Fernando P. da Costa

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In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations ċj = j−1 ∑ k=1 cj−kck − 2cj ∞ ∑ k=1 ck, j = 1, 2, . . . with general exponentially decreasing initial data, with density ρ, have the following asymptotic behaviour lim j, t→∞ ξ=j/t fixed j∈J tcj(t) = q ρ e−ξ/ρ, where J = {j :(More)
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 concentration of clusters of order i and mass j at time t, we derive a coagulationlike ordinary differential system for the time dynamics of these(More)
We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the(More)
In this work we study the rate of convergence to similarity profiles in a mean field model for the deposition of a submonolayer of atoms in a crystal facet, when there is a critical minimal size n ≥ 2 for the stability of the formed clusters. The work complements recently published related results by the same authors in which the rate of convergence was(More)
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