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R. M. Bradley, “Diffusion in a Two-Dimensional Channel with Curved Midline and Varying Width: Reduction to an Effective One-Dimensional Description,” Physical Review E, Vol. 80, No. 6, pp. 061142(1-7).

has been cited by the following article:

• 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.