A new approach to the problem of bulk-mediated surface diffusion
A new approach to the problem of bulk-mediated surface diffusion
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DOI：
10.1063/1.4928741
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发表时间：
2015-08-28
影响因子：
4.4
通讯作者：
Bezrukov, Sergey M.
中科院分区：
文献类型：
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作者：
Berezhkovskii, Alexander M.;Dagdug, Leonardo;Bezrukov, Sergey M.
本文研究了一种既可以在平面上扩散，也可以在表面上的体层中扩散的粒子的体介导表面扩散。假设粒子最初（在t = 0时）和时间t在表面上，而在这两者之间，它可以逃离表面并返回任意次数。我们提出了一种新的方法来解决这个问题，该方法将其解简化为粒子在表面和体层之间转移的两态问题，重点关注粒子在两种状态下花费的累积停留时间。这些时间是随机变量，之和等于总观察时间t。该方法的优点是,它允许一个简单的双拉普拉斯变换的精确解析解的条件概率密度累积停留时间花在粒子表面的观察时间t。这个解决方案是用来发现粒子均方位移的拉普拉斯变换的特点,分析其行为在整个范围的时间。我们还建立了条件概率密度的二重拉普拉斯变换与粒子传播子在表面上的傅里叶-拉普拉斯变换之间的关系。所提出的方法在同等基础上处理有限和无限体积层厚度的情况（其中体积介导的表面扩散分别在渐近长时间内是正常的和异常的）。(C) 2015 AIP出版有限责任公司
This paper is devoted to bulk-mediated surface diffusion of a particle which can diffuse both on a flat surface and in the bulk layer above the surface. It is assumed that the particle is on the surface initially (at t = 0) and at time t, while in between it may escape from the surface and come back any number of times. We propose a new approach to the problem, which reduces its solution to that of a two-state problem of the particle transitions between the surface and the bulk layer, focusing on the cumulative residence times spent by the particle in the two states. These times are random variables, the sum of which is equal to the total observation time t. The advantage of the proposed approach is that it allows for a simple exact analytical solution for the double Laplace transform of the conditional probability density of the cumulative residence time spent on the surface by the particle observed for time t. This solution is used to find the Laplace transform of the particle mean square displacement and to analyze the peculiarities of its time behavior over the entire range of time. We also establish a relation between the double Laplace transform of the conditional probability density and the Fourier-Laplace transform of the particle propagator over the surface. The proposed approach treats the cases of both finite and infinite bulk layer thicknesses (where bulk-mediated surface diffusion is normal and anomalous at asymptotically long times, respectively) on equal footing. (C) 2015 AIP Publishing LLC.