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On Hydrodynamic Equations And Their Relation To Kinetic Theory And Statistical Mechanics
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Book Synopsis On Hydrodynamic Equations and Their Relation to Kinetic Theory and Statistical Mechanics by : Jianfei Xue (dd)
Download or read book On Hydrodynamic Equations and Their Relation to Kinetic Theory and Statistical Mechanics written by Jianfei Xue (dd) and published by . This book was released on 2017 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish conditions on the Hamiltonian evolution of interacting molecules that imply hydrodynamic equations at the limit of infinitely many molecules and show that these conditions are satisfied whenever the solutions of the classical equations for N interacting molecules obey uniform in N bounds. We show that this holds when the initial conditions are bounded and the molecule interaction is weak enough at the initial time. We then obtain hydrodynamic equations that coincide with Maxwell's. We then construct explicit examples of spontaneous energy generation and nonuniqueness for the standard compressible Euler system, with and without pressure, agagin by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. The examples come from rescaling of well-posed, deterministic systems of molecules that either collide elastically or interact via singular pair potentials. We also obtain Percus macroscopic equation as the limit of a sequence of single systems of N hard rods with the number of hard rods going to infinity. Finally, we establish the strict convexity of the pressure as a thermodynamic limit for continuous systems. As a result we show the existence of a local bijection between macroscopic density, velocity, and energy on one hand and thermodynamic parameters on the other, for continuous systems.
Book Synopsis From Kinetic Models to Hydrodynamics by : Matteo Colangeli
Download or read book From Kinetic Models to Hydrodynamics written by Matteo Colangeli and published by Springer Science & Business Media. This book was released on 2013-03-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Kinetic Theory of Gases and Plasmas by : PPJM Schram
Download or read book Kinetic Theory of Gases and Plasmas written by PPJM Schram and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kinetic theory is the link between the non--equilibrium statistical mechanics of many particle systems and macroscopic or phenomenological physics. Therefore much attention is paid in this book both to the derivation of kinetic equations with their limitations and generalizations on the one hand, and to the use of kinetic theory for the description of physical phenomena and the calculation of transport coefficients on the other hand. The book is meant for researchers in the field, graduate students and advanced undergraduate students. At the end of each chapter a section of exercises is added not only for the purpose of providing the reader with the opportunity to test his understanding of the theory and his ability to apply it, but also to complete the chapter with relevant additions and examples that otherwise would have overburdened the main text of the preceding sections. The author is indebted to the physicists who taught him Statistical Mechanics, Kinetic Theory, Plasma Physics and Fluid Mechanics. I gratefully acknowledge the fact that much of the inspiration without which this book would not have been possible, originated from what I learned from several outstanding teachers. In particular I want to mention the late Prof. dr. H. C. Brinkman, who directed my first steps in the field of theoretical plasma physics, my thesis advisor Prof. dr. N. G. Van Kampen and Prof. dr. A. N. Kaufman, whose course on Non-Equilibrium Statistical Mechanics in Berkeley I remember with delight.
Book Synopsis The Kinetic Theory of Gases by : Chʻêng-shu Wang Chang
Download or read book The Kinetic Theory of Gases written by Chʻêng-shu Wang Chang and published by North-Holland. This book was released on 1970 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics by : Byung Chan Eu
Download or read book Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics written by Byung Chan Eu and published by Springer. This book was released on 2016-08-02 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.
Book Synopsis Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics by : Byung Chan Eu
Download or read book Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics written by Byung Chan Eu and published by Springer. This book was released on 2016-07-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on nonrelativistic contexts, it provides a comprehensive picture of the relativistic covariant kinetic theory of gases and relativistic hydrodynamics of gases.Relativistic theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids). They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. The irreversible covariant Boltzmann as well as the covariant form of the Boltzmann-Nordheim-Uehling-Uhlenbeck equation is used for deriving theories of irreversible transport equations and generalized hydrodynamic equations for either classical gases or quantum gases. They all conform rigorously to the tenet. All macroscopic observables described by the so-formulated theories therefore are likewise expected to strictly obey the tenet.
