Limited range coverage problems

Tal como o título indica, esta tese estuda problemas de cobertura com alcance limitado. Dado um conjunto de antenas (ou qualquer outro dispositivo sem fios capaz de receber ou transmitir sinais), o objectivo deste trabalho é calcular o alcance mínimo das antenas de modo a que estas cubram completamente um caminho entre dois pontos numa região. Um caminho que apresente estas características é um itinerário seguro. A definição de cobertura é variável e depende da aplicação a que se destina. No caso de situações críticas como o controlo de fogos ou cenários militares, a definição de cobertura recorre à utilização de mais do que uma antena para aumentar a eficácia deste tipo de vigilância. No entanto, o alcance das antenas deverá ser minimizado de modo a manter a vigilância activa o maior tempo possível. Consequentemente, esta tese está centrada na resolução deste problema de optimização e na obtenção de uma solução particular para cada caso. Embora este problema de optimização tenha sido investigado como um problema de cobertura, é possível estabelecer um paralelismo entre problemas de cobertura e problemas de iluminação e vigilância, que são habitualmente designados como problemas da Galeria de Arte. Para converter um problema de cobertura num de iluminação basta considerar um conjunto de luzes em vez de um conjunto de antenas e submetê-lo a restrições idênticas. O principal tema do conjunto de problemas da Galeria de Arte abordado nesta tese é a 1-boa iluminação. Diz-se que um objecto está 1-bem iluminado por um conjunto de luzes se o invólucro convexo destas contém o objecto, tornando assim este conceito num tipo de iluminação de qualidade. O objectivo desta parte do trabalho é então minimizar o alcance das luzes de modo a manter uma iluminação de qualidade. São também apresentadas duas variantes da 1-boa iluminação: a iluminação ortogonal e a boa !-iluminação. Esta última tem aplicações em problemas de profundidade e visualização de dados, temas que são frequentemente abordados em estatística. A resolução destes problemas usando o diagrama de Voronoi Envolvente (uma variante do diagrama de Voronoi adaptada a problemas de boa iluminação) é também proposta nesta tese.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Challenges in mercury speciation and fractionation in soil and sediment

This investigation focused on the development, test and validation of methodologies for mercury fractionation and speciation in soil and sediment. After an exhaustive review of the literature, several methods were chosen and tested in well characterised soil and sediment samples. Sequential extraction procedures that divide mercury fractions according to their mobility and potential availability in the environment were investigated. The efficiency of different solvents for fractionation of mercury was evaluated, as well as the adequacy of different analytical instruments for quantification of mercury in the extracts. Kinetic experiments to establish the equilibrium time for mercury release from soil or sediment were also performed. It was found that in the studied areas, only a very small percentage of mercury is present as mobile species and that mobility is associated to higher aluminium and manganese contents, and that high contents of organic matter and sulfur result in mercury tightly bound to the matrix. Sandy soils tend to release mercury faster that clayey soils, and therefore, texture of soil or sediment has a strong influence on the mobility of mercury. It was also understood that analytical techniques for quantification of mercury need to be further developed, with lower quantification limits, particularly for mercury quantification of less concentrated fractions: water-soluble e exchangeable. Although the results provided a better understanding of the distribution of mercury in the sample, the complexity of the procedure limits its applicability and robustness. A proficiency-testing scheme targeting total mercury determination in soil, sediment, fish and human hair was organised in order to evaluate the consistency of results obtained by different laboratories, applying their routine methods to the same test samples. Additionally, single extractions by 1 mol L-1 ammonium acetate solution, 0.1 mol L-1 HCl and 0.1 mol L-1 CaCl2, as well as extraction of the organometallic fraction were proposed for soil; the last was also suggested for sediment and fish. This study was important to update the knowledge on analytical techniques that are being used for mercury quantification, the associated problems and sources of error, and to improve and standardize mercury extraction techniques, as well as to implement effective strategies for quality control in mercury determination. A different, “non chemical-like” method for mercury species identification was developed, optimised and validated, based on the thermo-desorption of the different mercury species. Compared to conventional extraction procedures, this method has advantages: it requires little to no sample treatment; a complete identification of species present is obtained in less than two hours; mercury losses are almost neglectable; can be considered “clean”, as no residues are produced; the worldwide comparison of results obtained is easier and reliable, an important step towards the validation of the method. Therefore, the main deliverables of this PhD thesis are an improved knowledge on analytical procedures for identification and quantification of mercury species in soils and sediments, as well as a better understanding of the factors controlling the behaviour of mercury in these matrices.

