Self-organized branching process for a one-dimensional ricepile model

Details Self-organized branching process for a one-dimensional ricepile model Self-organized branching process for a one-dimensional ricepile model

2001-07-11

arxiv.org/abs/cond-mat/0107237v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 1 figure; an error corrected in this version

Scientific paper

10.1140/epjb/e20020023

A self-organized branching process is introduced to describe one-dimensional ricepile model with stochastic topplings. Although the branching processes are generally supposed to describe well the systems in high dimension, our modification grasps some of the peculiarities present in one dimension. We find analytically the crossover behavior from the trivial one-dimensional BTW behavior to self-organized criticality characterized by power-law distribution of avalanches. The finite-size effects, which are crucial in the crossover, are calculated.

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