Entropy Methods For The Boltzmann Equation
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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.
Modeling And Computational Methods For Kinetic Equations
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Author : Pierre Degond
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modeling And Computational Methods For Kinetic Equations written by Pierre Degond 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.
In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused theoretical or applied works. The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems. "Modeling and Computational Methods of Kinetic Equations" will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
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.
From Particle Systems To Partial Differential Equations
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Author : Eric Carlen
language : en
Publisher: Springer Nature
Release Date : 2024-09-25
From Particle Systems To Partial Differential Equations written by Eric Carlen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Science categories.
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations X, which was held at the University of Minho, Braga, Portugal, from 2022. It includes papers on mathematical problems motivated by various applications in physics, engineering, economics, chemistry, and biology.
The Method Of Intrinsic Scaling
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Author : José Miguel Urbano
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-20
The Method Of Intrinsic Scaling written by José Miguel Urbano 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 2008-05-20 with Mathematics categories.
This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs.In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions.
The Relativistic Boltzmann Equation Theory And Applications
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Author : Carlo Cercignani
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Relativistic Boltzmann Equation Theory And Applications written by Carlo Cercignani and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity. Though an attempt is made to present the basic concepts in a complete fashion, the style of presentation is chosen to be appealing to readers who want to understand how kinetic theory is used for explicit calculations. The book will be helpful not only as a textbook for an advanced course on relativistic kinetic theory but also as a reference for physicists, astrophysicists and applied mathematicians who are interested in the theory and applications of the relativistic Boltzmann equation.
Handbook Of Differential Equations Evolutionary Equations
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Author : C.M. Dafermos
language : en
Publisher: Elsevier
Release Date : 2005-10-05
Handbook Of Differential Equations Evolutionary Equations written by C.M. Dafermos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-05 with Mathematics categories.
The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications. Evolutionary partial differential equations made their first appearance in the 18th century, in the endeavor to understand the motion of fluids and other continuous media. The active research effort over the span of two centuries, combined with the wide variety of physical phenomena that had to be explained, has resulted in an enormous body of literature. Any attempt to produce a comprehensive survey would be futile. The aim here is to collect review articles, written by leading experts, which will highlight the present and expected future directions of development of the field. The emphasis will be on nonlinear equations, which pose the most challenging problems today.. Volume I of this Handbook does focus on the abstract theory of evolutionary equations. . Volume 2 considers more concrete problems relating to specific applications. . Together they provide a panorama of this amazingly complex and rapidly developing branch of mathematics.
From Particle Systems To Partial Differential Equations Iii
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Author : Patrícia Gonçalves
language : en
Publisher: Springer
Release Date : 2016-07-16
From Particle Systems To Partial Differential Equations Iii written by Patrícia Gonçalves and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-16 with Mathematics categories.
The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. This book will appeal to probabilists, analysts and those mathematicians whose work involves topics in mathematical physics, stochastic processes and differential equations in general, as well as those physicists whose work centers on statistical mechanics and kinetic theory.
Kinetic Boltzmann Vlasov And Related Equations
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Author : Alexander Sinitsyn
language : en
Publisher: Elsevier
Release Date : 2011-06-17
Kinetic Boltzmann Vlasov And Related Equations written by Alexander Sinitsyn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-17 with Mathematics categories.
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory.This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance.
Lectures On Gas Theory
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Author : Ludwig Boltzmann
language : en
Publisher: Courier Corporation
Release Date : 2012-08-15
Lectures On Gas Theory written by Ludwig Boltzmann and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Science categories.
A masterpiece of theoretical physics, this classic contains a comprehensive exposition of the kinetic theory of gases. It combines rigorous mathematic analysis with a pragmatic treatment of physical and chemical applications.