Phys. Rev. Lett. 75, 4071–4074 (1995)Self-Organized Branching Processes: Mean-Field Theory for AvalanchesReceived 29 June 1995; revised 25 September 1995; published in the issue dated 27 November 1995 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. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.75.4071
DOI:
10.1103/PhysRevLett.75.4071
PACS:
64.60.Ht, 05.20.-y, 05.40.+j, 05.70.Ln
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