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Hydrodynamic Limits Of The Boltzmann Equation

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Hydrodynamic Limits Of The Boltzmann Equation

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Author : Laure Saint-Raymond
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-26

Hydrodynamic Limits Of The Boltzmann Equation written by Laure Saint-Raymond and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Mathematics categories.

"The material published in this volume comes essentially from a course given at the Conference on "Boltzmann equation and fluidodynamic limits", held in Trieste in June 2006." -- preface.

Mathematical Methods For Hydrodynamic Limits

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Author : Anna DeMasi
language : en
Publisher: Springer
Release Date : 2006-11-14

Mathematical Methods For Hydrodynamic Limits written by Anna DeMasi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.

Hydrodynamic Limits And Related Topics

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Author : Shui Feng
language : en
Publisher: American Mathematical Soc.
Release Date :

Hydrodynamic Limits And Related Topics written by Shui Feng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.

This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.

Lecture Notes On The Mathematical Theory Of The Boltzmann Equation

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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 1995

Lecture Notes On The Mathematical Theory Of The Boltzmann Equation written by N. Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.

This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.

Kinetic Equations

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Author : Alexander V. Bobylev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12

Kinetic Equations written by Alexander V. Bobylev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.

This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.

Entropy Methods For The Boltzmann Equation

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Author : Fraydoun Rezakhanlou
language : en
Publisher: Springer
Release Date : 2007-12-22

Entropy Methods For The Boltzmann Equation written by Fraydoun Rezakhanlou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Mathematics categories.

Featuring updated versions of two research courses held at the Centre Émile Borel in Paris in 2001, this book describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields. It also discusses four conjectures for the kinetic behavior of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.

From Kinetic Models To Hydrodynamics

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Author : Matteo Colangeli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-25

From Kinetic Models To Hydrodynamics written by Matteo Colangeli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Science categories.

From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.

Hydrodynamic Limits And Related Topics

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Author : Shui Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

The Boltzmann Equation

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Author : E.G.D. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Boltzmann Equation written by E.G.D. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

In,1872, Boltzmann published a paper which for the first time provided a precise mathematical basis for a discussion of the approach to equilibrium. The paper dealt with the approach to equilibrium of a dilute gas and was based on an equation - the Boltzmann equation, as we call it now - for the velocity distribution function of such ~ gas. The Boltzmann equation still forms the basis of the kinetic theory of gases and has proved fruitful not only for the classical gases Boltzmann had in mind, but als- if properly generalized - for the electron gas in a solid and the excitation gas in a superfluid. Therefore it was felt by many of us that the Boltzmann equation was of sufficient interest, even today, to warrant a meeting, in which a review of its present status would be undertaken. Since Boltzmann had spent a good part of his life in Vienna, this city seemed to be a natural setting for such a meeting. The first day was devoted to historical lectures, since it was generally felt that apart from their general interest, they would furnish a good introduction to the subsequent scientific sessions. We are very much indebted to Dr. D.

Transport And Fluctuations In Granular Fluids

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Author : Andrea Puglisi
language : en
Publisher: Springer
Release Date : 2014-09-02

Transport And Fluctuations In Granular Fluids written by Andrea Puglisi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Science categories.

This brief offers a concise presentation of granular fluids from the point of view of non-equilibrium statistical physics. The emphasis is on fluctuations, which can be large in granular fluids due to the small system size (the number of grains is many orders of magnitude smaller than in molecular fluids). Firstly, readers will be introduced to the most intriguing experiments on fluidized granular fluids. Then granular fluid theory, which goes through increasing levels of coarse-graining and emerging collective phenomena, is described. Problems and questions are initially posed at the level of kinetic theory, which describes particle densities in full or reduced phase-space. Some answers become clear through hydrodynamics, which describes the evolution of slowly evolving fields. Granular fluctuating hydrodynamics, which builds a bridge to the most recent results in non-equilibrium statistical mechanics, is also introduced. Further and more interesting answers come when the dynamics of a massive intruder are discussed. Such non-equilibrium stochastic process offers a more precise and compact picture of the features foreseen at the more detailed levels of description. The dynamics of an intruder diffusing in a granular fluid reveal the clearest connection with recent theories on stochastic energetics and stochastic thermodynamics.

Hydrodynamic Limits Of The Boltzmann Equation

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