Synopses & Reviews
Kinetic Theory of granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics as it has been developed mainly during the past decade. The book is aimed at readers from the advanced undergraduate level onwards and leads up to the present state of
research. The text is self-contained, in the sense that no mathematical or physical knowledge is required that goes beyond standard undergraduate physics courses. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. 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 formulation are studies. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel
mathematical technique for the derivation of the kinetic properties which allows for the application of computer algebra. The book is accompanied by a web page where the molecular dynamics program as well as the computer-algebra programs are provided.
Review
"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."--Physics Today
Review
"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."--Physics Today
Review
"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."--James W. Duffy, Physics Today
"This appears to be the first introductory text in the rapidly growing field of the kinetic theory of granular materials, a subject with wide ranging applications in physics, astronomy, engineering, and chemistry....No mathematical knowledge is required beyond standard undergraduate level and the book is well adapted for use in graduate courses on kinetic theory, since it includes a broad range of exercises throughout the book."-- Journal of Statistical Physics
Synopsis
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.
Synopsis
Unlike molecular gases like air, the particles of granular gases (like a cloud of dust) lose at collisions part of their kinetic energy. This is the origin of many exciting physical properties. While the theory of molecular gases belongs to any undergraduate physics course, Kinetic Theory of Granular Gases provides a self-contained introduction to the subject of granular gases at the advanced undergraduate and beginning graduate level. It is mainly addressed to students and researchers of physics, astronomy (planetary sciences and cosmic dust) as well as mechanical and chemical engineering.
Table of Contents
1. Introduction
I Mechanics of Particle Collisions
2. Particle collisions
3. Coefficients of restitution
4. Applications to few-particle systems
II Granular Gases - Velocity Distribution
5. Cooling granular gas - Haff's law
6. Boltzmann equation
7. Sonine polynomials expansion of the velocity distribution function
8. Velocity distribution and temperature of a granular gas for the case epsilon = const.
9. Velocity distribution function and temperature for viscoelastic particles
10. High-energy tail of the velocity distribution function
11. Two-dimensional granular gases
III Single-particle transport. Self-Diffusion and Brownian Motion
12. Diffusion and self-diffusion
13. Pseudo-Liouville and binary collision operators in dissipative gas dynamics
14. Coefficient of self-diffusion
15. Brownian motion in granular gases
16. Two-dimensional granular gases
IV Transport Processes and Kinetic Coefficients
17. Granular gas as a continuum: hydrodynamic equations
18. Chapman-Enskog approach for non-uniform granular gases
19. Kinetic coefficients and velocity distribution for gases of elastic particles
20. Kinetic coefficients for granular gases of simplified particles
21. Kinetic coefficients for granular gases of viscoelastic particles
22. Chapman-Enskog method for self-diffusion coefficients
23. Two-dimensional granular gases
V Structure Formation
24. Instability of the homogeneous cooling state
25. Structure formation for epsilon = const.
26. Structure formation in granular gases of viscoelastic particles
27. Nonlinear mechanisms for structure formation
28. Two-dimensional granular gases
A. Functions of the collision integral
B. Molecular dynamics of granular gases
C. Solutions to the problems