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- The 9-antroate chromophore as a fluorescence probe for waterPublication . Costa, Fernando Pestana da; Costa, Sílvia B.; Melo, Eurico C.; Prieto, Manuel; Maçanita, António L.
- 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.
- Provas de Agregação em Matemática: lição, relatório e curriculumPublication . Costa, Fernando Pestana daNuma primeira parte faz-se uma descrição dos tipos de equações de coagulação-fragmentação mais comuns nas literaturas matemática e científica, referindo-se alguns aspectos históricos considerados relevantes, bem como várias áreas de aplicações. Na segunda parte descrevem-se resultados matemáticos relativos a existência e unicidade de soluções de alguns destes sistemas, nomeadamente os sistemas discretos de Smoluchowski e de coagulação-fragmentação: começando com uma breve apresentação dos espaços funcionais utilizados, passam- se depois em revista os resultados sobre existència de soluções fornecendo-se uma descrição breve das ideias subjacentes às demonstrações. Esta parte termina com uma secção dedicada aos problemas de unicidade. Nas terceira e quarta partes descrevem-se diversos aspectos do comportamento de soluções. Focam-se com especial atenção questões sobre a convergência para equilíbrios a tempos longos, sobre o comportamento auto-semelhante de soluções e sobre a conservação, ou não conservação, de densidade. Todas estas questões, além da óbvia relevância matemática, têm também interpretações físicas de clara importância para as aplicações.
- 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
- Dynamics of a differential system using invariant regionsPublication . Costa, Fernando Pestana daThe longtime behaviour of a two dimensional system of ordinary differential equations with singularities is studied using conveniently defined positively invariant sets and auxiliary functions. The approach uses only elementary techniques of phase plane analysis and provides a good geometric insight into the dynamical behaviour of the system. It provides dynamical information analogous to what is usually obtained via centre manifold techniques but does not require the flow to be defined at the limit point.
- Dynamics of a Non-Autonomous ODE System Occurring in Coagulation TheoryPublication . Costa, Fernando Pestana da; Sasportes, RafaelWe consider a constant coefficient coagulation equation with Becker–D¨oring type interactions and power law input of monomers J1(t)=αtω, with α > 0 and ω>−1 2 . For this infinite dimensional system we prove solutions converge to similarity profiles as t and j converge to infinity in a similarity way, namely with either j/ς or (j −ς)/√ς constants, where ς =ς(t) is a function of t only. This work generalizes to the non-autonomous case a recent result of da Costa et al. (2004). Markov Processes Relat. Fields 12, 367–398. and provides a rigorous derivation of formal results obtained by Wattis J. Phys. A: Math. Gen. 37, 7823–7841. The main part of the approach is the analysis of a bidimensional non-autonomous system obtained through an appropriate change of variables; this is achieved by the use of differential inequalities and qualitative theory methods. The results about rate of convergence of solutions of the bidimensional system thus obtained are fed into an integral formula representation for the solutions of the infinite dimensional system which is then estimated by an adaptation of methods used by da Costa et al. (2004). Markov Processes Relat. Fields 12, 367–398.
- 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.
- Long-time behaviour and self-similarity in a coagulation equation with input of monomersPublication . Costa, Fernando Pestana da; Roessel, Henry J. van; Wattis, Jonathan ADFor a coagulation equation with Becker-Doring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a self-similar function
- 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.