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Authors
Advisor(s)
Abstract(s)
We consider a cluster system in which each cluster is characterized
by two parameters: an \order" i; following Horton-Strahler's rules, and a
\mass" j following the usual additive rule. Denoting by ci;j (t) the concen-
tration of clusters of order i and mass j at time t; we derive a coagulation-
like ordinary di erential system for the time dynamics of these clusters.
Results about existence and the behaviour of solutions as t ! 1 are ob-
tained, in particular we prove that ci;j (t) ! 0 and Ni(c(t)) ! 0 as t ! 1;
where the functional Ni( ) measures the total amount of clusters of a given
xed order i: Exact and approximate equations for the time evolution of
these functionals are derived. We also present numerical results that sug-
gest the existence of self-similar solutions to these approximate equations
and discuss its possible relevance for an interpretation of Horton's law of
river numbers
Description
Keywords
Coagulation equations Cluster dynamics Horton-Strahler rules
Citation
Costa, Fernnado Pestana da; Grinfeld, Michael; Wattis, Jonathan A. D. - A hierarchical cluster system based on Horton-Strahler rules for river networks." Studies in Applied Mathematics" [Em linha]. ISSN 1467-9590. Vol.109, nº 3, (October 2002), p. 163-204
Publisher
Massachusetts Institute of Technology