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The Boltzmann Equation and Its Applications

  • Carlo Cercignani

Part of the Applied Mathematical Sciences book series (AMS, volume 67)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Carlo Cercignani
    Pages 40-103
  3. Carlo Cercignani
    Pages 104-157
  4. Carlo Cercignani
    Pages 158-231
  5. Carlo Cercignani
    Pages 232-285
  6. Carlo Cercignani
    Pages 286-350
  7. Carlo Cercignani
    Pages 351-391
  8. Back Matter
    Pages 431-456

About this book

Introduction

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.

Keywords

Mathematica Monte Carlo method Potential differential equation functional analysis

Authors and affiliations

  • Carlo Cercignani
    • 1
  1. 1.Department of MathematicsPolitecnico di MilanoMilano (I)Italy

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1039-9
  • Copyright Information Springer-Verlag New York Inc. 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6995-3
  • Online ISBN 978-1-4612-1039-9
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site