Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.

Regularization and Bang-bang conjugate times in optimal control

Consideramos o problema de controlo óptimo de tempo mínimo para sistemas de controlo mono-entrada e controlo afim num espaço de dimensão finita com condições inicial e final fixas, onde o controlo escalar toma valores num intervalo fechado. Quando aplicamos o método de tiro a este problema, vários obstáculos podem surgir uma vez que a função de tiro não é diferenciável quando o controlo é bang-bang. No caso bang-bang os tempos conjugados são teoricamente bem definidos para este tipo de sistemas de controlo, contudo os algoritmos computacionais directos disponíveis são de difícil aplicação. Por outro lado, no caso suave o conceito teórico e prático de tempos conjugados é bem conhecido, e ferramentas computacionais eficazes estão disponíveis. Propomos um procedimento de regularização para o qual as soluções do problema de tempo mínimo correspondente dependem de um parâmetro real positivo suficientemente pequeno e são definidas por funções suaves em relação à variável tempo, facilitando a aplicação do método de tiro simples. Provamos, sob hipóteses convenientes, a convergência forte das soluções do problema regularizado para a solução do problema inicial, quando o parâmetro real tende para zero. A determinação de tempos conjugados das trajectórias localmente óptimas do problema regularizado enquadra-se na teoria suave conhecida. Provamos, sob hipóteses adequadas, a convergência do primeiro tempo conjugado do problema regularizado para o primeiro tempo conjugado do problema inicial bang-bang, quando o parâmetro real tende para zero. Consequentemente, obtemos um algoritmo eficiente para a computação de tempos conjugados no caso bang-bang.

Systematics and evolution of coastal and deepwater Hydrozoa from the NE Atlantic

The study of the Portuguese Hydrozoa fauna has been abandoned for more than half a century, except for the Azores archipelago. One of the main aims of this Ph.D. project was to contribute new hydrozoan records leading to a more accurate perception of the actual hydrozoan diversity found in Portuguese waters, including the archipelagos of Azores and Madeira, and neighbouring geographical areas, for habitats ranging from the deep sea to the intertidal. Shallow water hydroids from several Portuguese marine regions (including the Gorringe Bank) were sampled by scuba-diving. Deep-water hydroids, from the Azores, Madeira, Gulf of Cadiz and Alboran Sea, were collected by researchers of different institutions during several oceanographic campaigns. Occasional hydroid sampling by scuba-diving was performed in the UK, Malta and Spain. Over 300 hydroid species were identified and about 600 sequences of the hydrozoan ‘DNA barcode’ 16S mRNA were generated. The families Sertulariidae, Plumulariidae, Lafoeidae, Hebellidae, Aglaopheniidae, Campanulinidae, Halopterididae, Kirchenpaueriidae, Haleciidae and Eudendriidae, were studied in greater detail. About 350 16S sequences were generated for these taxa, allowing phylogenetic, phylogeographic and evolutionary inferences, and also more accurate taxonomic identifications. Phylogenetic analyses integrated molecular and morphological characters. Subsequent results revealed: particularly high levels of cryptic biodiversity, polyphyly in many taxonomic groups, pairs of species that were synonymous, the identity of several varieties as valid species, and highlighted phylogeographic associations of hydroids in deep and shallow-water areas of the NE Atlantic and W Mediterranean. It was proved that many (but not all) marine hydroid species with supposedly widespread vertical and/or horizontal geographical distributions, correspond in fact to complexes of cryptic taxa. This study further revealed that, in the NE Atlantic, shallow environments sustain higher hydrozoan diversity and abundance, but the importance of bathyal habitats as a source of phylogenetic diversity was also revealed. The Azorean seamounts were shown to be particularly important in the segregation of populations of hydroids with reduced dispersive potential. The bathyal habitats of the Gulf of Cadiz proved to harbour a considerably high number of cryptic species, which may mainly be a consequence of habitat heterogeneity and convergence of various water masses in the Gulf. The main causes proposed for speciation and population divergence of hydroids were: species population size, dispersal mechanisms and plasticity to inhabit different environmental conditions, but also the influence of oceanic currents (and its properties), habitat heterogeneity, climate change and continental drift. Higher phylogenetic resolution obtained for the family Plumulariidae revealed particularly that glacial cycles likely facilitated population divergence, ultimately speciation, and also faunal evolutionary transitions from deep to shallow waters.

Communication between nodes for autonomic and distributed management

Over the last decade, the most widespread approaches for traditional management were based on the Simple Network Management Protocol (SNMP) or Common Management Information Protocol (CMIP). However, they both have several problems in terms of scalability, due to their centralization characteristics. Although the distributed management approaches exhibit better performance in terms of scalability, they still underperform regarding communication costs, autonomy, extensibility, exibility, robustness, and cooperation between network nodes. The cooperation between network nodes normally requires excessive overheads for synchronization and dissemination of management information in the network. For emerging dynamic and large-scale networking environments, as envisioned in Next Generation Networks (NGNs), exponential growth in the number of network devices and mobile communications and application demands is expected. Thus, a high degree of management automation is an important requirement, along with new mechanisms that promote it optimally and e ciently, taking into account the need for high cooperation between the nodes. Current approaches for self and autonomic management allow the network administrator to manage large areas, performing fast reaction and e ciently facing unexpected problems. The management functionalities should be delegated to a self-organized plane operating within the network, that decrease the network complexity and the control information ow, as opposed to centralized or external servers. This Thesis aims to propose and develop a communication framework for distributed network management which integrates a set of mechanisms for initial communication, exchange of management information, network (re) organization and data dissemination, attempting to meet the autonomic and distributed management requirements posed by NGNs. The mechanisms are lightweight and portable, and they can operate in di erent hardware architectures and include all the requirements to maintain the basis for an e cient communication between nodes in order to ensure autonomic network management. Moreover, those mechanisms were explored in diverse network conditions and events, such as device and link errors, di erent tra c/network loads and requirements. The results obtained through simulation and real experimentation show that the proposed mechanisms provide a lower convergence time, smaller overhead impact in the network, faster dissemination of management information, increase stability and quality of the nodes associations, and enable the support for e cient data information delivery in comparison to the base mechanisms analyzed. Finally, all mechanisms for communication between nodes proposed in this Thesis, that support and distribute the management information and network control functionalities, were devised and developed to operate in completely decentralized scenarios.