A Hierarchical Cluster System Based on Horton-Strahler Rules for River Networks

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 c i,j (t) the concentration of clusters of order i and mass j at time t, we derive a coagulationlike ordinary di#erential system for the time dynamics of these clusters

Long-Time Behaviour and Self-Similarity in a Coagulation Equation With Input of Monomers ∗

For a coagulation equation with Becker-Döring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a selfsimilar function. Keywords: Coagulation equations, Self-similar behaviour, Centre Manifolds, Asymptotic Evaluation of Integrals