PMID: 11909046Mar 23, 2002Paper

Urn model of separation of sand

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
A Lipowski, Michel Droz

Abstract

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 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).

References

Mar 15, 1993·Physical Review Letters·I Goldhirsch, G Zanetti
Mar 22, 2001·Nature·T Shinbrot, F J Muzzio
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D van der MeerD Lohse

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Citations

Jul 7, 2007·Chaos·L BogaczB Waclaw
Nov 13, 2003·Physical Review Letters·I BenaA Lipowski
Nov 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G M ShimHoyun Lee
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·René MikkelsenDetlef Lohse
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jun OhkuboKazuyuki Tanaka
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Giorgos Kanellopoulos, Ko van der Weele
Jan 20, 2018·Physical Review. E·Chun-Hsiung TsengChi-Ho Cheng
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·U Marini Bettolo Marconi, M Conti
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yee-Mou Kao
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jun Ohkubo
Apr 12, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yee-Mou Kao, Pi-Gang Luan
Jun 1, 2004·Physical Review Letters·Devaraj van der MeerDetlef Lohse
Dec 17, 2004·Physical Review Letters·R L Greenblatt, J L Lebowitz
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·François CoppexAdam Lipowski
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rui LiuMeiying Hou
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adam Lipowski, Michel Droz
Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Masashi FujiiHiraku Nishimori
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jaime ClarkJuan Alejandro Valdivia
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·U Marini Bettolo Marconi, A Puglisi
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G M ShimHoyun Lee

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