论文标题
通过可渗透的接口扩散：基本方程及其在第一步和本地时间统计中的应用
Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics
论文作者
论文摘要
扩散方程是研究游离布朗粒子的运动动力学的主要工具，但是当存在可渗透接口形式的空间异质性时，就没有得出基本方程。在这里，我们使用晶格随机步行模型从显微镜描述中获得了这样的方程。所追求的Fokker-Planck描述和相应的后退Kolmogorov方程被用来调查第一步和本地时间统计数据并获得新的见解。在其中一个令人惊讶的现象中，在半轨道的情况下，出现了依赖性和独立性对渗透性屏障在平均第一学期时间内的位置的看法。新的形式主义是完全笼统的：它允许在存在多个可渗透屏障以及有限或无界域的反应性异质性的情况下研究动力学，并在外部力量的影响下。
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we obtain such an equation from a microscopic description using a lattice random walk model. The sought after Fokker-Planck description and the corresponding backward Kolmogorov equation are employed to investigate first-passage and local time statistics and gain new insights. Among them a surprising phenomenon, in the case of a semibounded domain, is the appearance of a regime of dependence and independence on the location of the permeable barrier in the mean first-passage time. The new formalism is completely general: it allows to study the dynamics in the presence of multiple permeable barriers as well as reactive heterogeneities in bounded or unbounded domains and under the influence of external forces.
