From Kinetic Models to Hydrodynamics, 1st Edition

  • Published By:
  • ISBN-10: 1461463068
  • ISBN-13: 9781461463061
  • DDC: 532.500151
  • Grade Level Range: College Freshman - College Senior
  • 96 Pages | eBook
  • Original Copyright 2013 | Published/Released May 2014
  • This publication's content originally published in print form: 2013

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​​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.​

Table of Contents

Front Cover.
Editorial Board.
Title Page.
Copyright Page.
1: Introduction.
2: From the Phase Space to the Boltzmann Equation.
3: Methods of Reduced Description.
4: Hydrodynamic Spectrum of Simple Fluids.
5: Hydrodynamic Fluctuations from the Boltzmann Equation.
6: Grad's 13-Moments System.
7: Conclusions.