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Unbiased Diffusion to Escape through Small Windows: Assessing the Applicability of the Reduction to Effective One-Dimension Description in a Spherical Cavity

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DOI: 10.4236/jmp.2011.24037    4,729 Downloads   8,662 Views   Citations


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.

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M. Vazquez and L. Dagdug, "Unbiased Diffusion to Escape through Small Windows: Assessing the Applicability of the Reduction to Effective One-Dimension Description in a Spherical Cavity," Journal of Modern Physics, Vol. 2 No. 4, 2011, pp. 284-288. doi: 10.4236/jmp.2011.24037.


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