Breakdown of the Sonine expansion for the velocity distribution of granular gasesN. V. Brilliantov1, 2 and T. Pöschel3
1 Institute of Physics, University of Potsdam - 14469 Potsdam, Germany
2 Department of Physics, Moscow State University - 119899 Moscow, Russia
3 Charité - Augustenburger Platz 1, 10439 Berlin, Germany
received 19 November 2005; accepted in final form 3 March 2006
published online 5 April 2006
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 a3. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a2. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a4, a5 and a6 are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for . We conclude that this behavior of the Sonine coefficients manifests the breakdown of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.
51.10.+y - Kinetic and transport theory of gases.
45.70.-n - Granular systems.
05.20.-y - Classical statistical mechanics.
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