Qualidade e optimização do desmonte de maciços rochosos em geotecnia mineira

A perfuração é uma das operações envolvidas no desmonte de rocha com explosivos. A forma como esta operação é executada é determinante para o sucesso do desmonte. Quando é realizada correctamente o desmonte produz superfícies limpas com o mínimo de sobrescavação e perturbação. A selecção das ferramentas de perfuração é um dos factores preponderantes para os custos do desmonte de maciços rochosos. O objectivo deste trabalho é demonstrar a interdependência entre os parâmetros petrofísicos, geotécnicos e geomecânicos do maciço rochoso e as tecnologias de perfuração de forma a optimizar tanto técnica como economicamente. A forma como a perfuração é executada é determinante para a boa fragmentação do maciço rochoso. Este estudo irá centrar-se na perfurabilidade do maciço, linearidade dos furos, rendimento e desgaste das ferramentas de perfuração e desenvolvimento de metodologias do ciclo de perfuração. Neste trabalho, discute-se a importância de uma abordagem integrativa para fins de geoengenhara mineira em que foi aplicada a técnica de amostragem linear em superfícies expostas do maciço num ambiente de uma exploração granítica. As áreas seleccionadas para este estudo — Pedreira de Serdedelo (Ribeira, Ponte de Lima) e pedreira do Fojo (Ferreira, Paredes de Coura), NW de Portugal — estão situadas nas proximidades de falhas geológicas regionais. Em todo os casos de estudo foram desenvolvidos numa plataforma SIG usando as seguintes ferramentas: cartografia geo-aplicada, técnicas de geologia estrutural, da geotecnia e da geomecânica mineiras e avaliação de geotecnologias. Esta abordagem leva-nos a compreender a relevância da heterogeneidade do maciço rochoso para o dimensionamento da exploração a diferentes escalas. O controlo geomecânico do desmonte do maciço rochoso através de uma perfuração alinhada é salientado com o intuito de uma abordagem de geoengenharia integrada nos maciços rochosos.

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.

Biovalorização de soro de queijo por processos anaeróbios/aeróbios

Este trabalho abordou a valorização de um subproduto da indústria de lacticínios (soro de queijo) através da alteração do funcionamento de processos habitualmente utilizados no contexto do tratamento biológico. Foi avaliada a fermentação acidogénica deste subproduto para maximizar a conversão do seu elevado teor de matéria orgânica em ácidos orgânicos voláteis (AOV) que actualmente são produtos com elevada procura, nomeadamente para produção de polihidroxialcanoatos (PHA). Em ensaios descontínuos e semi-contínuos foi caracterizada a produção e composição de AOV a partir de soro de queijo variando a razão food-to-microorganism (F/M) e a concentração de alcalinidade. Recorrendo à modelação dos resultados através de superfícies de resposta, demonstrou-se que condições de F/M = 4 gCQO g-1SSV combinadas com uma adição elevada de alcalinidade (8 g L-1 expresso como CaCO3) resultaram na conversão de 72% da CQO alimentada em AOV. O acetato e o butirato foram os AOV predominantes (60%), mas elevadas razões F/M combinadas com elevadas alcalinidades promoveram o alongamento da cadeia carboxílica, tendo sido produzidos AOV de maior massa molecular (iso-valerato e n-caproato). O processo de fermentação acidogénica foi posteriormente desenvolvido em modo contínuo num reactor MBBR acidogénico operado a longo prazo. Cargas orgânicas entre 30 e 50 gCQO L-1d-1 permitiram obter um grau de acidificação máximo de 68% no efluente fermentado. Foi ainda demonstrado que uma adição dinâmica de alcalinidade (0 – 4,8 g CaCO3 L-1) nestas condições estimulou a produção de AOV de cadeia ímpar (propionato e n-valerato) até 42%. O efluente acidificado no processo anaeróbio foi usado como substrato em reactores SBR operados para selecção de culturas microbianas mistas acumuladoras de PHA, nos quais foi aplicado um regime de alimentação dinâmica em condições aeróbias (“fartura-fome”). Estes sistemas operaram também a longo prazo, e demonstraram ser capazes de remover mais de 96% da CQO alimentada e simultaneamente convertê-la em PHA, até 36% do peso celular seco. A velocidade de remoção de substrato (valor máximo de 1,33 gCQO g-1SSV h-1) foi proporcional ao teor de polímero acumulado, evidenciando o estabelecimento de uma fase de “fome” prolongada que estimulou a selecção de microrganismos com elevada capacidade de acumulação de PHA. Além disso, o teor molar de hidroxivalerato (HV) no copolímero produzido [P(HB-co-HV)] foi directamente proporcional ao teor de AOV de cadeia ímpar (propionato e n-valerato) presente no soro fermentado que serviu de substrato. Uma estratégia de operação do reactor SBR com variação da carga orgânica, aliada ao regime “fartura-fome” estabelecido, permitiu ainda simular a realidade dos processos de tratamento biológico de efluentes, nos quais a composição e concentração inicial de matéria orgânica variam frequentemente. Este modo de operação do sistema estimulou notavelmente o processo de selecção de culturas acumuladoras de PHA tendo resultado num aumento da acumulação de PHA de 7% para 36%. Os resultados demonstraram com sucesso a possibilidade de valorização do soro de queijo através de eco-biotecnologia, contribuindo para uma mudança de paradigma no tratamento convencional de efluentes: ao invés de serem eliminados enquanto poluentes, os componentes orgânicos presentes neste subproduto industrial podem assim ser convertidos em materiais de valor acrescentado.

