The Boltzmann Equation And Its Applications
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The Boltzmann Equation And Its Applications
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Author : Carlo Cercignani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Boltzmann Equation And Its Applications written by Carlo Cercignani 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.
Statistical mechanics may be naturally divided into two branches, one dealing with equilibrium systems, the other with nonequilibrium systems. The equilibrium properties of macroscopic systems are defined in principle by suitable averages in well-defined Gibbs's ensembles. This provides a frame work for both qualitative understanding and quantitative approximations to equilibrium behaviour. Nonequilibrium phenomena are much less understood at the present time. A notable exception is offered by the case of dilute gases. Here a basic equation was established by Ludwig Boltzmann in 1872. The Boltzmann equation still forms the basis for the kinetic theory of gases and has proved fruitful not only for a study of the classical gases Boltzmann had in mind but also, properly generalized, for studying electron transport in solids and plasmas, neutron transport in nuclear reactors, phonon transport in superfluids, and radiative transfer in planetary and stellar atmospheres. Research in both the new fields and the old one has undergone a considerable advance in the last thirty years.
Theory And Application Of The Boltzmann Equation
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Author : Carlo Cercignani
language : en
Publisher:
Release Date : 1975
Theory And Application Of The Boltzmann Equation written by Carlo Cercignani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Science categories.
Appendix after each chapter
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.
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.
Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows
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Author : V.V. Aristov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Direct Methods For Solving The Boltzmann Equation And Study Of Nonequilibrium Flows written by V.V. Aristov 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.
This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.
Lattice Boltzmann Method And Its Application In Engineering
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Author : Zhaoli Guo
language : en
Publisher: World Scientific
Release Date : 2013-03-25
Lattice Boltzmann Method And Its Application In Engineering written by Zhaoli Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Technology & Engineering categories.
Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh.This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.With these coverage LBM, the book intended to promote its applications, instead of the traditional computational fluid dynamic method.
Fluid Dynamic Applications Of The Discrete Boltzmann Equation
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Author : Roberto Monaco
language : en
Publisher: World Scientific
Release Date : 1991
Fluid Dynamic Applications Of The Discrete Boltzmann Equation written by Roberto Monaco and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book presents applications to several fluid dynamics problems in both the bounded and unbounded domains in the framework of the discrete velocity models of kinetic theory. The proposition of new models for dense gases, gases with multi-components, and gases with chemical reactions are also included. This is an up-to-date book on the applications of the discrete Boltzmann equation.
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. Reviews the whole field from the beginning to today Includes practical applications Provides classical and modern (semi-analytical) solutions
An Introduction To The Theory Of The Boltzmann Equation
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Author : Stewart Harris
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
An Introduction To The Theory Of The Boltzmann Equation written by Stewart Harris and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Science categories.
This introductory graduate-level course for students of physics and engineering features detailed presentations of Boltzmann's equation, including applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes physical aspects of the theory and offers a practical resource for researchers and other professionals. 1971 edition.
Lecture Notes On The Discretization Of The Boltzmann Equation
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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 2003
Lecture Notes On The Discretization 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 2003 with Science categories.
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.