Author
Mario Pulvirenti
Other affiliations: Accademia Nazionale dei Lincei, University of L'Aquila
Bio: Mario Pulvirenti is an academic researcher from Sapienza University of Rome. The author has contributed to research in topics: Boltzmann equation & BBGKY hierarchy. The author has an hindex of 34, co-authored 136 publications receiving 4818 citations. Previous affiliations of Mario Pulvirenti include Accademia Nazionale dei Lincei & University of L'Aquila.
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01 Jan 1994
TL;DR: In this article, the authors present rigorous mathematical results in the kinetic theory of a gas of hard spheres, including the Boltzmann equations, global existence theory, and the fluid-dynamical limits.
Abstract: This book is devoted to the presentation of rigorous mathematical results in the kinetic theory of a gas of hard spheres. Recent developments as well as classical results are presented in a unified way, such that the book should become the standard reference on the subject. There is no such book available at present. The reader will find a systematic treatment of the main mathematical results, a discussion of open problems, and a guide to the existing literature. There is a rigorous and comprehensive presentation of strict validation of the Boltzmann equations, global existence theory, and the fluid-dynamical limits. The authors also review and discuss classical derivation and properties of the Boltzmann equation, particle simulation methods, and boundary conditions.
1,450 citations
TL;DR: In this paper, a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so-called quasi-elastic limit was corrected.
Abstract: In this short note we correct a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so called quasi-elastic limit, presented by the same authors in reference (1). The equation we derived is however correct so that, the rigorous analysis on this equation, which constituted the main purpose of that paper, remains unchanged. AMS Subject Classication. 82C21, 82C40.
205 citations
TL;DR: In this article, a nonlinear Fokker-Planck equation for a one-dimensional granular medium is considered and homogeneous solutions tend asymptotically in time toward a unique non-Maxwellian stationary distribution.
Abstract: We consider a nonlinear Fokker–Planck equation for a one-dimensional granular medium. This is a kinetic approximation of a system of nearly elastic particles in a thermal bath. We prove that homogeneous solutions tend asymptotically in time toward a unique non-Maxwellian stationary distribution.
166 citations
01 Jan 2004
TL;DR: Granvorka et al. as discussed by the authors present le Ceregmia de Travail, le document de travail published en 2010 by the International Association of Christians and Jews (IAC) in Haiti.
Abstract: Cette derniere Newsletter avant les Grandes Vacances est, pur concours de circonstances, entierement consacree a l’Education. Mais l’Education sous l’angle de son importance pour la consecration dans l’excellence. La consecration, c’est ce qu’a obtenu Gisele Mophou-Massengo, quand son jury de soutenance l’a declaree Habilitee a Diriger des Recherches. C’est egalement la reconnaissance qui est accordee a Elina Marie Devoue par le jury du prix « Religions et Developpement » pour son article consacre aux Religions et a leurs impacts sur la societe dans la Caraibe.La reconnaissance du savoir et du savoir-faire ne passe pas forcement par sa consecration. Elle passe egalement par sa diffusion la plus large. C’est ce que tente de faire le Ceregmia en organisant depuis 2009 ses « seminaires intra Ceregmia » qui permettent l’expression de la transversalite du laboratoire sur des chantiers en cours ou deja finalises autour de thematiques que nous vous invitons a decouvrir en page 2. De meme, le Ceregmia a lance une nouvelle publication en 2010, ses « Documents de Travail ». Ces Documents d’audience plus confidentielle sont reellement reserves a un public de scientifiques. Diffuser le savoir en l’adaptant aux evolutions de l’environnement et aux exigences du marche. C’est ce qu’a fait le Ceregmia grâce a sa nouvelle offre de formation en Masters qui a ete habilitee par le Ministere et qui ouvrira des la rentree 2010 (p. 4). Par ailleurs, nous avions eu l’occasion de vous entretenir des changements intervenus a l’IFGCar suite au seisme du 12 janvier 2010 en Haiti. Nous sommes heureux aujourd’hui, de vous annoncer que l’IFGCar qui est desormais l’IAC retourne s’installer en Haiti. Les formations en Master reprendront des le 1 er . Octobre. Enfin, Nous vous signalons la parution de deux ouvrages aux Editions Ibis Rouge ils vous invitent a decouvrir la Guyane sous un angle moins connu, celui de l’anthropologie. Charley Granvorka
160 citations
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TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
TL;DR: This work reviews many significant developments over the past decade of the lattice-Boltzmann method and discusses higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number.
Abstract: With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.
1,585 citations
TL;DR: In this article, the authors studied the large-data Cauchy problem for Boltzmann equations with general collision kernels and proved that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution.
Abstract: We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in L' to a solution. From this stability result we deduce global existence of a solution to the Cauchy problem. Our method relies upon recent compactness results for velocity averages, a new formulation of the Boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions. It allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations.
1,155 citations
TL;DR: In this article, a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory is derived, and the first member of the hierarchy is the Euler system based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions.
Abstract: This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a “14-moment” closure, which also recovers the behavior of the Grad “13-moment” system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.
903 citations
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Abstract: Recent developments of meshfree and particle methods and their applications in applied mechanics are surveyed. Three major methodologies have been reviewed. First, smoothed particle hydrodynamics ~SPH! is discussed as a representative of a non-local kernel, strong form collocation approach. Second, mesh-free Galerkin methods, which have been an active research area in recent years, are reviewed. Third, some applications of molecular dynamics ~MD! in applied mechanics are discussed. The emphases of this survey are placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics. This review article includes 397 references. @DOI: 10.1115/1.1431547#
833 citations