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Subject: Physics  Book Title: Kinetic Theory of Granular Gases
Kinetic Theory of Granular Gases Kinetic Theory of Granular Gases
Brilliantov, Nikolai V., Institute for Biochemistry, Humboldt University, Germany
Pöschel, Thorsten, Institute for Biochemistry, Humboldt University, Germany
Print publication date: 2004
Published to Oxford Scholarship Online: January 2010
Print ISBN-13: 978-0-19-853038-1
doi:10.1093/acprof:oso/9780198530381.001.0001


 
Abstract: 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.

Keywords: dissipative gas dynamics, pairwise particle collisions, coefficient of restitution, many-particle system, Boltzmann equation, velocity distribution function, self-diffusion, Brownian motion, hydrodynamical methods, molecular dynamics
Table of Contents
Preface
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1. Introduction
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2. Particle Collisions
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3. Coefficient Of Restitution
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4. Application to Few-Particle Systems
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5. Cooling Granular Gas — Haff's Law
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6. Boltzmann Equation
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7. Sonine Polynomials Expansion of The Velocity Distribution Function
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8. Velocity Distribution And Temperature Of A Granular Gas For The Case U+03B5 =Const.
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9. Velocity Distribution Function and Temperature for Viscoelastic Particles
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10. High-Energy Tail of the Velocity Distribution Function
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11. Two-Dimensional Granular Gases
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12. Diffusion and Self-Diffusion
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13. Pseudo-Liouville and Binary Collision Operators in Dissipative Gas Dynamics
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14. Coefficient of Self-Diffusion
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15. Brownian Motion in Granular Gases
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16. Two-Dimensional Granular Gases
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17. Granular Gas as A Continuum: Hydrodynamic Equations
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18. Chapman-Enskog Approach for Non-Uniform Granular Gases
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19. Kinetic Coefficients and Velocity Distribution for Gases of Elastic Particles
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20. Kinetic Coefficients For Granular Gases Of Simplified Particles (U+03B5 = CONST)
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21. Kinetic Coefficients for Granular Gases of Viscoelastic Particles
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22. Chapman-Enskog Method for the Self-Diffusion Coefficient
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23. Two-Dimensional Granular Gases
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24. Instability of The Homogeneous Cooling State
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25. Structure Formation for U+03B5 =Const.
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26. Structure Formation in Granular Gases of Viscoelastic Particles
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27. Nonlinear Mechanisms of Structure Formation
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28. Two-Dimensional Granular Gases
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Appendix
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Bibliography
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Index
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doi:10.1093/acprof:oso/9780198530381.001.0001



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I Mechanics of Particle Collisions
II Granular Gases – Velocity Distribution Function
III Single-Particle Transport – Self-Diffusion and Brownian Motion
IV Transport Processes and Kinetic Coefficients
V Structure Formation