Randomly driven granular fluids: Collisional statistics and short scale structure

We present a molecular-dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short-distance correlations in the nonequilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e., factorization of the two-particle distribution function, $f^{\mathrm{}\left(2\right)\mathrm{}}{(x}_1{,x}_2\left)\simeq \chi f^{\mathrm{}\left(1\right)\mathrm{}}{(x}_1{)f}^{\mathrm{}\left(1\right)\mathrm{}}{(x}_2\right)$ in a product of single-particle ones, where $x_i=\{{\mathbf{r}}_i,{\mathbf{v}}_i\}$ with $i=1,2\mathrm{}$ and $\chi$ represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space $\{x_1{,x}_2\},$ where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle- and noise-induced recollisions magnifies the departure from mean-field behavior. The implications of this breakdown in several physical quantities are explored.