中文摘要：

我们在场二维的 polydisperse 的一个动态模型有分数维的尺寸分发，磁盘在服从于无弹性的相互的碰撞的小粒的气体并且由标准白噪音开车。磁盘尺寸分发的不同类能被分数维的尺寸 d _f 。由蒙特卡罗模拟，我们主要在一样的无弹力案例中在系统的统计性质上调查了不同类的效果。一些新奇结果被发现系统的平均精力与最后完成稳定的 asymptotic 价值，和系统的一个趋势指数地腐烂，这到达一非平衡在一长进化时间以后的稳定的状态。而且，不同类在不变的统计性质上有大影响。随分数维的尺寸 d _f , 在碰撞之间的路径长度和空闲的时间的分布为有弹性的范围从期望的理论形式更显然背离并且有短距离和时间箱的人中过剩。有 d _f , 而是它独立于时间。同时，速度分发从 Gaussian 那更强烈背离，但是不表明任何明显的通用行为。

英文摘要：

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.