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 [Formula presented] 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.
| Original language | English |
|---|---|
| Pages (from-to) | 5 |
| Number of pages | 1 |
| Journal | Physical Review E |
| Volume | 70 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2004 |