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Kinetic Theory of Granular Gases$
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Nikolai V. Brilliantov and Thorsten Pöschel

Print publication date: 2004

Print ISBN-13: 9780198530381

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198530381.001.0001

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Two-Dimensional Granular Gases

Two-Dimensional Granular Gases

Chapter:
(p.162) 16 Two-Dimensional Granular Gases
Source:
Kinetic Theory of Granular Gases
Author(s):

Nikolai V. Brilliantov

Thorsten Pöschel

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198530381.003.0016

It has been shown for molecular fluids that the velocity-time correlation function in ddimensions exhibits a power-law dependence for t >> 1. This function reveals a long time tail compared with an exponentially decaying function. According to the fluctuation-dissipation theorem, the kinetic coefficients are expressed by time integrals of the corresponding correlation functions. For d > 2, these integrals converge; for two-dimensional systems the convergence of these integrals is problematic and hence, the existence of the kinetic coefficients is questionable. For force-free granular fluids, one can expect convergence of these integrals, since there exists an additional decay of correlation functions due to the decay of temperature. This problem has not been addressed for granular gases. This chapter presents the results for d-dimensionless gases.

Keywords:   granular fluids, velocity-time correlation function, integrals

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