注意：具有周期性吸收弧的圆的边界均匀化。有效捕获率的精确表达式。
Note: Boundary homogenization for a circle with periodic absorbing arcs. Exact expression for the effective trapping rate.
作者信息
Skvortsov Alexei T, Berezhkovskii Alexander M, Dagdug Leonardo
机构信息
Maritime Division, Defence Science and Technology Organisation, Fishermans Bend, Victoria 3207, Australia.
Mathematical and Statistical Computing Laboratory, Division for Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
出版信息
J Chem Phys. 2015 Dec 14;143(22):226101. doi: 10.1063/1.4936866.
This study deals with trapping of particles diffusing on a flat surface by a circle whose boundary contains identical, evenly spaced absorbing arcs separated by reflecting arcs. This means that the particle concentration on the circle satisfies heterogeneous boundary conditions which make the trapping problem rather complicated for analytical treatment. Boundary homogenization discussed in this note allows to bypass this difficulty by the approximate replacement of heterogeneous boundary conditions on the circle by an effective homogeneous one with a properly chosen effective trapping rate. We obtain a formula which gives this rate in terms of the circle radius, number of absorbing arcs, the fraction of the circle boundary occupied by the arcs, and the particle diffusivity.
本研究涉及通过一个圆来捕获在平面上扩散的粒子，该圆的边界包含由反射弧分隔的相同且等距的吸收弧。这意味着圆上的粒子浓度满足非均匀边界条件，这使得捕获问题对于解析处理而言相当复杂。本笔记中讨论的边界均匀化通过用适当选择的有效捕获率的有效均匀边界条件近似替代圆上的非均匀边界条件，从而得以绕过这一困难。我们得到了一个公式，该公式根据圆半径、吸收弧的数量、弧所占据的圆边界的比例以及粒子扩散率给出了这个速率。
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