Self-organized branching process for a one-dimensional rice-pile model |
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Authors: | F. Slanina |
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Affiliation: | (1) Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 18221 Praha, Czech Republic, CZ |
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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. Received 21 June 2001 and Received in final form 14 November 2001 |
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Keywords: | PACS. 05.65.+b Self-organized systems – 05.70.Jk Critical point phenomena – 45.70.-n Granular systems |
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