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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    4,730 Downloads   8,664 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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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