We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.
Self-Organized Branching Processes: Mean-Field Theory for Avalanches / S. Zapperi, K. Bækgaard Lauritsen, H. Eugene Stanley. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 75:22(1995 Nov 27), pp. 4071-4074.
Self-Organized Branching Processes: Mean-Field Theory for Avalanches
S. Zapperi;
1995
Abstract
We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.File | Dimensione | Formato | |
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