Velocity distributions and correlations in homogeneously heated granular media

We compare the steady state velocity distributions from our three-dimensional inelastic hard sphere molecular dynamics simulation for homogeneously heated granular media, with the predictions of a mean field-type Enskog-Boltzmann equation for inelastic hard spheres [T. P. C. van Noije and M. H. Ernst, Granular Matter 1, 57 (1998)]. Although we find qualitative agreement for all values of density and inelasticity, the quantitative disagreement approaches approximately 40% at high inelasticity or density. By contrast the predictions of the pseudo-Maxwell molecule model [J. A. Carrillo, C. Cercignani, and I. M. Gamba, Phys. Rev. E, 62, 7700 (2000)] are both qualitatively and quantitatively different from those of our simulation. We also measure short-range and long-range velocity correlations exhibiting nonzero correlations at contact before the collision, and being consistent with a slow algebraic decay over a decade in the unit of the diameter of the particle, proportional to r(-(1+alpha)), where 0.2