well balanced unstaggered central schemes for the euler equations with gravitation we consider the euler equations with gravitational source term and propose a new well balanced unstaggered central finite volume scheme which can preserve the hydrostatic balance state exactly the proposed scheme evolves a nonoscillatory numerical solution on a single grid avoids the time consuming process of solving riemann problems arising at the cell interfaces and is second order accurate both in time and space furthermore the numerical scheme follows a well balanced discretization that first discretizes the gravitational source term according to the discretization of the flux terms and then mimics the surface gradient method and discretizes the density and energy according to the discretization of steady state density and energy functions respectively finally several numerical experiments demonstrating the performance of the well balanced schemes in both one and two spatial dimensions are presented the results indicate that the new scheme is accurate simple and robust

stability of the difference type methods for linear volterra equations in hilbert spaces we study the stability of backward difference timestepping method for linear volterra equations of scalar type in a hilbert space framework the results and methods extend and simulate numerically those introduced by pruss for integrability with respect to continuous solutions

weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

a second order kinetic scheme for gas dynamics on arbitrary grids cartesian meshes for domains with complicated boundaries give rise to cut cells with arbitrarily small volumes explicit integration schemes over such meshes have a time step restriction proportional to the smallest cell volume we present an implementation of the kinetic scheme for gas dynamics by perthame b perthame boltzmann type schemes for gas dynamics and the entropy property siam j num anal 27 1990 1405 1421 on arbitrary cartesian meshes the formulation allows a time step based on the underlying regular cell size and retains l 1 stability positivity and second order convergence numerical convergence studies on arbitrary grids are presented

subdivisions and local h vectors in part i a general theory of f vectors of simplicial subdivisions or triangulations of simplicial complexes is developed based on the concept of lo cal h vector as an application we prove that the h vector of a cohen macaulay complex increases under quasi geometric subdivision thus establishing a spe cial case of a conjecture of kalai and this author techniques include com mutative algebra homological algebra and the intersection homology of toric varieties in part ii we extend the work of part i to more general situations first a formal generalization of subdivision is given based on incidence alge bras special cases are then developed in particular one based on subdivisions of eulerian posets and involving generalized h vectors other cases deal with kazhdan lusztig polynomials ehrhart polynomials and a q analogue of eule rian posets many applications and examples are given throughout department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address rstan math mit edu this content downloaded from 157 55 39 210 on sat 30 jul 2016 05 59 16 utc all use subject to http about jstor org terms

peturbation theory of abstract cauchy problems and volterra equations abstract some multiplicative perturbation theorems and additive perturbation theorems for resolvent families are presented

numerical solution of non isothermal non adiabatic flow of real gases in pipelines a finite volume scheme for the numerical solution of a mathematical model for non isothermal non adiabatic compressible flow of a real gas in a pipeline is introduced in order to make an upwind discretization of the flux the q scheme of van leer is used unlike standard euler equations the model takes into account wall friction variable height and heat transfer between the pipe and the environment since all these terms are sources in order to get a well balanced scheme they are discretized by making a similar upwinding to the one in the flux term the performance of the overall method has been shown for some usual numerical tests the final goal which is beyond the scope of this paper is to consider a network including several pipelines connected at junctions as those employed for natural gas transport

high order entropy based closures for linear transport in slab geometry ii a computational study of the optimization problem we present a numerical algorithm to implement entropy based m n moment models in the context of a simple linear kinetic equation for particles moving through a material slab the closure for these models as is the case for all entropy based models is derived through the solution of a constrained convex optimization problem the algorithm has two components the first component is a discretization of the moment equations which preserves the set of realizable moments thereby ensuring that the optimization problem has a solution in exact arithmetic the discretization is a second order kinetic scheme which uses muscl type limiting in space and a strong stability preserving runge kutta time integrator the second component of the algorithm is a newton based solver for the dual optimization problem which uses an adaptive quadrature to evaluate integrals in the dual objective and its derivatives the accuracy of the numerical solution to the dual problem plays a key role in the time step restric

