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.
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Received 21 June 2001 and Received in final form 14 November 2001
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Slanina, F. Self-organized branching process for a one-dimensional rice-pile model. Eur. Phys. J. B 25, 209–216 (2002). https://doi.org/10.1140/epjb/e20020023
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DOI: https://doi.org/10.1140/epjb/e20020023