TITLE:
Unbiased Diffusion to Escape through Small Windows: Assessing the Applicability of the Reduction to Effective One-Dimension Description in a Spherical Cavity
AUTHORS:
Marco-Vinicio Vazquez, Leonardo Dagdug
KEYWORDS:
Diffusion, Brownian Particle, Fick-Jacobs Equation, Narrow-Escape Time
JOURNAL NAME:
Journal of Modern Physics,
Vol.2 No.4,
April
22,
2011
ABSTRACT: This study is devoted to unbiased motion of a point Brownian particle that escapes from a spherical cavity through a round hole. Effective one-dimensional description in terms of the generalized Fick-Jacobs equation is used to derive a formula which gives the mean first-passage time as a function of the geometric parameters for any value of a, where a is the hole’s radius. This is our main result and is given in equation (19). This result is a generalization of the Hill’s formula, which is restricted to small values of a.