Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
Partially Reflected Brownian Motion: A Stochastic Approach to Transport Phenomena
复制标题
部分反射布朗运动：传输现象的随机方法
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
D. Grebenkov
中科院分区：
文献类型：
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作者：
D. Grebenkov
输运现象在自然界中是普遍存在的，并且对各个科学领域都具有重要意义。在物理学、电化学、多相催化、生理学等领域都可以找到这样的例子。为了获得关于向半渗透或阻性界面的扩散或拉普拉斯输运的新信息，人们可以研究由部分反射布朗运动在第一近似中模拟的扩散粒子的随机轨迹。这一随机过程为离散、半连续和连续的扩散输运理论描述提供了方便的数学基础。本文概述了这些主题，特别强调了部分反射随机过程与拉普拉斯输运现象之间的密切关系。我们给出了这些现象的一些例子，然后简要介绍了部分反射布朗运动和相关的概率主题（例如，局部时间过程和传播谐波测度）。特别注意的是狄利克雷-诺伊曼算子的使用。讨论了一些实际结果和进一步的展望。
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive or Laplacian transport towards a semi-permeable or resistive interface, one can study the random trajectories of diffusing particles modeled, in a first approximation, by the partially refle cted Brownian motion. This stochastic process turns out to be a convenient mathematical foundation for discrete, semi-continuous and continuous theoretical descriptions of diffusive transport. This paper presents an overview of these topics with a special emphasis on the close relation between stochastic processes with partial reflections and Laplacian transport phenomena. We give selected examples of these phenomena followed by a brief introduction to the partially reflected Brownian motion and related probabilistic topics (e.g., local t ime process and spread harmonic measure). A particular attention is paid to the use of the Dirichlet-to-Neumann operator. Some practical consequences and further perspectives are discussed.