Synchronization and Coarsening (without SOC) in a Forest-Fire Model
Abstract
We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length <L> grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as <L>^{-2}M(L/<L>), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.
Cite
@article{arxiv.cond-mat/0203356,
title = {Synchronization and Coarsening (without SOC) in a Forest-Fire Model},
author = {K. E. Chan and P. L. Krapivsky and S. Redner},
journal= {arXiv preprint arXiv:cond-mat/0203356},
year = {2009}
}
Comments
5 pages, 4 figures, 2-column revtex format. To be submitted to PRE