Kinetic Theory of Granular Gases by Nikolai V. Brilliantov

Kinetic Theory of Granular Gases

byNikolai V. Brilliantov, Thorsten Poschel

Paperback | December 11, 2010

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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 ofresearch. 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 derivationof 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 secondappendix 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 fora 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.

About The Author

Nikolai V. Brilliantov and Thorsten Poschel are both Professors at the Institute for Biochemistry at Humboldt University, Germany.

Details & Specs

Title:Kinetic Theory of Granular GasesFormat:PaperbackDimensions:344 pages, 9.21 × 6.14 × 0.03 inPublished:December 11, 2010Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199588139

ISBN - 13:9780199588138

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Table of Contents

1. IntroductionI: Mechanics of Particle Collisions2. Particle collisions3. Coefficients of restitution4. Applications to few-particle systemsII: Granular Gases - Velocity Distribution Function5. Cooling granular gas - Haff's law6. Boltzmann equation7. Sonine polynomials expansion of the velocity distribution function8. Velocity distribution and temperature of a granular gas for the case epsilon = const.9. Velocity distribution function and temperature for viscoelastic particles10. High-energy tail of the velocity distribution function11. Two-dimensional granular gasesIII: Single-particle Transport, Self-Diffusion and Brownian Motion12. Diffusion and self-diffusion13. Pseudo-Liouville and binary collision operators in dissipative gas dynamics14. Coefficient of self-diffusion15. Brownian motion in granular gases16. Two-dimensional granular gasesIV: Transport Processes and Kinetic Coefficients17. Granular gas as a continuum: hydrodynamic equations18. Chapman-Enskog approach for non-uniform granular gases19. Kinetic coefficients and velocity distribution for gases of elastic particles20. Kinetic coefficients for granular gases of simplified particles21. Kinetic coefficients for granular gases of viscoelastic particles22. Chapman-Enskog method for self-diffusion coefficients23. Two-dimensional granular gasesV: Structure Formation24. Instability of the homogeneous cooling state25. Structure formation for epsilon = const.26. Structure formation in granular gases of viscoelastic particles27. Nonlinear mechanisms for structure formation28. Two-dimensional granular gasesA. Functions of the collision integralB. Molecular dynamics of granular gasesC. Solutions to the problems

Editorial Reviews

"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 andthe 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, March 2005