On the Escape of a Diffusing Particle from a Cavity

Abstract

The problem about an exit of a Brownian particle from a cylindrical cavity through an opening on the surface of one of the cylinder ends is considered. A one-dimensional description of the process using the surface homogenization method is proposed. The solution obtained by this method allows us to find the average lifetime of a particle in such a cavity with any hole size. The qualitative difference from the well-known solution for the average lifetime of a particle diffusing in an isometric (sphere-like) cavity lies in the fact that the previously obtained result depends only on the cavity volume, while the solution found in this work depends not only on the cylinder volume, but also on its length.