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

weak solutions of hyperbolic parabolic volterra equations the existence of a global weak solution satisfying certain a priori l bounds of the equation ut t x ft k t s a ux x s x ds f t x is established the kernel k is locally integrable and log convex and a has only one local minimum which is positive introduction the purpose of this paper is to establish the existence of a global weak solution of the equation 1 t ut t x k k t s a ux x s x ds f t x t o x e 0 1 u o x uo x x e o 1 u t o u t 1 o t o where the subscripts denote differentiation with respect to the corresponding variables and to show that this weak solution satisfies certain a priori l bounds equation 1 is of interest because it appears in mathematical models of viscoelasticity see 18 and 31 but also because it is of a form somewhere between a parabolic and a hyperbolic equation this is due to the fact that when k 1 we get the nonlinear wave equation utt t x a ux x t x ft t x and if on the other hand k is replaced by the delta functional then we get the nonlinear diffusion equation ut t x a ux x t x f t x the nonlinear wave equation that corresponds to the completely elastic case in mechanics has a weak solution with both ux and ut bounded and initially smooth solutions develop singularities in the derivatives in finite time the received by the editors september 22 1992 1991 mathematics subject classification primary 45k05 secondary 45d05 45n05 35k99 35l99 73f99

lifting inequalities for polytopes we present a method of lifting linear inequalities for the flag f vector of polytopes to higher dimensions known inequalities that can be lifted using this technique are the non negativity of the toric g vector and that the simplex minimizes the cd index we obtain new inequalities for six dimensional polytopes in the last section we present the currently best known inequalities for dimensions 5 through 8

strong solutions to stochastic volterra equations in this paper stochastic volterra equations admitting exponentially bounded resolvents are studied after obtaining convergence of resolvents some properties for stochastic convolutions are studied our main results provide sufficient conditions for strong solutions to stochastic volterra equations

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

runge kutta methods for hyperbolic conservation laws with stiff relaxation terms underresolved numerical schemes for hyperbolic conservation laws with stiff relaxation terms may generate unphysical spurious numerical results or reduce to lower order if the small relaxation time is not temporally well resolved we design a second order runge kutta type splitting method that possesses the discrete analogue of the continuous asymptotic limit which thus is able to capture the correct physical behaviors with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved

singular perturbation for volterra equations of convolution type under the assumption that a is the generator of a twice integrated cosine family and k is a scalar valued kernel we solve the singular perturbation problem e e e 2u e t u e t au e t k au e t f e t t 0 e 0 when e 0 for the integrodifferential equation e w t aw t k aw t f t t 0 on a banach space if the kernel k verifies some regularity conditions then we show that problem e e has a unique solution u e t for each small e 0 moreover u e t converges as e 0 to the unique solution u t of equation e

an h adaptive mesh method for boltzmann bgk hydrodynamics coupling we introduce a coupled method for hydrodynamic and kinetic equations on 2 dimensional h adaptive meshes we adopt the euler equations with a fast kinetic solver in the region near thermodynamical equilibrium while use the boltzmann bgk equation in kinetic regions where fluids are far from equilibrium a buffer zone is created around the kinetic regions on which a gradually varying numerical flux is adopted based on the property of a continuously discretized cut off function which describes how the flux varies the coupling will be conservative in order for the conservative 2 dimensional specularly reflective boundary condition to be implemented conveniently the discrete maxwellian is approximated by a high order continuous formula with improved accuracy on a disc instead of on a square domain the h adaptive method can work smoothly with a time split numerical scheme through h adaptation the cell number is greatly reduced this method is particularly suitable for problems with hydrodynamics breakdown on only a small part of the whole domain so that the total efficiency of the algorithm can be greatly improved three numerical examples are presented to validate the proposed method and demonstrate its efficiency

on boundary feedback stabilisability of a viscoelastic beam it is shown that a cantilevered beam with weak viscoelastic damping of boltzmann type can be uniformly stabilised by velocity feedback applied as a shearing force at the free end of the beam estimates for the viscoelastic energy are derived using the energy multiplier method the energy decay is related to the decay of the relaxation modulus associated with the viscoelastic material

