Self-Organized Criticality in Non-conserved Systems
Abstract
The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized'' region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter is examined.
Cite
@article{arxiv.cond-mat/9407082,
title = {Self-Organized Criticality in Non-conserved Systems},
author = {A. Alan Middleton and Chao Tang},
journal= {arXiv preprint arXiv:cond-mat/9407082},
year = {2009}
}
Comments
11 pages, 4 separate figures, REVTEX