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

Makoto Katori and Hirotsugu Kobayashi

Physica A: Statistical Mechanics and its Applications, 1996, vol. 229, issue 3, 461-477

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.

Keywords: Self-organized critical states; Sandpile models; Avalanches; Mean-field theory; Cluster variation method (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:229:y:1996:i:3:p:461-477

DOI: 10.1016/0378-4371(96)00003-9

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