construction of bgk models with a family of kinetic entropies for a given system of conservation laws we introduce a general framework for kinetic bgk models we assume to be given a system of hyperbolic conservation laws with a family of lax entropies and we characterize the bgk models that lead to this system in the hydrodynamic limit and that are compatible with the whole family of entropies this is obtained by a new characterization of maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies we deduce a general procedure to construct such bgk models and we show how classical examples enter the framework we apply our theory to isentropic gas dynamics and full gas dynamics and in both cases we obtain new bgk models satisfying all entropy inequalities

singular perturbations of integro differential equations abstract we study the singular perturbation problem e 2 u t u t au t k au t f t t 0 0 for the integro differential equation e w t aw t k aw t f t t 0 in a banach space when 0 we assume that a is the generator of a strongly continuous cosine family then under some regularity conditions on the scalar valued kernel k we show that problem e has a unique solution u t for each small 0 moreover u t converges to u t as 0 the unique solution of equation e

shellable nonpure complexes and posets ii this is a direct continuation of shellable nonpure complexes and posets i which appeared in transactions of the american mathematical society 348 1996 1299 1327 8 interval generated lattices and dominance order in this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets let f i1 i2 in be a family of intervals of integers by which is meant sets of the form a b a a 1 b a b we assume that there are no containments among these intervals and that they are ordered so that their left and right endpoints are increasing let l f be the lattice of all sets that are unions of subfamilies of f ordered by inclusion such interval generated lattices l f were introduced and studied by greene g define an edge labeling of l f as follows if a b is a covering and a max b a then a b a if a 1 a and a is the left endpoint of some i f

effectiveness and robustness with respect to time delays of boundary feedback stabilization in one dimensional viscoelasticity the damping effect of a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod is examined a characteristic equation is derived for the oscillatory modes and the solutions of this equation are studied by analytic and numerical methods as functions of the feedback gain parameter and of a parameter for feedback delay results are compared to recent studies of elastic materials where a feedback delay can cause exponential instability here this phenomenon depends significantly on the short time behavior of the viscoelastic memory kernel finally an existence result is given showing that the behavior of a weak solution corresponds in the expected way to the location of the characteristic roots

entropy satisfying flux vector splittings and kinetic bgk models we establish forward and backward relations between entropy satisfying bgk relaxation models such as those introduced previously by the author and the first order flux vector splitting numerical methods for general systems of conservation laws classically to a kinetic bgk model that is compatible with some family of entropies we can associate an entropy flux vector splitting we prove that the converse is true any entropy flux vector splitting can be interpreted by a kinetic model and we obtain an explicit characterization of entropy satisfying flux vector splitting schemes we deduce a new proof of discrete entropy inequalities under a sharp cfl condition that generalizes the monotonicity criterion in the scalar case in particular this gives a stability condition for numerical kinetic methods with noncompact velocity support a new interpretation of general kinetic schemes is also provided via approximate riemann solvers we deduce the construction of finite velocity relaxation systems for gas dynamics and obtain a hllc scheme for which we are able to prove positiveness of density and internal energy and discrete entropy inequalities

a semi implicit spectral method for compressible convection of rotating and density stratified flows in cartesian geometry in this paper we have described a stratified semi implicit spectral method to study compressible convection in cartesian geometry the full set of compressible hydrodynamic equations are solved in conservative forms the numerical scheme is accurate and efficient based on fast fourier sin cos spectral transforms in the horizontal directions chebyshev spectral transform or second order finite difference scheme in the vertical direction and second order semi implicit scheme in time marching of linear terms we have checked the validity of both the fully pseudo spectral scheme and the mixed finite difference pseudo spectral scheme by studying the onset of compressible convection the difference of the critical rayleigh number between our numerical result and the linear stability analysis is within two percent besides we have computed the mach numbers with different rayleigh numbers in compressible convection it shows good agreement with the numerical results of finite difference methods and finite volume method this model has wide application in studying laminar and turbulent flow illustrative examples of application on horizontal convection gravity waves and long lived vortex are given in this paper

