A description of random walks with collision anisotropy and with a nonconstant mean free path
A description of random walks with collision anisotropy and with a nonconstant mean free path
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具有碰撞各向异性和非常量平均自由程的随机游走的描述
DOI：
10.1139/p90-128
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发表时间：
1990
影响因子：
1.2
通讯作者：
J. Jay
中科院分区：
文献类型：
--
作者：
T. Goulet;Isabelle Mattél;J. Jay
我们用解析方法和蒙特卡罗模拟技术研究了粒子随机游走的各种特性。利用解析方法，我们推导出了均方位移与(i)行走步数N， （ii）每一步的均方位移，以及（iii）碰撞各向异性系数a的表达式，该系数定义为散射角余弦值θ的平均值。这个表达式在某种意义上是通用的，它适用于任何N和a的值。然而，它仅限于在整个随机漫步过程中平均自由路径是常数的情况。模拟结果允许进一步推广到具有非恒定平均自由路径的随机行走。它们还允许研究行走后粒子的径向分布f(r)。我们发现，对于任意N和a值的粒子径向分布，必须有六个函数fi(r)的集合才能给出令人满意的描述。
We study various characteristics of a particle's random walk both analytically and with the help of Monte-Carlo simulation techniques. With the analytical approach, we derive the expressionwhich relates the mean-square displacement to (i) the number of steps N in the walk, (ii) the mean-square displacement on each of the steps, and (iii) a coefficient of collision anisotropy A defined as the average value of the cosine of the scattering angle θ. This expression is general in the sense that it holds for any value of N and A. It is, however, restricted to cases where the mean free path is constant throughout the random walk. The results of the simulations allow a further generalization to random walks with a nonconstant mean free path. They also allow the study of the radial distribution f(r) of particles after the walk. We find that a set of six functions fi(r) is necessary to give a satisfactory description of the particles' radial distribution for arbitrary values of N and A.