An Exactly Soluble Hierarchical Clustering Model: Inverse Cascades, Self-Similarity, and Scaling

Abstract

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as ``self-organized critical,'' including forest-fire, sandpile, and slider-block models.

Resubmitted to Physical Review E; document prepared using RevTeX

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