Kinetic Theory of Granular Gases
Series: Oxford Graduate Texts;
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Product details:
- Publisher OUP Oxford
- Date of Publication 1 July 2004
- ISBN 9780198530381
- Binding Hardback
- No. of pages344 pages
- Size 242x162x23 mm
- Weight 718 g
- Language English
- Illustrations 6 halftones, numerous line drawings 0
Categories
Short description:
This is the first introductory text in the rapidly growing field of granular gases. In contrast to molecular gases (for example, air), the particles of granular gases, such as a cloud of dust, lose part of their kinetic energy when they collide, giving rise to many exciting physical properties. The book provides a self-contained introduction to the theory of granular gases for advanced undergraduates and beginning graduates.
MoreLong description:
"Kinetic Theory of Granular Gases" provides an introduction to the rapidly developing theory of dissipative gas dynamics - a theory which has mainly evolved over the last decade. The book is aimed at readers from the advanced undergraduate level upwards and leads on to the present state of research. Throughout, special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity-dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formation are studied. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for derivation of kinetic properties, which allows for the application of computer algebra. The text is self-contained, requiring no mathematical or physical knowledge beyond that of standard physics undergraduate level. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. The molecular dynamics and computer-algebra programs can be downloaded from a companion web page.
Kinetic Theory of Granular Gases is an admirable contribution by two experts of this rapidly evolving field. In addition to technical details, it provides important insights that are essential for graduate students thinking about the similarities and differences between normal and granular gases. The book fills a significant gap, and I expect it will be adopted for graduate courses in both physics and engineering programs.
Table of Contents:
Introduction
I Mechanics of Particle Collisions
Particle collisions
Coefficients of restitution
Applications to few-particle systems
II Granular Gases - Velocity Distribution Function
Cooling granular gas - Haff's law
Boltzmann equation
Sonine polynomials expansion of the velocity distribution function
Velocity distribution and temperature of a granular gas for the case epsilon = const.
Velocity distribution function and temperature for viscoelastic particles
High-energy tail of the velocity distribution function
Two-dimensional granular gases
III Single-particle Transport, Self-Diffusion and Brownian Motion
Diffusion and self-diffusion
Pseudo-Liouville and binary collision operators in dissipative gas dynamics
Coefficient of self-diffusion
Brownian motion in granular gases
Two-dimensional granular gases
IV Transport Processes and Kinetic Coefficients
Granular gas as a continuum: hydrodynamic equations
Chapman-Enskog approach for non-uniform granular gases
Kinetic coefficients and velocity distribution for gases of elastic particles
Kinetic coefficients for granular gases of simplified particles
Kinetic coefficients for granular gases of viscoelastic particles
Chapman-Enskog method for self-diffusion coefficients
Two-dimensional granular gases
V Structure Formation
Instability of the homogeneous cooling state
Structure formation for epsilon = const.
Structure formation in granular gases of viscoelastic particles
Nonlinear mechanisms for structure formation
Two-dimensional granular gases
Functions of the collision integral
Molecular dynamics of granular gases
Solutions to the problems
