Self-organized branching processes: avalanche models with dissipation
Bækgaard Lauritsen, Kent
Stanley, H. Eugene
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Citation (published version)Kent Bækgaard Lauritsen, Stefano Zapperi, H. Eugene Stanley. 1996. "Self-organized branching processes: Avalanche models with dissipation." PHYSICAL REVIEW E, Volume 54, Issue 3, pp. 2483 - 2488. 10.1103/PhysRevE.54.2483
We explore, in the mean-field approximation, robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.
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