title: Analytic study of the three-urn model for separation of sand.
abstract: We present an analytic study of the three-urn model for separation of sand, which can be regarded as a zero-range process. 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 free energy. We find that the characteristic lifetime of a cluster diverges algebraically with exponent 1/3 at the limit of stability. We also give a general argument that the scaling behavior is robust with respect to different expressions of the flux.
authors.affiliation: Department of Physics, Chungnam National University, Daejeon 305-764, Korea.
authors.forename: G M
authors.initials: GM
authors.lastname: Shim
authors.forename: B Y
authors.initials: BY
authors.lastname: Park
authors.forename: J D
authors.initials: JD
authors.lastname: Noh
authors.forename: Hoyun
authors.initials: H
authors.lastname: Lee