The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain’s boundary. Here we develop a formalism which allows us to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some cases the nonescape probability allows us to evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and the recently developed macroscopic fluctuation theory. We also uncover an unexpected connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.

中文翻译：

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相互作用扩散粒子的狭窄逸出

狭窄逃逸问题涉及计算布朗粒子从有界域通过域边界上的一个小孔的平均逃逸时间（MET）。在这里，我们开发了一种形式主义，该形式主义使我们能够评估气体相互扩散可能扩散的气体的无逸散概率。在某些情况下，无逸出概率使我们能够评估第一个粒子的MET。形式主义是基于波动流体力学和最近发展的宏观波动理论。我们还发现了相互作用颗粒的狭窄逸出与化学反应器中的热失控之间的意外连接。