Book Synopsis Classical Kinetic Theory of Fluids by : Pierre M. V. Résibois
Download or read book Classical Kinetic Theory of Fluids written by Pierre M. V. Résibois and published by John Wiley & Sons. This book was released on 1977 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.
Book Synopsis Kinetic Theory and Fluid Dynamics by : Yoshio Sone
Download or read book Kinetic Theory and Fluid Dynamics written by Yoshio Sone and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to provide a comprehensive description of the rela tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented. In addition, various interesting physical phenomena derived from the asymptotic theory are explained. The background of the asymptotic studies is explained in Chapter 1, accord ing to which the fluid-dynamic-type equations that describe the behavior of a gas in the continuum limit are to be studied carefully. Their detailed studies depending on physical situations are treated in the following chapters. What is striking is that the classical gas dynamic system is incomplete to describe the behavior of a gas in the continuum limit (or in the limit that the mean free path of the gas molecules vanishes). Thanks to the asymptotic theory, problems for a slightly rarefied gas can be treated with the same ease as the corresponding classical fluid-dynamic problems. In a rarefied gas, a temperature field is di rectly related to a gas flow, and there are various interesting phenomena which cannot be found in a gas in the continuum limit.
Book Synopsis The Statistical Basis of Hydrodynamics and Kinetic Theory by : Lawrence William Davis
Download or read book The Statistical Basis of Hydrodynamics and Kinetic Theory written by Lawrence William Davis and published by . This book was released on 1960 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Basis of Hydrodynamics and Kinetic Theory by : Stanford University. Microwave Laboratory
Download or read book Statistical Basis of Hydrodynamics and Kinetic Theory written by Stanford University. Microwave Laboratory and published by . This book was released on 1960 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A General Kinetic Theory of Liquids by : Max Born
Download or read book A General Kinetic Theory of Liquids written by Max Born and published by CUP Archive. This book was released on with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Kinetic Equations by : Richard L. Liboff
Download or read book Kinetic Equations written by Richard L. Liboff and published by Gordon & Breach Publishing Group. This book was released on 1971 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented at a symposium held at Cornell University, June, 1969.
Book Synopsis Hydrodynamic Limits of the Boltzmann Equation by : Laure Saint-Raymond
Download or read book Hydrodynamic Limits of the Boltzmann Equation written by Laure Saint-Raymond and published by Springer. This book was released on 2009-04-20 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Synopsis Kinetic Boltzmann, Vlasov and Related Equations by : Alexander Sinitsyn
Download or read book Kinetic Boltzmann, Vlasov and Related Equations written by Alexander Sinitsyn and published by Elsevier. This book was released on 2011-06-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Introduction to the Theory of Kinetic Equations by : Richard L. Liboff
Download or read book Introduction to the Theory of Kinetic Equations written by Richard L. Liboff and published by . This book was released on 1969 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Kinetic Theory written by George Kyzas and published by BoD – Books on Demand. This book was released on 2018-02-14 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world is governed by motions. The term kinetics partially originated from the Greek word "kinisis," which means motion. How important is motion in our life is easily understood. But, how the kinetic theories have been developed during years? Which are the new kinetic theories and updates in recent years? This question and many others can be answered with this book. Some important areas discussed in this book are the kinetic theory of gases, kinetic theory of liquids and vapors, thermodynamic aspects, transportation phenomena, adsorption-kinetic theories, linear and nonlinear kinetic equations, quantum kinetic theory, kinetic theory of nucleation, plasma kinetic theory, and relativistic kinetic theory.
Book Synopsis Molecular Hydrodynamics by : Jean Pierre Boon
Download or read book Molecular Hydrodynamics written by Jean Pierre Boon and published by Courier Corporation. This book was released on 1991-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level introduction to the theory and applications of time correlation functions and the molecular theory of fluid dynamics. "Quite well organized . . . the literature coverage is impressive." — Physics Today. 110 illustrations.
