Nakanishi Hiizu
Department of Physics, Kyushu University 33, Fukuoka 812-8581, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 1):010301. doi: 10.1103/PhysRevE.67.010301. Epub 2003 Jan 15.
The velocity distribution of inelastic granular gas is examined numerically on a two-dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after several inelastic collisions per particle, the system falls in the state that the Boltzmann's equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time independent, but gradually returns to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state (Haff state), where the energy decays exponentially as a function of collision number, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction of the Boltzmann's equation fails.
利用分子动力学模拟，在二维硬盘系统中对近弹性区域内非弹性颗粒气体的速度分布进行了数值研究。该系统最初处于具有麦克斯韦 - 玻尔兹曼分布的平衡态，然后每个粒子经过几次非弹性碰撞后，系统进入玻尔兹曼方程所预测的具有稳定速度分布形式的状态。然而，结果表明，由于速度相关性，分布函数的形式并非与时间无关，而是在初始瞬态之后立即逐渐恢复到麦克斯韦分布，直到聚集不稳定性出现。这表明，即使在能量随碰撞数呈指数衰减的均匀冷却状态（哈夫状态）下，非弹性系统中的速度相关性也使分子混沌假设失效，玻尔兹曼方程的预测也失败了。
