Mathematical Methods For Hydrodynamic Limits
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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.
Mathematical Methods For Hydrodynamic Limits
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Author : Anna Demasi
language : en
Publisher:
Release Date : 2014-09-01
Mathematical Methods For Hydrodynamic Limits written by Anna Demasi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Hydrodynamic Limits And Related Topics
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Author : Shui Feng
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
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 2000 with Percolation (Statistical physics) 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.
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.
Hydrodynamic Limits Of The Boltzmann Equation
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Author : Laure Saint-Raymond
language : en
Publisher: Springer
Release Date : 2009-04-20
Hydrodynamic Limits Of The Boltzmann Equation written by Laure Saint-Raymond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-20 with Science categories.
The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.
Scaling Limits Of Interacting Particle Systems
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Author : Claude Kipnis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Scaling Limits Of Interacting Particle Systems written by Claude Kipnis 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 2013-03-09 with Mathematics categories.
This book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.
Nonlinear Stochastic Pdes
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Author : Tadahisa Funaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Stochastic Pdes written by Tadahisa Funaki 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 Mathematics categories.
This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.
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.
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.
Nonequilibrium Problems In Many Particle Systems
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Author : Carlo Cercignani
language : en
Publisher: Springer
Release Date : 1993-08-30
Nonequilibrium Problems In Many Particle Systems written by Carlo Cercignani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-30 with Mathematics categories.
This volume contains the text of four sets of lectures delivered at the third session of the Summer School organized by C.I.M.E. (Centro Internazionale Matematico Estivo). These texts are preceded by an introduction written by C. Cercignani and M. Pulvirenti which summarizes the present status in the area of Nonequilibrium Problems in Many-Particle Systems and tries to put the contents of the different sets of lectures in the right perspective, in order to orient the reader. The lectures deal with the global existence of weak solutions for kinetic models and related topics, the basic concepts of non-standard analysis and their application to gas kinetics, the kinetic equations for semiconductors and the entropy methods in the study of hydrodynamic limits. CONTENTS: C. Cercignani, M. Pulvirenti: Nonequilibrium Problems in Many-Particle Systems. An Introduction.- L. Arkeryd: Some Examples of NSA in Kinetic Theory.- P.L. Lions: Global Solutions of Kinetic Models and Related Problems.- P.A. Markowich: Kinetic Models for Semiconductors.- S.R.S. Varadhan: Entropy Methods in Hydrodynamic Scaling.