Exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling.
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.
Gabrielov
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Departments of Mathematics and Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana 47907, USA.
Newman
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WI
Turcotte
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DL