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Generalized Boltzmann physical kinetics
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ISBN: 1423708016 9781423708018 0080478018 9780080478012 1281008869 9781281008862 9786611008864 9780444515827 0444515828 Year: 2004 Publisher: Amsterdam ; Boston : Elsevier,

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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. Partic


Book
Theory of the lattice Boltzmann method : lattice Boltzmann models for non-ideal gases
Authors: ---
Year: 2001 Publisher: Hampton, VA : Hanover, MD : ICASE, NASA Langley Research Center ; Available from NASA Center for Aerospace Information,

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Unified non-local theory of transport processes : generalized Boltzmann physical kinetics
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ISBN: 0444634878 0444634789 9780444634870 9780444634788 9780444634788 Year: 2015 Publisher: Amsterdam, Netherlands ; Oxford, England ; Waltham, Massachusetts : Elsevier,

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Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann equation, which is the basis of the classical kinetic theory, is incorrect in the definite sense. Additional terms need to be added leading to a dramatic change in transport theory. The result is a strict theory of turbulence and the possibility to calculate turbulent flows from the first principles of physics. Fully revised and expanded edition, providing applications in quantum non-local hydrodynamics, quantum sol

Generalized Boltzmann physical kinetics
Author:
ISBN: 1281008869 9786611008864 0080478018 0444515828 1423708016 9781423708018 9780080478012 9781281008862 9780444515827 Year: 2004 Publisher: Amsterdam Boston Elsevier

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Abstract

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. Partic

Lecture notes on the mathematical theory of generalized Boltzmann models
Authors: ---
ISBN: 9812813330 9789812813336 9810240783 9789810240783 Year: 2000 Publisher: River Edge, NJ World Scientific

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This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions. Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

Lattice Boltzmann modeling : an introduction for geoscientists and engineers.
Authors: ---
ISBN: 9783540279822 9783540279815 3540279814 9786610337989 1280337982 3540279822 Year: 2006 Publisher: Berlin Springer

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Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful "quick start" guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet. .

Entropy methods for the Boltzmann equation : lectures from a special semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
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ISBN: 3540737049 3540737057 Year: 2008 Publisher: Berlin ; Heidelberg ; New York : Springer,

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Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.


Book
Hydrodynamic limits of the Boltzmann equation
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ISBN: 3540928464 3540928472 Year: 2009 Publisher: Berlin : Springer,

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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.


Book
Principles of thermodynamics and statistical mechanics
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ISBN: 0471911720 9780471911722 Year: 1987 Publisher: Chichester Wiley

Lattice-gas cellular automata and lattice Boltzmann models : an introduction.
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ISBN: 3540669736 3540465863 Year: 2000 Volume: 1725 Publisher: New York Springer

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Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

Keywords

Classical mechanics. Field theory --- Thermodynamics --- Cellular automata --- Lattice gas --- Maxwell-Boltzmann distribution law --- Algebra --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical models --- Automates cellulaires --- Boltzmann distribution law --- Cellulaire automaten --- Maxwell distribution --- Maxwell-Boltzmann density function --- Cellular automata. --- Maxwell-Boltzmann distribution law. --- 519.6 --- 681.3*J2 --- 681.3*J2 Physical sciences and engineering (Computer applications) --- Physical sciences and engineering (Computer applications) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Distribution (Probability theory) --- Kinetic theory of gases --- Gas, Lattice --- Crystal lattices --- Computers, Iterative circuit --- Iterative circuit computers --- Structures, Tessellation (Automata) --- Tessellation structures (Automata) --- Parallel processing (Electronic computers) --- Pattern recognition systems --- Sequential machine theory --- Mathematical models. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical logic. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Numerical analysis. --- Applied mathematics. --- Engineering mathematics. --- Mechanics. --- Analysis. --- Mathematical Logic and Foundations. --- Global Analysis and Analysis on Manifolds. --- Numerical Analysis. --- Mathematical and Computational Engineering. --- Classical Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering --- Engineering analysis --- Mathematical analysis --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- 517.1 Mathematical analysis

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