The Redner - Ben-Avraham - Kahng cluster system

We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j-k|-cluster, and not, as in Smoluchowski's model, of a (j+k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.Comment: 24 pages. 2 figures. Dedicated to Carlos Rocha and Luis Magalhaes on the occasion of their sixtieth birthday

On the convergence to critical scaling profiles in submonolayer deposition models

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 $n\geq 2$ 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 studied outside of a critical direction $x=\tau$ in the cluster size $x$ vs. time $\tau$ plane. In this paper we consider a different similarity variable, $\xi := (x-\tau)/\sqrt{\tau}$, corresponding to an inner expansion of that critical direction, and prove the convergence of solutions to a similarity profile $\Phi_{2,n}(\xi)$ when $x, \tau\to +\infty$ with $\xi$ fixed, as well as the rate at which the limit is approached.Comment: Dedicated to the memory of Jack Car

Ecologia populacional dE Copaifera pubiflora BENTH. na Amazônia Setentrional e suas implicações para o manejo do oleorresina.

O oleorresina de copaíba é um metabólito secundário produzido por espécies florestais do gênero Copaifera L. (Fabaceae), utilizado como fitoterápico e com potencial para aplicações industriais. O aumento da demanda pode comprometer o fornecimento do produto e a conservação das espécies, sendo necessário mais estudos para a definição de práticas e planos de manejo. Densidade e estrutura populacional são informações essenciais para que se possa determinar o status de conservação e potencial produtivo de diferentes espécies. Neste contexto, este trabalho teve por objetivo caracterizar aspectos ecológicos e avaliar o impacto de diferentes intervalos de coleta sobre a fenologia reprodutiva de Copaifera pubiflora Benth. em duas populações em diferentes tipos florestais em Roraima.Tese (Doutorado) - Universidade Federal de Rondônia. Orientador Dra. Lúcia Helena de Oliveira Wad