A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations
A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations
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DOI：
10.1016/j.advwatres.2009.01.002
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发表时间：
2009-04-01
影响因子：
4.7
通讯作者：
Meerschaert, Mark M.
中科院分区：
文献类型：
--
作者：
Benson, David A.;Meerschaert, Mark M.
我们扩展了粒子跟踪方法来模拟一般的多速率传质（MRMT）方程。以前的单速率方程的方法使用两个状态的马尔可夫链，并发现一个粒子花费在等待时间的时期之间的移动的状态的时间是随机的和指数分布。利用马尔可夫过程的Bochner从属技术，我们发现随机移动的时间仍然是指数的随机过程，对应于MRMT方程。固定相中的随机时间具有与MRMT方程的记忆函数直接相关的分布。这种联系使我们能够将MRMT记忆函数解释为一定年龄的粒子（通过在非移动的区中的停留时间测量）退出以再次变为移动的的速率。由于从MRMT方程中可以知道移动的和非移动的时间的精确分布，因此可以使用随机游动非常简单有效地模拟它们。(C)2009爱思唯尔有限公司保留所有权利。
We extend the particle-tracking method to simulate general multi-rate mass transfer (MRMT) equations. Previous methods for single-rate equations used two-state Markov chains and found that the time a particle spends in the mobile state between waiting time epochs is random and exponentially distributed. Using Bochner's subordination technique for Markov processes, we find that the random mobile times are still exponential for the stochastic process that corresponds to the MRMT equations. The random times in the immobile phase have a distribution that is directly related to the memory function of the MRMT equation. This connection allows us to interpret the MRMT memory function as the rate at which particles of a certain age, measured by residence time in the immobile zone, exit to become mobile once again. Because the exact distributions of mobile and immobile times are known from the MRMT equations, they can be simulated very simply and efficiently using random walks. (C) 2009 Elsevier Ltd. All rights reserved.