Narrow escape of interacting diffusing particles

Abstract

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 that allows us to evaluate the \emph{non-escape probability} of a gas of diffusing particles that may interact with each other. In some cases the non-escape 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.

6 pages, 2 figures, final version

References in corpus (7)

• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Diffusive escape through a narrow opening: new insights into a classic problem
• Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models
• Narrow escape and leakage of Brownian particles
• Survival of a static target in a gas of diffusing particles with exclusion
• Survival probability of an immobile target surrounded by mobile traps
• First Invader Dynamics in Diffusion-Controlled Absorption

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