Polyhedral study of mixed integer sets arising from inventory problems

“Branch-and-cut” algorithm is one of the most efficient exact approaches to solve mixed integer programs. This algorithm combines the advantages of a pure branch-and-bound approach and cutting planes scheme. Branch-and-cut algorithm computes the linear programming relaxation of the problem at each node of the search tree which is improved by the use of cuts, i.e. by the inclusion of valid inequalities. It should be taken into account that selection of strongest cuts is crucial for their effective use in branch-and-cut algorithm. In this thesis, we focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc. In order to achieve this goal, we first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting plane algorithms to solve the general mixed integer problems. We study three mixed integer sets in this dissertation. The first two mixed integer sets arise as a subproblem of the lot-sizing with supplier selection, the network design and the vendor-managed inventory routing problems. These sets are variants of the well-known single node fixed-charge network set where a binary or integer variable is associated with the node. The third set occurs as a subproblem of mixed integer sets where incompatibility between binary variables is considered. We generate families of valid inequalities for those sets, identify classes of facet-defining inequalities, and discuss the separation problems associated with the inequalities. Then cutting plane frameworks are implemented to solve some mixed integer programs. Preliminary computational experiments are presented in this direction.

Regional and urban air quality modelling under a climate change scenario

The better understanding of the interactions between climate change and air quality is an emerging priority for research and policy. Climate change will bring changes in the climate system, which will affect the concentration and dispersion of air pollutants. The main objective of the current study is to assess the impacts of climate change on air quality in 2050 over Portugal and Porto urban area. First, an evaluation and characterization of the air quality over mainland Portugal was performed for the period between 2002 and 2012. The results show that NO2, PM10 and O3 are the critical pollutants in Portugal. Also, the influence of meteorology on O3, NO2 and PM10 levels was investigate in the national main urban areas (Porto and Lisboa) and was verified that O3 has a statistically significant relationship with temperature in most of the components. The results also indicate that emission control strategies are primary regulators for NO2 and PM10 levels. After, understanding the national air quality problems and the influence that meteorology had in the historical air quality levels, the air quality modelling system WRF-CAMx was tested and the required inputs for the simulations were prepared to fulfil the main goal of this work. For the required air quality modelling inputs, an Emission Projections under RCP scenarios (EmiPro-RCP) model was developed to assist the estimation of future emission inventories for GHG and common air pollutants. Also, the current emissions were estimated for Portugal with a higher detailed disaggregation to improve the performance of the air quality simulations. The air quality modelling system WRF/CAMx was tested and evaluated over Portugal and Porto urban area and the results point out that is an adequate tool for the analysis of air quality under climate change. For this purpose, regional simulations of air quality during historical period and future (2045-2050) were conducted with CAMx version 6.0 to evaluate the impacts of simulated future climate and anthropogenic emission projections on air quality over the study area. The climate and the emission projections were produced under the RCP8.5 scenario. The results from the simulations point out, that if the anthropogenic emissions keep the same in 2050, the concentrations of NO2, PM10 and O3 will increase in Portugal. When, besides the climate change effects, is consider the projected anthropogenic emissions the annual mean concentrations of NO2 decrease significantly in Portugal and Porto urban area, and on the contrary the annual mean PM10 concentrations increases in Portugal and decrease in Porto urban area. The O3 results are mainly caused by the reduction of ozone precursors, getting the higher reductions in urban areas and increases in the surrounding areas. All the analysis performed for both simulations for Porto urban area support that, for PM10 and O3, there will be an increase in the occurrence of extreme values, surpassing the annual legislated parameters and having more daily exceedances. This study constitutes an innovative scientific tool to help in future air quality management in order to mitigate future climate change impacts on air quality.