Velocity Distributions in Homogeneously Cooling and Heated Granular Fluids

Details Velocity Distributions in Homogeneously Cooling and Heated Granular Fluids Velocity Distributions in Homogeneously Cooling and Heated Granular Fluids

1998-03-03

arxiv.org/abs/cond-mat/9803042v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, Latex, 2 figures

Scientific paper

We study the single particle velocity distribution for a granular fluid of inelastic hard spheres or disks, using the Enskog-Boltzmann equation, both for the homogeneous cooling of a freely evolving system and for the stationary state of a uniformly heated system, and explicitly calculate the fourth cumulant of the distribution. For the undriven case, our result agrees well with computer simulations of Brey et al. \cite{brey}. Corrections due to non-Gaussian behavior on cooling rate and stationary temperature are found to be small at all inelasticities. The velocity distribution in the uniformly heated steady state exhibits a high energy tail $\sim \exp(-A c^{3/2})$, where $c$ is the velocity scaled by the thermal velocity and $A\sim 1/\sqrt{\eps}$ with $\eps$ the inelasticity.

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