Author : Stewart Harris
Publisher : Courier Corporation
Page : 242 pages
File Size : 13,56 MB
Release : 2012-12-27
Category : Science
ISBN : 0486143821
This introductory graduate-level text emphasizes physical aspects of the theory of Boltzmann's equation in a detailed presentation that doubles as a practical resource for professionals. 1971 edition.
Author : Gilberto M. Kremer
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 16,22 MB
Release : 2010-08-18
Category : Technology & Engineering
ISBN : 3642116965
This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.
Author : E.G.D. Cohen
Publisher : Springer Science & Business Media
Page : 647 pages
File Size : 45,44 MB
Release : 2012-12-06
Category : Science
ISBN : 3709183367
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.
Author : Carlo Cercignani
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 25,64 MB
Release : 2012-12-06
Category : Science
ISBN : 1461210399
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.
Author : Boris V. Alexeev
Publisher : Elsevier
Page : 377 pages
File Size : 47,80 MB
Release : 2004-05-25
Category : Mathematics
ISBN : 0080478018
The most important result obtained by Prof. B. Alexeev and reflected in the book is connected with new theory of transport processes in gases, plasma and liquids. It was shown by Prof. B. Alexeev that well-known Boltzmann equation, which is the basement of the classical kinetic theory, is wrong in the definite sense. Namely in the Boltzmann equation should be introduced the additional terms which generally speaking are of the same order of value as classical ones. It leads to dramatic changing in transport theory. The coincidence of experimental and theoretical data became much better. Particularly it leads to the strict theory of turbulence and possibility to calculate the turbulent flows from the first principles of physics.·Boltzmann equation (BE) is valid only for particles, which can be considered as material points, generalized Boltzmann equation (GBE) removes this restriction.·GBE contains additional terms in comparison with BE, which cannot be omitted·GBE leads to strict theory of turbulence·GBE gives all micro-scale turbulent fluctuations in tabulated closed analytical form for all flows ·GBE leads to generalization of electro-dynamic Maxwell equations·GBE gives new generalized hydrodynamic equations (GHE) more effective than classic Navier-Stokes equations·GBE can be applied for description of flows for intermediate diapason of Knudsen numbers·Asymptotical solutions of GBE remove contradictions in the theory of Landau damping in plasma
Author : Sauro Succi
Publisher : Oxford University Press
Page : 784 pages
File Size : 27,11 MB
Release : 2018-04-13
Category : Technology & Engineering
ISBN : 0192538853
Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task. The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines. Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.
Author : Laure Saint-Raymond
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 32,66 MB
Release : 2009-03-26
Category : Mathematics
ISBN : 3540928464
"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.
Author : Alexander Sinitsyn
Publisher : Elsevier
Page : 321 pages
File Size : 40,9 MB
Release : 2011-06-17
Category : Mathematics
ISBN : 0123877806
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
Author : Ludwig Boltzmann
Publisher : Univ of California Press
Page : 500 pages
File Size : 10,34 MB
Release : 2023-11-15
Category : Science
ISBN : 0520327470
This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
Author : S. Succi
Publisher : Oxford University Press
Page : 308 pages
File Size : 34,36 MB
Release : 2001-06-28
Category : Mathematics
ISBN : 9780198503989
Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.
