Breakdown of the Sonine expansion for the velocity distribution of Granular Gases

Details Breakdown of the Sonine expansion for the velocity distribution of Granular Gases Breakdown of the Sonine expansion for the velocity distribution of Granular Gases

2005-11-19

arxiv.org/abs/cond-mat/0511483v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 3 figures

Scientific paper

10.1209/epl/i2005-10555-6

The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a_3. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a_2. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a_4, a_5 and a_6 are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0< epsilon < 0.6. We conclude that this behavior of the Sonine coefficients manifests the break down of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.

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