Maxwell perturbations on asymptotically Anti-de-Sitter spacetimes: generic boundary conditions and a new branch of quasinormal modes

Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation applies also for other spin fields. Imposing VEF BCs, we find a set of two Robin BCs, even for Schwarzschild-AdS black holes. The Robin BCs on the Teukolsky variables can be used to study quasinormal modes, superradiant instabilities and vector clouds. As a first application, we consider here the quasinormal modes of Schwarzschild-AdS black holes. We find that one of the Robin BCs yields the quasinormal spectrum reported in the literature, while the other one unveils a new branch for the quasinormal spectrum.

Cálculo das variações fraccional generalizado

Nesta tese de doutoramento apresentamos um cálculo das variações fraccional generalizado. Consideramos problemas variacionais com derivadas e integrais fraccionais generalizados e estudamo-los usando métodos directos e indirectos. Em particular, obtemos condições necessárias de optimalidade de Euler-Lagrange para o problema fundamental e isoperimétrico, condições de transversalidade e teoremas de Noether. Demonstramos a existência de soluções, num espaço de funções apropriado, sob condições do tipo de Tonelli. Terminamos mostrando a existência de valores próprios, e correspondentes funções próprias ortogonais, para problemas de Sturm- Liouville.

Higher-order variational problems of Herglotz type

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

Existência de minimizantes relaxados e fenómeno de Lavrentiev

Neste trabalho prova-se a existência de minimizantes relaxados em problemas de controlo óptimo não convexos usando técnicas de compactificação. Faz-se a extensão do exemplo de Manià a dimensão dois, obtendo-se uma classe de problemas variacionais em 2D que apresentam Fenómeno de Lavrentiev. Prova-se que o fenómeno persiste a certas perturbações, obtendo- -se assim uma classe de funcionais cujos Lagrangianos são coercivos e convexos em relação ao gradiente. Adicionalmente, apresentam-se exemplos de problemas do cálculo das variações com diferentes condições de fronteira, e em diferentes tipos de domínios (incluindo domínios com fronteira fractal), que exibem Fenómeno de Lavrentiev.

Assessing the combined effect of land management and wildfire on runoff and soil erosion in north central Portugal

Strong and sometimes extreme responses in runoff and soil erosion following wildfires have been reported worldwide. However, in the case of North-Central Portugal, little research had been carried out regarding the hydrologic and erosive impacts of several land management activities in recently burnt areas (such as ground preparation, post-fire logging or post-fire mitigation treatments). This study aims to assess post-fire runoff and soil erosion response on Eucalypt and Maritime pine plantations during the first, second and third years following wildfires. The effect of several pre-fire ground preparation operations (ploughed down-slope, contour ploughed and inclined terraces), post-fire logging activities (on both the eucalypt and pine plantations), as well as the application of hydromulch (a post-fire emergency treatment) on overland flow and soil erosion were compared to burnt but undisturbed and untreated areas. The intensive monitoring of runoff, soil erosion and selected soil properties served to determine the main factors involved in post-fire runoff and soil erosion and their spatial and temporal variation. Soil water repellency deserved special attention, due to its supposed important role for overland flow generation. Repeated rainfall simulation experiments (RSE’s), micro-scale runoff plots and bounded sediment fences were carried out and/or installed immediately after the wildfire on seven burnt slopes. Micro-scale runoff plots results under natural rainfall conditions were also compared to the RSE’s results, which was useful for assessing the representativeness of the data obtained with artificial rainfall. The results showed comparable runoff coefficient (20-60%) but lower sediment losses (125-1000 g m-2) than prior studies in Portugal, but especially outside Portugal. Lower sediment losses were related with the historic intensive land use in the area. In evaluating these losses, however, the shallowness and stoniness of the soils, as well as the high organic matter fraction of the eroded sediments (50%) must not be overlooked. Sediment limited erosion was measured in all the ploughed sites, probably due to the time since ploughing (several years). The disturbance of the soil surface cover due to post-fire logging and wood extraction substantially increased sediment losses at both the pine and eucalypt sites. Hydromulch effectiveness in reducing the runoff (70%) and sediment losses (83%) was attributed to the protective high coverage provided by hydromulch. The hydromulch significantly affected the soil cover and other soil properties and these changes also reduced the soil erosion risk. The rainfall amount was the main factor explaining the variance in runoff. However, a shift from rainfall amount to rainfall intensity was detected when either the surface cover or the infiltration capacity (hydrophilic conditions) increased. Sediment losses were controlled by rainfall intensity and surface cover. The role of soil water repellency on runoff generation was not consistent; the overall repellency levels alone were not enough to assess its hydrological impact. Soil water repellency explained runoff generation in the specific-sites model better than in the overall model. Additionally, soil moisture content was a better predictor for soil water repellency than antecedent rainfall. The natural rainfall results confirmed that RSE’s were able to capture the specific sediment losses and its organic matter content as well as the differences between the ploughed and unploughed sites. Repeated RSE’s also captured the seasonal variations in runoff and sediment losses attributed to soil water repellency. These results have implications for post-fire soil erosion modelling and soil conservation practices in the region, or areas with the same land use, climate and soil characteristics. The measured sediment loss, as well as the increasing frequency of ploughing in recently burnt and unburnt eucalypt stands, suggests ploughing is not an effective as a soil conservation measure. Logging activities with less impact are recommended in order to maintain the forest litter protecting the soil surface. Due to its high effectiveness in reducing runoff and soil erosion, hydromulch is recommended for highly sensitive and vulnerable areas.

