is performed

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

the riemann problem and the existence of weak solutions to a system of mixed type in dynamic phase transition abstract we discuss the riemann problem and the existence of weak solutions to a dynamic phase transition problem to estimate the wave strength of outgoing waves containing the phase boundary we obtain the reflection and transmission coefficients for phase boundary then employing the entropy rate admissibility criterion and the initiation criterion we prove the existence of global weak solutions via glimm scheme

euclidean distance based canonical forms for non rigid 3d shape retrieval retrieval of 3d shapes is a challenging problem especially for non rigid shapes one approach giving favourable results uses multidimensional scaling mds to compute a canonical form for each mesh after which rigid shape matching can be applied however a drawback of this method is that it requires geodesic distances to be computed between all pairs of mesh vertices due to the super quadratic computational complexity canonical forms can only be computed for low resolution meshes we suggest a linear time complexity method for computing a canonical form using euclidean distances between pairs of a small subset of vertices this approach has comparable retrieval accuracy but lower time complexity than using global geodesic distances allowing it to be used on higher resolution meshes or for more meshes to be considered within a time budget highlightsour method computes canonical forms of 3d meshes without using geodesic distances our method maximises the euclidean distance between a small set of feature points our method has a lower time complexity than other approaches yet provides comparable retrieval results

diffusion maps and coarse graining a unified framework for dimensionality reduction graph partitioning and data set parameterization we provide evidence that nonlinear dimensionality reduction clustering and data set parameterization can be solved within one and the same framework the main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise our construction which is based on a markov random walk on the data offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry we show that clustering in embedding spaces is equivalent to compressing operators the objective of data partitioning and clustering is to coarse grain the random walk on the data while at the same time preserving a diffusion operator for the intrinsic geometry or connectivity of the data set up to some accuracy we show that the quantization distortion in diffusion space bounds the error of compression of the operator thus giving a rigorous justification for k means clustering in diffusion space and a precise measure of the performance of general clustering algorithms

a limiting viscosity approach to the riemann problem for materials exhibiting a change of phase ii describes the one dimensional isothermal motion of a compressible elastic fluid or solid in lagrangian coordinates considerable study has been made for the case p w 0 in which the system 1 i a b is hyperbolic however in some material models for instance in the van der waals fluid p w may be positive for some values of w in this paper we consider a function p w with graph shown in fig 1 more precisely we assume that p e c1 and

embedding retrieval of articulated geometry models due to the popularity of computer games and animation research on 3d articulated geometry model retrieval has attracted a lot of attention in recent years however most existing works extract high dimensional features to represent models and suffer from practical limitations first misalignment in high dimensional features may produce unreliable euclidean distances and affect retrieval accuracy second the curse of dimensionality also degrades efficiency in this paper we propose an embedding retrieval framework to improve the practicability of these methods it is based on a manifold learning technique the diffusion map dm we project all pairwise distances onto a low dimensional space this improves retrieval accuracy because intercluster distances are exaggerated then we adapt the density weighted nystrom extension and further propose a novel step to locally align the nystrom embedding to the eigensolver embedding so as to reduce extension error and preserve retrieval accuracy finally we propose a heuristic to handle disconnected manifolds by augmenting the kernel matrix with multiple similarity measures and shortcut edges and further discuss the choice of dm parameters we have incorporated two existing matching algorithms for testing our experimental results show improvement in precision at high recalls and in speed our work provides a robust retrieval framework for the matching of multimedia data that lie on manifolds

high order entropy conservative schemes and kinetic relations for van der waals fluids abstract we consider the mixed hyperbolic elliptic system of two conservation laws modeling the dynamics of van der waals fluids viscosity and capillarity effects are taken into account we introduce a new class of semidiscrete high order schemes which are entropy conservative in the sense of tadmor when the viscosity is neglected and otherwise dissipate the associated mathematical entropy our numerical schemes generalize the works by e tadmor 1987 math comput 49 91 and p g lefloch and c rohde 2000 siam j numer anal 37 2023 who proposed second order and third order entropy conservative schemes respectively following b t hayes and p g lefloch 1998 siam j numer anal 35 2169 we demonstrate numerically that balanced viscosity and capillarity terms in van der waals fluids may generate nonclassical shock waves or subsonic propagating phase transitions such waves are undercompressive and do not satisfy standard entropy criteria they must be characterized by a kinetic function which we determine numerically in this paper from vanishing viscosity and capillarity the kinetic relation is an efficient tool to discuss the interplay among the viscosity capillarity and discretization parameters in van der waals fluids

dynamics of propagating phase boundaries adiabatic theory for thermoelastic solids this paper examines adiabatic processes in a thermoelastic material undergoing a solid solid phase transition it is shown that an initial value problem of riemann type based on momentum balance energy balance kinematic compatibility and the entropy inequality has a one parameter family of solutions for a range of given data within this adiabatic setting the notions of driving traction and kinetic relation are discussed the enforcement of a kinetic relation at phase boundaries is shown to single out a particular solution of this riemann problem from among the family of available solutions

thermal creep of a rarefied gas on the basis of non linear korteweg theory the study of thermal transpiration more commonly called thermal creep is accomplished by use of korteweg s theory of capillarity incorporation of this theory into the balance laws of continuum mechanics allows resolution of boundary value problems via solutions to systems of ordinary differential equations the problem was originally considered by maxwell in his classic 1879 paper maxwell phil trans roy soc london 170 231 256 1879 in that paper maxwell derived what is now called the burnett higher order contribution to the cauchy stress but was not able to solve his newly derived system of partial differential equations in this paper the authors note that a more appropriate higher order contribution to the cauchy stress follows from korteweg s 1901 theory korteweg arch neerl sci exactes nat ser ii 6 1 24 1901 the appropriateness of korteweg s theory is based on the exact summation of the chapman enskog expansion given by gorban and karlin the resulting balance laws are solved exactly qualitatively and numerically and the results are qualitatively similar to the numerical and exact results given by aoki et al loyalka et al and struchtrup et al