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

✍ Scribed by Makoto Katori; Hirotsugu Kobayashi

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 731 KB
• Volume: 229
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(96)00003-9

✦ Synopsis

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, our 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.