Wind energy resource modelling in Portugal and its future large-scale alteration due to anthropogenic induced climate changes

The high dependence of Portugal from foreign energy sources (mainly fossil fuels), together with the international commitments assumed by Portugal and the national strategy in terms of energy policy, as well as resources sustainability and climate change issues, inevitably force Portugal to invest in its energetic self-sufficiency. The 20/20/20 Strategy defined by the European Union defines that in 2020 60% of the total electricity consumption must come from renewable energy sources. Wind energy is currently a major source of electricity generation in Portugal, producing about 23% of the national total electricity consumption in 2013. The National Energy Strategy 2020 (ENE2020), which aims to ensure the national compliance of the European Strategy 20/20/20, states that about half of this 60% target will be provided by wind energy. This work aims to implement and optimise a numerical weather prediction model in the simulation and modelling of the wind energy resource in Portugal, both in offshore and onshore areas. The numerical model optimisation consisted in the determination of which initial and boundary conditions and planetary boundary layer physical parameterizations options provide wind power flux (or energy density), wind speed and direction simulations closest to in situ measured wind data. Specifically for offshore areas, it is also intended to evaluate if the numerical model, once optimised, is able to produce power flux, wind speed and direction simulations more consistent with in situ measured data than wind measurements collected by satellites. This work also aims to study and analyse possible impacts that anthropogenic climate changes may have on the future wind energetic resource in Europe. The results show that the ECMWF reanalysis ERA-Interim are those that, among all the forcing databases currently available to drive numerical weather prediction models, allow wind power flux, wind speed and direction simulations more consistent with in situ wind measurements. It was also found that the Pleim-Xiu and ACM2 planetary boundary layer parameterizations are the ones that showed the best performance in terms of wind power flux, wind speed and direction simulations. This model optimisation allowed a significant reduction of the wind power flux, wind speed and direction simulations errors and, specifically for offshore areas, wind power flux, wind speed and direction simulations more consistent with in situ wind measurements than data obtained from satellites, which is a very valuable and interesting achievement. This work also revealed that future anthropogenic climate changes can negatively impact future European wind energy resource, due to tendencies towards a reduction in future wind speeds especially by the end of the current century and under stronger radiative forcing conditions.

Photodegradation of sertraline by solar radiation and influencing factors

Photodegradation is considered to be one of the most important processes of elimination of pharmaceutical drugs from natural water matrices. The high consumption and discharge of these substances, in particular antidepressants, to the aquatic environment supports the need to study degradation processes. This dissertation aimed at studying the direct and indirect photodegradation of sertraline, an antidepressant known for its persistence in the environment, and the evaluation of the influence of environmentally relevant factors in its photodegradation. The photodegradation experiments were developed under simulated solar light and the irradiation times converted to summer sunny days (SSD), an equivalent time in natural environmental conditions. The direct photodegradation was evaluated in solutions of sertraline prepared in ultrapure water and the indirect photodegradation was studied through the addition of photosensitizers (humic substances, Fe(III), nitrates and oxygen). Further irradiation studies were perfomed in aqueous samples collected from two wastewater treatment plants, Vouga river and Ria de Aveiro. The samples were chemically characterized (dissolved organic carbon, nitrates and nitrites and iron determination and UV/Vis spectroscopy). The quantification of sertraline was done by HPLC-UV and photoproducts from direct photodegradation were identified by electrospray mass spectrometry. An observed direct photodegradation rate of sertraline of 0.0062 h-1 was determined, corresponding to a half-life time of 111 h (equivalent to 29 SSD). A significant influence of photosensitizers was observed, the best results being achieved in irradiations of sertraline with humic acids, obtaining a half-life time of 12 h. This was attributed to the hydrophobicity of this substance and higher absortivity in the UV/Vis wavelength, which promote processes of indirect photodegradation. The degradation of sertraline in natural samples was also enhanced comparatively to the direct photodegradation, achieving half-life times between 10 and 25h; the best results were achieved in samples from the primary treatment of a wastewater treatment plant and Ria de Aveiro, with half-life times of 10 and 16 h, respectively. A total of six photoproducts formed during the direct photodegradation of sertraline were identified, three of which were not yet identified in the literature. The main factors contributing to the degradation of sertraline were analysed but this was not fully accomplished, requiring further studies of the composition of the natural matrices and the combined influence of distinct photosensitizers during the irradiation. Nevertheless, it was concluded that the photodegradation of sertraline is greatly influenced by indirect photodegradation processes, promoted by the presence of photosensitizers.