a parallel method for the numerical solution of integro differential equation with positive memory abstract an efficient parallel numerical method is proposed for an integro differential equation with positive memory instead of solving the equation in classical time marching methods which require massive storage of solutions of previous time steps in order to advance to a next time step the fourier laplace transformation in time is applied to obtain a set of complex valued elliptic problems parameterized by points on a contour in the complex plane using the independence of an elliptic problem corresponding to one contour point is independent of those elliptic problems corresponding to other contour points all elliptic problems can be solved in parallel essentially without data communications then the time domain solution can be obtained by the fourier laplace inversion formula an error analysis and the numerical implementation of this parallel method is presented

maps of convex sets and invariant regions for finite difference systems of conservation laws general results about maps of convex sets in r n are proved we outline their extensions to an infinite dimensional context such extensions have applications in nonlinear analysis such as in the study of the invariance of convex sets under nonlinear maps here we explore applications only in the finite dimensional context more specifically we apply the general results to the problem of finding sufficient conditions for a region of the state space to be globally or locally invariant under finite difference schemes applied to systems of conservation laws in several space variables in particular we establish a final characterization of the invariant regions under the lax friedrichs scheme and also give sufficient conditions for the local invariance further we give sufficient conditions for the global and local invariance of regions under flux splitting finite difference schemes an example of the multi dimensional euler equations for non isentropic gas dynamics is discussed

fluid solver independent hybrid methods for multiscale kinetic equations in some recent works g dimarco and l pareschi comm math sci 1 2006 pp 155 177 multiscale model simul 6 2008 pp 1169 1197 we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems here in contrast to previous methods we construct a method form fitting to any type of finite volume or finite difference scheme for the reduced equilibrium system thanks to the coupling of monte carlo techniques for the solution of the kinetic equations with macroscopic methods for the limiting fluid equations we show how it is possible to solve multiscale fluid dynamic phenomena faster than using traditional deterministic stochastic methods for the full kinetic equations in addition due to the hybrid nature of the schemes the numerical solution is affected by fewer fluctuations than are standard monte carlo schemes applications to the boltzmann bgk equation are presented to show the performance of the new methods in comparison with classical approaches used in the simulation of kinetic equations

a new perspective on kinetic schemes compared to standard numerical methods for hyperbolic systems of conservation laws kinetic schemes model propagation of information by particles instead of waves in this article the wave and the particle concept are shown to be closely related moreover a general approach to the construction of kinetic schemes for hyperbolic conservation laws is given that summarizes several approaches discussed by other authors

convergence of a weighted particle method for solving the boltzmann b g k equation we consider in this paper the numerical solution of the b g k model for the boltzmann equation the numerical method used here was introduced by mas gallic transport theory statist phys 16 1987 pp 885 887 using the results of perthame and pulvirenti arch rational mech anal 125 1993 pp 289 295 we first derive a uniqueness result for the b g k model and also regularity properties of the solution which are necessary for our analysis we then prove following mas gallic and poupaud transport theory statist phys 17 1988 pp 311 345 the convergence of the numerical approximation for the b g k model finally some numerical experiments are presented

an immersed boundary method based on the gas kinetic bgk scheme for incompressible viscous flow in this paper an immersed boundary ib method based on the gas kinetic bhatnagar gross krook bgk scheme is proposed to simulate the incompressible viscous flow around stationary and moving rigid bodies in the presented ib method a set of lagrangian points represent the solid boundary and will exert force on the surrounding eulerian points which are the cell centers within the finite volume framework this force is calculated by a special iterative procedure and has an effect on the flux at the interface of cell which guarantees the fulfillment of the no slip boundary condition and entirely avoids the flow penetration the flow field is obtained from the bgk scheme with local grid refinement without complex mesh generation and transformation the present technique can be conveniently applied to simulations with complex and moving solid boundaries the second order temporal accuracy and better than first order spatial accuracy in l 2 norm are testified by the simulation of stokes first problem other three different test cases including flows around a stationary circular cylinder two circular cylinders in tandem and an oscillating circular cylinder demonstrate the good capability of the present method expanding the immersed boundary ib method to the finite volume gas kinetic bhatnagar gross krook bgk scheme the flux across the cell s interface will be influenced by the immersed boundary force the flow penetration to the immersed boundary is completely eliminated the present method can be conveniently applied to problems with moving objects

