Eur. Phys. J. B 25, 209-216 (2002)
https://doi.org/10.1140/epjb/e20020023

Self-organized branching process for a one-dimensional rice-pile model

Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha, Czech Republic

Corresponding author: ^a slanina@fzu.cz

Received: 21 June 2001
Revised: 14 November 2001
Published online: 15 January 2002

Abstract

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