Collision Statistics of Driven Polydisperse Granular Gases

We present a dynamical model oftwo-dimensional polydisperse granular gases with fractal size distribution,in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomogeneity of the disk size distribution can be measured by a fractal dimension d_f. By Monte Carlo simulations, we havemainly investigated the effect of the inhomogeneity on the statisticalproperties of the system in the same inelasticity case. Some novel results are found that the average energy of the system decays exponentially with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state after a long evolution time. Furthermore, the inhomogeneity has great influence on the steady-state statistical properties. With the increase of the fractal dimension d_f,the distributions of path lengths and free times between collisions deviatemore obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with d_f, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but doesnot demonstrate any apparent universal behavior.