Urn model of separation of sand.

@article{Lipowski2002UrnMO,
  title={Urn model of separation of sand.},
  author={Adam Lipowski and Michel Droz},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2002},
  volume={65 3 Pt 1},
  pages={031307}
}
We introduce an urn model that 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. The master equation and the first-passage problem for the model are solved numerically and the results are used to locate first-order… CONTINUE READING

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