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

Physics – Condensed Matter – Disordered Systems and Neural Networks

Scientific paper

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5pages, 4 figures included

Scientific paper

10.1103/PhysRevE.70.031305

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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