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Urn model of separation of sand

Adam Lipowski·Michel Droz
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Abstract

We introduce an urn model which describes spatial separation of sand. In this dynamical model, in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken. The steady-state equation for an order parameter, a critical line, and the tricritical point on the phase diagram are found exactly. Master equation and the first-passage problem for the model are solved numerically and the results are used to locate first-order transitions. Exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability. In certain cases characteristic time diverges as N^{z}, where N is the number of balls and z=1/2 (critical line), 2/3 (tricritical point), or 1/3 (limits of stability).

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Adam Lipowski, Michel Droz. 2001-11-26. Urn model of separation of sand. https://doi.org/10.1103/physreve.65.031307

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