向非重叠部分反应球形陷阱的扩散：对经典问题的新认识
Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems
摘要：
几个经典问题的粒子扩散外的任意配置的非重叠的部分反应性球形陷阱在三维空间中重新审视。为此目的，我们描述了广义分离变量法解决相关的修改Helmholtz方程的边值问题。特别是，我们推导出一个半解析解的格林函数，是关键成分，以确定各种扩散反应特性，如生存概率，首次通过时间分布，和反应速率。我们还提出了修改的方法，以确定数值或渐近的拉普拉斯算子和狄利克雷-诺依曼算子在这样的穿孔域的本征值和本征函数。讨论了在化学物理和生物物理中的一些潜在应用，包括致命粒子的扩散控制反应。
英文摘要：
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 of 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.
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