Velocity distributions in homogeneous granular fluids: The free and the heated case

Non-Gaussian properties (cumulants, high energy tails) of the single particle velocity distribution for homogeneous granular fluids of inelastic hard spheres or disks are studied, based on the Enskog-Boltzmann equation for the unforced and heated case. The latter is in a steady state. The non-Gaussian corrections have small effects on the cooling rate, and on the stationary temperature in the heated case, at all inelasticities. The velocity distribution in the heated steady state exhibits a high energy tail ∼ exp(-Ac3/2), where c is the velocity scaled by the thermal velocity and A ∼ 1/√∈ with ∈ the inelasticity. The results are compared with molecular dynamics simulations, as well as direct Monte Carlo simulations of the Boltzmann equation.