SpringerBriefs in Mathematics

From Kinetic Models to Hydrodynamics

Some Novel Results

Authors: Colangeli, Matteo

  • 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
Show all benefits

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-6306-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-6305-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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)

Table of contents (7 chapters)

  • Introduction

    Colangeli, Matteo

    Pages 1-2

  • From the Phase Space to the Boltzmann Equation

    Colangeli, Matteo

    Pages 3-21

  • Methods of Reduced Description

    Colangeli, Matteo

    Pages 23-35

  • Hydrodynamic Spectrum of Simple Fluids

    Colangeli, Matteo

    Pages 37-47

  • Hydrodynamic Fluctuations from the Boltzmann Equation

    Colangeli, Matteo

    Pages 49-73

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-6306-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-6305-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
From Kinetic Models to Hydrodynamics
Book Subtitle
Some Novel Results
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Matteo Colangeli
eBook ISBN
978-1-4614-6306-1
DOI
10.1007/978-1-4614-6306-1
Softcover ISBN
978-1-4614-6305-4
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 96
Number of Illustrations and Tables
12 b/w illustrations, 9 illustrations in colour
Topics