TRAPPING OF PLANAR BROWNIAN MOTION: FULL FIRST PASSAGE TIME DISTRIBUTIONS BY KINETIC MONTE CARLO, ASYMPTOTIC, AND BOUNDARY INTEGRAL METHODS
TRAPPING OF PLANAR BROWNIAN MOTION: FULL FIRST PASSAGE TIME DISTRIBUTIONS BY KINETIC MONTE CARLO, ASYMPTOTIC, AND BOUNDARY INTEGRAL METHODS
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DOI：
10.1137/21m146380x
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发表时间：
2022-12-01
影响因子：
1.6
通讯作者：
Quaife, Bryan
中科院分区：
文献类型：
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作者：
Cherry, Jake;Lindsay, Alan E.;Quaife, Bryan
我们考虑了确定复杂目标配置下无偏平面随机游走者的到达统计量的问题。与有限域中提出的问题不同，首次通过时间分布的简单矩，如其均值和方差，没有被定义。因此，有必要获得完整的到达统计数据。我们描述了几种获得这些分布和其他关联量的方法，例如分裂概率。一种方法是将基本抛物线方程的拉普拉斯变换与匹配的渐近分析相结合，然后进行数值变换反演。第二种方法类似，但使用边界积分方程法来求解变换后的变量。为了验证这一理论的结果，并在非常一般的吸收体构型中获得到达时间统计，我们引入了一种有效的动力学蒙特卡罗(KMC)方法，该方法将轨迹描述为大但精确可解的投影步长的组合。这些方法的有效性在各种具有挑战性的例子上得到了证明，这些例子突出了这些方法对各种实际情况的适用性，例如来源推理。从这些结果中得出的一个特别有用的发现是，齐化理论在描述到达时间统计方面非常有效。在齐化理论中，复杂的构型被等价的简单构型取代。
We consider the problem of determining the arrival statistics of unbiased planar random walkers to complex target configurations. In contrast to problems posed in finite domains, simple moments of the first passage time distribution, such as its mean and variance, are not defined. Therefore, it is necessary to obtain the full arrival statistics. We describe several methods to obtain these distributions and other associated quantities such as splitting probabilities. One approach combines a Laplace transform of the underlying parabolic equation with matched asymptotic analysis followed by numerical transform inversion. The second approach is similar but uses a boundary integral equation method to solve for the transformed variable. To validate the results of this theory, and to obtain the arrival time statistics in very general configurations of absorbers, we introduce an efficient kinetic Monte Carlo (KMC) method that describes trajectories as a combination of large but exactly solvable projection steps. The effectiveness of these methodologies is demonstrated on a variety of challenging examples highlighting the applicability of these methods to a variety of practical scenarios, such as source inference. A particularly useful finding arising from these results is that homogenization theories, in which complex configurations are replaced by equivalent simple ones, are remarkably effective at describing arrival time statistics.