Velocity distributions and correlations in homogeneously heated granular media - art. no. 031303

We compare the steady state velocity distributions from our three-dimension al inelastic hard sphere molecular dynamics simulation for homogeneously he ated granular media, with the predictions of a mean field-type Enskog-Boltz mann 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 a ll values of density and inelasticity, the quantitative disagreement approa ches similar to 40% at high inelasticity or density, By contrast the predic tions 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 q uantitatively 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 algebrai c decay over a decade in the unit of the diameter of the particle, proporti onal to r(-(1+alpha)), where 0.2<<alpha><0.3. The existence of these correl ations implies the failure of the molecular chaos assumption and the mean f ield approximation, which is responsible for the quantitative disagreement of the inelastic hard sphere kinetic theory.