weighted l1 paley wiener theorem with applications to stability of the linear multi step methods for volterra equations in hilbert spaces abstract we study the weighted l 1 paley wiener theorem with applications to stability of the linear multi step time discretization for a linear volterra equation of scalar type in a hilbert space the results extend to weighted l 1 stability some recent l 1 stability theorem due to the author numer math 109 2008 571 595 our theoretical results are applied to investigate the asymptotic behavior as t n of the numerical solutions of certain integro differential equations in hilbert space

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

regular article a new discrete velocity method for navier stokes equations the relation between the lattice boltzmann method which has recently become popular and the kinetic schemes which are routinely used in computational fluid dynamics is explored a new discrete velocity method for the numerical solution of navier stokes equations for incompressible fluid flow is presented by combining both the approaches the new scheme can be interpreted as a pseudo compressibility method and for a particular choice of parameters this interpretation carries over to the lattice boltzmann method

kinetic derivation of a finite difference scheme for the incompressible navier stokes equation in the present paper the low mach number limit of kinetic equations is used to develop a discretization for the incompressible navier stokes equation the kinetic equation is discretized with a first and second order discretization in space the discretized equation is then considered in the low mach number limit using this limit a second order discretization for the convective part in the incompressible navier stokes equation is obtained numerical experiments are shown comparing different approaches

positivity and regularity of hyperbolic volterra equations in banach spaces soit x un espace de banach a un operateur lineaire clos non borne dans x a domaine dense d a a l loc 1 r f c j x avec j 0 t et on considere l equation de volterra de type scalaire u t f t 0 t a t au d t j on etudie l existence la positivite la regularite et la compacite ainsi que l integrabilite de l operateur resolvant s t defini par s t x x 0 t a t as xd t 0 x d a pour deux classes particulieres de noyaux a et d operateurs a

on monotone solutions of an integrodifferential equation in linear viscoelasticity we consider the integrodifferential equation u t x int 0 t a t s u xx s x ds with initial and boundary conditions corresponding to the rayleigh problem the kernel has the form a t a 0 a infty t int 0 t a 1 s ds where a 0 geq 0 a infty geq 0 and a 1 in l loc 1 bf r is of positive type and satisfies the condition int 0 infty e epsilon t ert a 1 t ert dt 0 by solving the equation numerically and performing a careful error analysis we show that the solution u t x need not be nondecreasing in t geq 0 for fixed x 0 if a 1 is nonnegative nonincreasing and convex the same result is shown to hold under the assumption that a 1 is completely positive this answers a question that remained unsolved in j pru ss it math ann 279 1987 p 330 in the case where a 1 is convex piecewise linear the solution is shown to be almost everywhere equal to a function which is discontinuous across infinitely many parallel lines

discontinuous galerkin method for navier stokes equations using kinetic flux vector splitting kinetic schemes for compressible flow of gases are constructed by exploiting the connection between boltzmann equation and the navier stokes equations this connection allows us to construct a flux splitting for the navier stokes equations based on the direction of molecular motion from which a numerical flux can be obtained the naive use of such a numerical flux function in a discontinuous galerkin dg discretization leads to an unstable scheme in the viscous dominated case stable schemes are constructed by adding additional terms either in a symmetric or non symmetric manner which are motivated by the dg schemes for elliptic equations the novelty of the present scheme is the use of kinetic fluxes to construct the stabilization terms in the symmetric case interior penalty terms have to be added for stability and the resulting schemes give optimal convergence rates in numerical experiments the non symmetric schemes lead to a cell energy entropy inequality but exhibit sub optimal convergence rates these properties are studied by applying the schemes to a scalar convection diffusion equation and the 1 d compressible navier stokes equations in the case of navier stokes equations entropy variables are used to construct stable schemes