Multiplicity results for some classes of Schrödinger-Poisson systems

In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp 2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq 2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.

Minimal state-space realizations of 2D convolutional codes

In this thesis we consider two-dimensional (2D) convolutional codes. As happens in the one-dimensional (1D) case one of the major issues is obtaining minimal state-space realizations for these codes. It turns out that the problem of minimal realization of codes is not equivalent to the minimal realization of encoders. This is due to the fact that the same code may admit different encoders with different McMillan degrees. Here we focus on the study of minimality of the realizations of 2D convolutional codes by means of separable Roesser models. Such models can be regarded as a series connection between two 1D systems. As a first step we provide an algorithm to obtain a minimal realization of a 1D convolutional code starting from a minimal realization of an encoder of the code. Then, we restrict our study to two particular classes of 2D convolutional codes. The first class to be considered is the one of codes which admit encoders of type n 1. For these codes, minimal encoders (i.e., encoders for which a minimal realization is also minimal as a code realization) are characterized enabling the construction of minimal code realizations starting from such encoders. The second class of codes to be considered is the one constituted by what we have called composition codes. For a subclass of these codes, we propose a method to obtain minimal realizations by means of separable Roesser models.

Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Understanding and modelling hydrological and soil erosion processes in burnt forest catchments

Forest fires implications in overland flow and soil erosion have been researched for several years. Therefore, is widely known that fires enhance hydrological and geomorphological activity worldwide as also in Mediterranean areas. Soil burn severity has been widely used to describe the impacts of fire on soils, and has being recognized as a decisive factor controlling post-fire erosion rates. However, there is no unique definition of the term and the relationship between soil burn severity and post-fire hydrological and erosion response has not yet been fully established. Few studies have assessed post-fire erosion over multiple years, and the authors are aware of none which assess runoff. Small amount of studies concerning pre-fire management practices were also found. In the case of soil erosion models, the Revised Universal Soil Loss Equation (RUSLE) and the revised Morgan–Morgan–Finney (MMF) are well-known models, but not much information is available as regards their suitability in predicting post-fire soil erosion in forest soils. The lack of information is even more pronounced as regards post-fire rehabilitation treatments. The aim of the thesis was to perform an extensive research under the post fire hydrologic and erosive response subject. By understanding the effect of burn severity in ecosystems and its implications regarding post fire hydrological and erosive responses worldwide. Test the effect of different pre-fire land management practices (unplowed, downslope plowed and contour plowed) and time-since-fire, in the post fire hydrological and erosive response, between the two most common land uses in Portugal (pine and eucalypt). Assess the performance of two widely-known erosion models (RUSLE and Revised MMF), to predict soil erosion rates during first year following two wildfires of distinctive burn severity. Furthermore, to apply these two models considering different post-fire rehabilitation treatments in an area severely affected by fire. Improve model estimations of post-fire runoff and erosion rates in two different land uses (pine and eucalypt) using the revised MMF. To assess these improvements by comparing estimations and measurements of runoff and erosion, in two recently burned sites, as also with their post fire rehabilitation treatments. Model modifications involved: (1) focusing on intra-annual changes in parameters to incorporate seasonal differences in runoff and erosion; and (2) inclusion of soil water repellency in runoff predictions. Additionally, validate these improvements with the application of the model to other pine and eucalypt sites in Central Portugal. The review and meta-analysis showed that fire occurrence had a significant effect on the hydrological and erosive response. However, this effect was only significantly higher with increasing soil burn severity for inter-rill erosion, and not