Urn model of separation of sand

Details Urn model of separation of sand Urn model of separation of sand

2001-11-26

arxiv.org/abs/cond-mat/0111499v1

Phys.Rev.E 65, 031307 (2002)

Physics

Condensed Matter

Statistical Mechanics

10 pages, eps figures included

Scientific paper

10.1103/PhysRevE.65.031307

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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