treating network junctions in finite volume solution of transient gas flow models abstract a finite volume scheme for the numerical solution of a non isothermal non adiabatic compressible flow model for gas transportation networks on non flat topography is introduced unlike standard euler equations the model takes into account wall friction variable height and heat transfer between the pipe and the environment which are source terms the case of one single pipe was considered in a previous reference by the authors 8 where a finite volume method with upwind discretization of the flux and source terms has been proposed in order to get a well balanced scheme the main goal of the present paper is to go a step further by considering a network of pipes the main issue is the treatment of junctions for which container like 2d finite volumes are introduced the couplings between pipes 1d and containers 2d are carefully described and the conservation properties are analyzed numerical tests including real gas networks are solved showing the performance of the proposed methodology

explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems we design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection these schemes are based on discrete bgk models where both characteristic velocities and the source term depend singularly on the relaxation parameter general stability conditions are derived and convergence is proved to the entropy solutions for scalar equations

a three dimensional multidimensional gas kinetic scheme for the navier stokes equations under gravitational fields this paper extends the gas kinetic scheme for one dimensional inviscid shallow water equations k xu a well balanced gas kinetic scheme for the shallow water equations with source terms j comput phys 178 2002 533 562 to multidimensional gas dynamic equations under gravitational fields four important issues in the construction of a well balanced scheme for gas dynamic equations are addressed first the inclusion of the gravitational source term into the flux function is necessary second to achieve second order accuracy of a well balanced scheme the chapman enskog expansion of the boltzmann equation with the inclusion of the external force term is used third to avoid artificial heating in an isolated system under a gravitational field the source term treatment inside each cell has to be evaluated consistently with the flux evaluation at the cell interface fourth the multidimensional approach with the inclusion of tangential gradients in two dimensional and three dimensional cases becomes important in order to maintain the accuracy of the scheme many numerical examples are used to validate the above issues which include the comparison between the solutions from the current scheme and the strang splitting method the methodology developed in this paper can also be applied to other systems such as semi conductor device simulations under electric fields

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

a moving interface method for dynamic kinetic fluid coupling this paper is a continuation of earlier work p degond s jin l mieussens a smooth transition between kinetic and hydrodynamic equations journal of computational physics 209 2005 665 694 in which we presented an automatic domain decomposition method for the solution of gas dynamics problems which require a localized resolution of the kinetic scale the basic idea is to couple the macroscopic hydrodynamics model and the microscopic kinetic model through a buffer zone in which both equations are solved discontinuities or sharp gradients of the solution are responsible for locally strong departures to local equilibrium which require the resolution of the kinetic model the buffer zone is drawn around the kinetic region by introducing a cut off function which takes values between zero and one and which is identically zero in the fluid zone and one in the kinetic zone in the present paper we specifically consider the possibility of moving the kinetic region or creating new kinetic regions by evolving the cut off function with respect to time we present algorithms which perform this task by taking into account indicators which characterize the non equilibrium state of the gas the method is shown to be highly flexible as it relies on the time evolution of the buffer cut off function rather than on the geometric definition of a moving interface which requires remeshing by contrast to many previous methods numerical examples are presented which validate the method and demonstrate its performances

euler flag enumeration of whitney stratified spaces abstract the flag vector contains all the face incidence data of a polytope and in the poset setting the chain enumerative data it is a classical result due to bayer and klapper that for face lattices of polytopes and more generally eulerian graded posets the flag vector can be written as a c d index a non commutative polynomial which removes all the linear redundancies among the flag vector entries this result holds for regular cw complexes we relax the regularity condition to show the c d index exists for whitney stratified manifolds by extending the notion of a graded poset to that of a quasi graded poset this is a poset endowed with an order preserving rank function and a weighted zeta function this allows us to generalize the classical notion of eulerianness and obtain a c d index in the quasi graded poset arena we also extend the semi suspension operation to that of embedding a complex in the boundary of a higher dimensional ball and study the simplicial shelling components

on linear volterra equations of parabolic type in banach spaces linear integrodifferential equations of volterra type in a banach space are studied in case the main part of the equation generates an analytic co semigroup under very general assumptions it is shown that a resolvent operator exists and that many of the solution properties of parabolic evolu tion equations are inherited the results are then applied to integro partial differential equations of parabolic type