for runoff. This study furthermore highlighted the incoherencies between existing burn severity classifications, and proposed an unambiguous classification. In the case of the erosion plots with natural rainfall, land use factor affected annual runoff while land management affected both annual runoff and erosion amounts significantly. Time-since-fire had an important effect in erosion amounts among unplowed sites, while for eucalypt sites time affected both annual runoff and erosion amounts. At all studied sites runoff coefficients increase over the four years of monitoring. In the other hand, sediment concentration in the runoff, recorded a decrease during the same period. Reasons for divergence from the classic post-fire recovery model were also explored. Short fire recurrence intervals and forest management practices are viewed as the main reasons for the observed severe and continuing soil degradation. The revised MMF model presented reasonable accuracy in the predictions while the RUSLE clearly overestimated the observed erosion rates. After improvements: the revised model was able to predict first-year post-fire plot-scale runoff and erosion rates for both forest types, these predictions were improved both by the seasonal changes in the model parameters; and by considering the effect of soil water repellency on the runoff, individual seasonal predictions were considered accurate, and the inclusion of the soil water repellency in the model also improved the model at this base. The revised MMF model proved capable of providing a simple set of criteria for management decisions about runoff and erosion mitigation measures in burned areas. The erosion predictions at the validation sites attested both to the robustness of the model and of the calibration parameters, suggesting a potential wider application.

Development of polymeric materials to inhibit bacterial quorum sensing

Bacterial infections are an increasing problem for human health. In fact, an increasing number of infections are caused by bacteria that are resistant to most antibiotics and their combinations. Therefore, the scientific community is currently searching for new solutions to fight bacteria and infectious diseases, without promoting antimicrobial resistance. One of the most promising strategies is the disruption or attenuation of bacterial Quorum Sensing (QS), a refined system that bacteria use to communicate. In a QS event, bacteria produce and release specific small chemicals, signal molecules - autoinducers (AIs) - into the environment. At the same time that bacterial population grows, the concentration of AIs in the bacterial environment increases. When a threshold concentration of AIs is reached, bacterial cells respond to it by altering their gene expression profile. AIs regulate gene expression as a function of cell population density. Phenotypes mediated by QS (QSphenotypes) include virulence factors, toxin production, antibiotic resistance and biofilm formation. In this work, two polymeric materials (linear polymers and molecularly imprinted nanoparticles) were developed and their ability to attenuate QS was evaluated. Both types of polymers should to be able to adsorb bacterial signal molecules, limiting their availability in the extracellular environment, with expected disruption of QS. Linear polymers were composed by one of two monomers (itaconic acid and methacrylic acid), which are known to possess strong interactions with the bacterial signal molecules. Molecularly imprinted polymer nanoparticles (MIP NPs) are particles with recognition capabilities for the analyte of interest. This ability is attained by including the target analyte at the synthesis stage. Vibrio fischeri and Aeromonas hydrophila were used as model species for the study. Both the linear polymers and MIP NPs, tested free in solutions and coated to surfaces, showed ability to disrupt QS by decreasing bioluminescence of V. fischeri and biofilm formation of A. hydrophila. No significant effect on bacterial growth was detected. The cytotoxicity of the two types of polymers to a fibroblast-like cell line (Vero cells) was also tested in order to evaluate their safety. The results showed that both the linear polymers and MIP NPs were not cytotoxic in the testing conditions. In conclusion, the results reported in this thesis, show that the polymers developed are a promising strategy to disrupt QS and reduce bacterial infection and resistance. In addition, due to their low toxicity, solubility and easy integration by surface coating, the polymers have potential for applications in scenarios where bacterial infection is a problem: medicine, pharmaceutical, food industry and in agriculture or aquaculture.