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From Kinetic Models to Hydrodynamics

Some Novel Results

  • Book
  • © 2013

Overview

Authors:
  1. Matteo Colangeli

    1. , Department of Mathematics, Politecnico di Torino, Torino, Italy

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  • Bridges 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
  • Addresses a functional equation for the nonequilibrium single-particle distribution function
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • Matteo Colangeli
    Pages 1-2

  3. From the Phase Space to the Boltzmann Equation

    • Matteo Colangeli
    Pages 3-21

  4. Methods of Reduced Description

    • Matteo Colangeli
    Pages 23-35

  5. Hydrodynamic Spectrum of Simple Fluids

    • Matteo Colangeli
    Pages 37-47

  6. Hydrodynamic Fluctuations from the Boltzmann Equation

    • Matteo Colangeli
    Pages 49-73

  7. Grad’s 13-Moments System

    • Matteo Colangeli
    Pages 75-94

  8. Conclusions

    • Matteo Colangeli
    Pages 95-96
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Keywords

About this book

​​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.​

Reviews

From the reviews:

“It gives an excellent introduction to this area of research to graduate students of applied mathematics, nonspecialists and the mathematical community in general and draws attention to some very interesting questions.” (Mark Thompson, Mathematical Reviews, November, 2013)

Authors and Affiliations

  • , Department of Mathematics, Politecnico di Torino, Torino, Italy

    Matteo Colangeli

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