We present a dynamical model of two-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 inhomog...We present a dynamical model of two-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 df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties 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 df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10675048the Natural Science Foundation of Education Department of Hubei Province of China under Grant Nos.D200628002 and kz0627
文摘We present a dynamical model of two-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 df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties 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 df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.