singular relaxation moduli and smoothing in three dimensional viscoelasticity we develop a semigroup setting for linear viscoelasticity in threedimensional space with tensor valued relaxation modulus and give a criterion on the relaxation kernel for differentiability and analyticity of the solutions the method is also extended to a simple problem in thermoviscoelasticity

stable lattice boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves we follow the mathematical framework proposed by bouchut 2003 22 and present in this contribution a dual entropy approach for determining equilibrium states of a lattice boltzmann scheme this method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law it appears as a good mathematical framework for establishing a h theorem for the system of equations with discrete velocities the dual entropy approach is used with d1q3 lattice boltzmann schemes for the burgers equation it conducts to the explicitation of three different equilibrium distributions of particles and induces naturally a nonlinear stability condition satisfactory numerical results for strong nonlinear shocks and rarefactions are presented we prove also that the dual entropy approach can be applied with a d1q3 lattice boltzmann scheme for systems of linear and nonlinear acoustics and we present a numerical result with strong nonlinear waves for nonlinear acoustics we establish also a negative result with the present framework the dual entropy approach cannot be used for the shallow water equations

high order positivity preserving kinetic schemes for the compressible euler equations we present a new class of high order kinetic flux splitting schemes for the compressible euler equations and we prove that these schemes are positivity preserving i e rho and t remain geq 0 the first order kinetic scheme is based on the maxwellian equilibrium function and was initially proposed by pullin j comput phys 34 1980 pp 231 244 our higher order extension can be seen as a variant of the corrected antidiffusive flux approach the necessity of a limitation on the antidiffusive correction appears naturally in order to satisfy the constraint of positivity

peak algebras paths in the bruhat graph and kazhdan lusztig polynomials we obtain a nonrecursive combinatorial formula for the kazhdan lusztig polynomials which holds in complete generality and which is simpler and more explicit than any existing one and which cannot be linearly simplified our proof uses a new basis of the peak subalgebra of the algebra of quasisymmetric functions

kinetic approximation of a boundary value problem for conservation laws we design numerical schemes for systems of conservation laws with boundary conditions these schemes are based on relaxation approximations taking the form of discrete bgk models with kinetic boundary conditions the resulting schemes are riemann solver free and easily extendable to higher order in time or in space for scalar equations convergence is proved we show numerical examples including solutions of euler equations

monotonicity of the cd index for polytopes we prove that the cd index of a convex polytope satisfies a strong monotonicity property with respect to the cd indices of any face and its link as a consequence we prove for d dimensional polytopes a conjecture of stanley that the cd index is minimized on the d dimensional simplex moreover we prove the upper bound theorem for the cd index namely that the cd index of any d dimensional polytope with n vertices is at most that of c n d the d dimensional cyclic polytope with n vertices

boltzmann type schemes for gas dynamics and the entropy property let h be a convex function a boltzmann equation is built following the b g k model for which h is an entropy in the fluid limit the compressible euler equations are obtained with a convex entropy naturally associated to h the motivation is to define numerical boltzmann schemes with finite speed of propagation corresponding to an equilibrium density function with bounded support the classical scheme obtained with h f f log f is based on the equilibrium density function exp v 2 2 which has infinite support

new developments in kinetic schemes kinetic schemes for the numerical solution of pde of fluid dynamics are a new class of upwind schemes the moment method strategy used in constructing these schemes is based on the connection between the boltzmann equation of kinetic theory of gases and governing equations of fluid dynamics any upwind scheme for the solution of the boltzmann equation becomes an upwind scheme for the solution of pde of fluid dynamics by taking suitable moments this idea has been exploited in the present paper in developing least squares kinetic upwind method lskum and kinetic flux vector splitting method on moving grid kfmg the robustness and versatility of lskum has been demonstrated by applying it to 2 d flow problems of inviscid gas dynamics the lskum has been found to operate on any type of grid and can be called a grid fault tolerant scheme in view of the use of least squares approximation to the space derivatives the kfmg is a promising new method showing how easily the kinetic schemes lend themselves easily to problems involving moving grids which are generally employed while solving problems in unsteady aerodynamics