论文标题
扩散非重叠的部分反应性球形陷阱：对经典问题的新见解
Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems
论文作者
论文摘要
重新审视了三个维度中非重叠的部分反应球形陷阱的任意构型的颗粒的几个经典问题。为此，我们描述了用于解决相关修改的Helmholtz方程的边界值问题的变量分离的广义方法。特别是，我们为绿色函数得出了半分析溶液，该解是确定各种扩散反应特征的关键成分，例如生存概率，第一学期时间分布和反应速率。我们还提出了该方法的修改，以在这种穿孔域中在数值或渐近上确定Laplace操作员以及Dirichlet到Neumann Operator的特征值和本征函数。讨论了化学物理学和生物物理学中的一些潜在应用，包括致命颗粒的扩散控制反应。
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.
