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

A. Gabrielov·W. I. Newman·D. L. Turcotte
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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.

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A. Gabrielov, W. I. Newman, D. L. Turcotte. 1999-07-26. An Exactly Soluble Hierarchical Clustering Model: Inverse Cascades, Self-Similarity, and Scaling. https://doi.org/10.1103/physreve.60.5293

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