Steady states of a Boltzmann equation for driven granular media

We study a three-dimensional model for driven granular media in which parti cles interact inelastically while they follow Brownian dynamics in between collisions. A steady Boltzmann-type kinetic equation associated with a pseu do-Maxwellian model is analyzed. Homogeneous steady states are found by a s mall inelasticity expansion. These states are given by a Maxwellian distrib ution corrected by the second Sonine polynomial up to third order in the ex pansion. The resulting correction is a quartic polynomial in velocity space . This result agrees qualitatively with the molecular dynamics simulation i n C. Bizon, M. D. Shattuck, J. B. Swift, and H. L. Swinney, Phys. Rev. E 60 , 4340 (1999).