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

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

1999-06-04

arxiv.org/abs/adap-org/9906003v2

Nonlinear Sciences

Adaptation and Self-Organizing Systems

Resubmitted to Physical Review E; document prepared using RevTeX

Scientific paper

10.1103/PhysRevE.60.5293

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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