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- 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
- Mathematical models of chiral symmetry-breaking: a review of general theories, and adiabatic approximations of the APED systemPublication . Diniz, Priscila Costa; Wattis, Jonathan AD; Costa, Fernando Pestana daWe review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma’s crystal grinding systems and the APED model. We include a few new results based on asymptotic analysis of the APED system.
- Differential equations and applicationsPublication . Costa, Fernando Pestana daTexto utilizado na lecionação da disciplina homónima lecionada pelo autor no German-Mongolian Institute for Resources and Technology, Nalaikh, Ulaanbaatar, Mongolia, em setembro de 2024.
- 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