title: 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.
authors.affiliation: Departments of Mathematics and Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana 47907, USA.
authors.forename: A
authors.initials: A
authors.lastname: Gabrielov
authors.forename: W I
authors.initials: WI
authors.lastname: Newman
authors.forename: D L
authors.initials: DL
authors.lastname: Turcotte