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Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

Stefano Zapperi·Kent Baekgaard Lauritsen·H. Eugene Stanley
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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.

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Stefano Zapperi, Kent Baekgaard Lauritsen, H. Eugene Stanley. 1995-09-26. Self-Organized Branching Processes: A Mean-Field Theory for Avalanches. https://doi.org/10.1103/physrevlett.75.4071

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