Phys. Rev. E 60, 5293 - 5300 (1999)Exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling |
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A. Gabrielov
Departments of Mathematics and Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana 47907
W. I. Newman
Departments of Earth and Space Sciences, Physics and Astronomy, and Mathematics, University of California, Los Angeles, California 90095
D. L. Turcotte
Department of Geological Sciences, Cornell University, Ithaca, New York 14853
Received 2 June 1999
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.
©1999 The American Physical Society
URL: http://link.aps.org/abstract/PRE/v60/p5293
DOI: 10.1103/PhysRevE.60.5293
PACS: 05.65.+b, 45.70.Qj, 05.10.Cc
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