Loading...
50 results
Search Results
Now showing 1 - 10 of 50
- The Redner–Ben-Avraham–Kahng coagulation system with constant coefficients: the finite dimensional casePublication . Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, RafaelWe study the behaviour as t → ∞ of solutions (cj (t)) to the Redner–Ben-Avraham–Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established in [4] by means of formal arguments.
- On the convergence to critical scaling profiles in submonolayer deposition modelsPublication . Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, RafaelIn 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, $\xi:= (x − \tau )/ \tau$ , 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.
- Álgebra linear I : cálculo de determinantes por aplicação do teorema de LaplacePublication . Costa, Fernando Pestana da; Barrela, Nuno; Silva, Fátima Ferreira daVídeo sobre " Cálculo de determinantes por aplicação do teorema de Laplace" para apoio à unidade curricular Álgebra Linear I da Universidade Aberta, Lisboa, Portugal
- The Redner - Ben-Avraham - Kahng cluster systemPublication . Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, RafaelWe consider a coagulation model first introduced by Redner, Ben-Avraham and Kahng in [11], 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.
- Álgebra linear I : matrizes : definição e conceitos elementaresPublication . Costa, Fernando Pestana da; Barrela, Nuno; Silva, Fátima Ferreira daVídeo sobre "Matrizes: definição e conceitos elementares" para apoio à unidade curricular Álgebra Linear I da Universidade Aberta, Lisboa, Portugal
- Álgebra linear I : resolução de sistemas de equações algébricas pelo método de eliminação de GaussPublication . Costa, Fernando Pestana da; Barrela, Nuno; Silva, Fátima Ferreira daVídeo sobre "Resolução de sistemas de equações algébricas pelo método de eliminação de Gauss" para apoio à unidade curricular Álgebra Linear I da Universidade Aberta, Lisboa, Portugal
- Álgebra linear I : representação matricial de aplicações linearesPublication . Costa, Fernando Pestana da; Firmino, Joaquim; Silva, Fátima Ferreira daVídeo sobre "Representação matricial de aplicações lineares" para apoio à unidade curricular Álgebra Linear I da Universidade Aberta, Lisboa, Portugal
- Álgebra linear I : transformações elementares sobre as linhas de uma matrizPublication . Costa, Fernando Pestana da; Barrela, Nuno; Silva, Fátima Ferreira daVídeo sobre "Transformações elementares sobre as linhas de uma matriz" para apoio à unidade curricular Álgebra Linear I da Universidade Aberta, Lisboa, Portugal
- A survey of articles in the Newsletter of the EMS about the history and activities of full member Societies of the EMS (Issue 1, September 1991 – Issue 104, June 2017)Publication . Costa, Fernando Pestana daIn order to have a clearer idea of what has been published and so to be able to plan future actions, the Editorial Board of the Newsletter has recently compiled a survey of articles on the history and activities of full member societies of the EMS. We believe this survey may also be of interest to all EMS members and to the general readership of the Newsletter, as it provides a direct pointer to reliable published information about mathematical societies in Europe that can be difficult to obtain otherwise.
- Scaling behaviour in a coagulation-annihilation model and Lotka-Volterra competition systemsPublication . Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael; Roessel, Henry J. vanIn a recent paper, Laurencot and van Roessel (2010 J. Phys. A: Math. Theor., 43, 455210) studied the scaling behaviour of solutions to a two-species coagulation–annihilation system with total annihilation and equal strength coagulation, and identified cases where self-similar behaviour occurs, and others where it does not. In this paper, we proceed with the study of this kind of system by assuming that the coagulation rates of the two different species need not be equal. By applying Laplace transform techniques, the problem is transformed into a two-dimensional ordinary differential system that can be transformed into a Lotka–Volterra competition model. The long-time behaviour of solutions to this Lotka–Volterra system helps explain the different cases of existence and nonexistence of similarity behaviour, as well as why, in some cases, the behaviour is nonuniversal, in the sense of being dependent on initial conditions.