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Analytic study of the three-urn model for separation of sand

G. M. Shim·B. Y. Park·J. D. Noh·Hoyun Lee
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Abstract

We present an analytic study of the three-urn model for separation of sand. We solve analytically the master equation and the first-passage problem. We find that the stationary probability distribution obeys the detailed balance and is governed by the {\it free energy}. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability.

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G. M. Shim, B. Y. Park, J. D. Noh, Hoyun Lee. 2004-02-04. Analytic study of the three-urn model for separation of sand. https://doi.org/10.1103/physreve.70.031305

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