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Mean-field theory of avalanches in self-organized critical states

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  • Katori, Makoto
  • Kobayashi, Hirotsugu

Abstract

A new mean-field approximation is proposed for the sandpile model of Bak, Tang and Wiesenfeld and the distribution of heights in the self-organized critical state is calculated. We treat several series of successive topples to approximate various avalanches. In contrast to the previous mean-field theory given by Tang and Bak, which assumes the stationary condition among topples in an avalanche, out theory takes into account long-term behavior of the system. The results are in good agreement with the values estimated by computer simulations even in low dimensions d = 2 and 3. Higher approximations obtained by including local correlations or by imposing a reducibility condition, which is used in the cluster variation method, are also shown.

Suggested Citation

  • Katori, Makoto & Kobayashi, Hirotsugu, 1996. "Mean-field theory of avalanches in self-organized critical states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 229(3), pages 461-477.
    • Handle: RePEc:eee:phsmap:v:229:y:1996:i:3:p:461-477
    DOI: 10.1016/0378-4371(96)00003-9
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    References listed on IDEAS

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    1. Caldarelli, G. & Vespignani, A. & Pietronero, L., 1995. "Fixed scale transformation for fracture growth processes governed by vectorial fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 215(3), pages 223-232.
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