Monte Carlo Simulations of Dynamic Behavior in Polydisperse Granular Gases System

Monte Carlo simulations are employed to investigate the dynamic behavior in a polydisperse granular media with fractal size distribution. The dispersion of size distribution can be described by a fractal dimension d_f, and the smooth hard disks are engaged in a two-dimensional horizontal rectangular box, colliding inelastically with each other and driven by Gaussian white noise. We have mainly studied the effect of the dispersion on the steady-state dynamic properties of the system in the same inelasticity case. With the increase of d_f, the distributions of path lengths between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances. The collision rate increases with d_f, but it is independent of time. The tails of the velocity distribution functions rise significantly above a Gaussian as d_f increases, but the non-Gaussian velocity distribution functions do not demonstrate any apparent universal form. Moreover, the spatial velocity correlations are apparently stronger with the increase of d_f. The d_f-dependent nature of the dynamic behavior is induced by the more dissipation due to the more dispersion of the disk size distribution in the inelastic collisions as d_f is increased.