Analytic study of the three-urn model for separation of sand.
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.
Shim
G M
GM
Department of Physics, Chungnam National University, Daejeon 305-764, Korea.
Park
B Y
BY
Noh
J D
JD
Lee
Hoyun
H