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Diffusion toward non-overlapping partially reactive spherical traps: Fresh insights onto classic problems.
The Journal of Chemical Physics ( IF 4.4 ) Pub Date : 2020-06-22 , DOI: 10.1063/5.0012719
Denis S Grebenkov 1
Affiliation  

Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation of variables for solving boundary value problems of the associated modified Helmholtz equation. In particular, we derive a semi-analytical solution for the Green function that is the key ingredient to determine various diffusion–reaction characteristics such as the survival probability, the first-passage time distribution, and the reaction rate. We also present modifications of the method to determine numerically or asymptotically the eigenvalues and eigenfunctions of the Laplace operator and the Dirichlet-to-Neumann operator in such perforated domains. Some potential applications in chemical physics and biophysics are discussed, including diffusion-controlled reactions for mortal particles.

中文翻译:

向非重叠的部分反应性球形阱的扩散:对经典问题的新见解。

讨论了粒子在三维的非重叠部分反应性球形阱的任意构型外扩散的几个经典问题。为此,我们描述了用于解决关联的修改的亥姆霍兹方程的边值问题的变量分离的通用方法。特别是,我们导出了Green函数的半解析解,这是确定各种扩散反应特征(例如生存率,首次通过时间分布和反应速率)的关键因素。我们还介绍了该方法的修改形式,以在此类穿孔域中以数值或渐近方式确定Laplace算子和Dirichlet-to-Neumann算子的特征值和特征函数。
更新日期:2020-06-30
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