锉中非均匀硬球的动力学
Dynamics of heterogeneous hard spheres in a file
摘要：
分析了N个硬球组成的准一维长L通道（\to \infty）中的正常动力学。球体是异质的：每一个都具有扩散系数D，该扩散系数D是从概率密度函数（PDF）W D^（-γ）中得出的，对于小D，其中0 \leq γ<1。初始球体的密度ρ是不均匀的，并且随着距离（从原点）l的变化而变化，ρ l^（-a），0 \leqa \leq 1。这个问题的N粒子PDF的近似推导。从这个解、标度律分析和数值模拟，我们证明了在这样的系统中，粒子的均方位移服从<r^2>~t^（1-γ）/（2c-γ），其中c=1/（1+a）.标记颗粒的PDF在位置上是高斯分布的。这些结果的推广被认为是。
英文摘要：
Normal dynamics in a quasi-one-dimensional channel of length L (\to\infty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(-γ), for small D, where 0\leqγ<1. The initial spheres' density ρ is non-uniform and scales with the distance (from the origin) l as, ρ l^(-a), 0\leqa\leq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2>~t^(1-γ)/(2c-γ), where c=1/(1+a). The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.
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