As microalgas são conhecidas pela sua elevada capacidade fotossintética e pela produção de compostos de alto valor agregado. Nutrientes essenciais como nitrogênio e carbono, a intensidade da luz e a temperatura são responsáveis por mudanças substanciais na produção de biomassa e compostos de interesse. Este trabalho teve como objetivo estudar os fatores como concentração de nitrogênio, variação da temperatura, regime de iluminação e regime de operação do fotobiorreator (batelada, batelada repetida e contínuo) que afetam a formação e a composição da biomassa (proteínas, lipídeos, carboidratos, ácidos graxos e carotenoides) da microalga Heterochlorella luteoviridis e desenvolver um sistema de cultivo para a utilização do CO2 formado durante a fermentação alcoólica na produção de vinho. Primeiramente foram avaliados os efeitos da temperatura (22 °C a 32 °C) e concentrações de nitrogênio (75 mg L-1 a 375 mg L-1 NaNO3) sobre a formação de biomassa H. luteoviridis e sua composição química. A concentração de nitrogênio e a temperatura influenciaram no teor de carboidratos, carotenoides e proteínas, contudo não afetaram o perfil qualitativo de carotenoides e ácidos graxos. A maior concentração de biomassa (3,35 g L-1) foi obtida com a maior concentração de nitrogênio testada. Mantendo-se a temperatura fixa (27 °C) realizaram-se cultivos com concentração de nitrogênio entre 300 mg L-1 e 750 mg L-1 NaNO3. A máxima produção de biomassa (5,26 g L-1) e carotenoides (2,06 mg g-1) foi obtida com concentração de nitrogênio de 650 mg L-1 NaNO3. As cinéticas de crescimento e consumo de nitrogênio em batelada foram ajustadas a modelos fenomenológicos. O modelo matemático proposto neste trabalho mostrou o melhor ajuste para biomassa (R2 = 0,994) e consumo de nitrogênio (R2 = 0,996). A partir deste modelo foram realizadas simulações de cultivo em modo de operação batelada repetida e contínuo com diferentes taxas de diluição e os cultivos com as maiores produtividades de biomassa preditas foram validados experimentalmente. As culturas em batelada repetida apresentaram produtividade de biomassa menor que a predita, enquanto que a contínua apresentou produtividade similar à predita pelo modelo (1,09 ± 0,01 g L-1 d-1). Os cultivos em batelada-repetida e contínuo apresentaram biomassa com maiores teores de proteínas, ácidos graxos poli-insaturados ômega 3 e carotenoides quando comparados à batelada. O cultivo contínuo foi repetido utilizando CO2 proveniente da fermentação alcoólica da produção de vinho como fonte de carbono, o qual apresentou comportamento similar ao cultivo com a CO2 comercial. Por fim, avaliou-se os efeitos da intensidade e dos comprimentos de onda da luz no crescimento e na composição da microalga H. luteoviridis. As culturas iluminadas por LED brancos com intensidade máxima de 1500 μmol m-2 s-1 apresentaram maiores produtividades de biomassa (0,29 g L-1 d-1). Comparando culturas iluminadas por LEDs vermelhos e/ou azuis, os primeiros estimularam o crescimento da biomassa enquanto que os últimos estimularam a biossíntese de carotenoides, lipídeos e proteínas. / Microalgae are known for their high photosynthetic activity and by the production of high-value products. Essential nutrients, like nitrogen and carbon, light intensity, and temperature are responsible for substantial changes in biomass and compounds production. This work aimed to study the parameters as concentration of nitrogen, temperature variation, lighting regime and operation regime of the photobioreactor (batch, repeated-batch and continuous) that affect biomass production and composition (proteins, lipids, carbohydrates, fatty acids and carotenoids) of the microalga Heterochlorella luteoviridis, and to develop an integrated culture system to use the CO2 from alcoholic wine fermentation to grow the microalga. Firstly, the effects of temperature (22 °C to 32 °C) and nitrogen concentration (75 mg L-1 to 375 mg L-1 NaNO3) were evaluated. Both parameters affected carbohydrates, carotenoids and protein contents in the biomass but did not affect the qualitative profile of carotenoids and fatty acids. The highest biomass concentration (3.35 g L-1) was achieved at the highest nitrogen concentration. New cultures were performed using nitrogen concentration between 300 mg L-1 and 750 mg L-1 NaNO3, and keeping temperature fixed at 27 °C. The maximal biomass and carotenoid production, 5.26 g L-1 and 2.06 mg g-1, were achieved using 650 mg L-1 NaNO3. The biomass growth and nitrogen consumption were adjusted by phenomenological models. The model proposed in this work showed the highest adjust for biomass (R² = 0.994) and nitrogen (R² = 9.996) data. This model was used to simulate repeated-batch and continuous cultures using several dilution rates. The cultures with the highest predicted biomass productivities were experimentally validated. The repeated-batch cultures showed lower biomass productivities than the predicted one, while the continuous culture showed biomass productivity similar to the one predicted by the model (1.09 ± 0.01 g L-1 d-1). The biomass resultant from these cultures had higher contents of proteins, omega-3 polyunsaturated fatty acids and carotenoids, compared to the biomass from batch cultures. The continuous culture was repeated using CO2 from wine fermentation as a carbon source. The results were similar to the ones using commercial CO2, showing the feasibility of the integrated process. Finally, the effects of light intensity and wavelength were evaluated on the growth and composition of H. luteoviridis biomass. Cultures illuminated with white LEDs at maximum intensity of 1500 μmol m-2 s-1 showed the higher biomass productivity, 0.29 g L-1 d-1. Comparing cultures illuminated with red and/or blue LEDs, the former stimulated biomass growth and the latter the carotenoid, lipids and protein biosynthesis.

Dynamic contrast enhanced (DCE) cardiac magnetic resonance imaging (MRI) is well-established as a non-invasive method for qualitatively detecting obstructive coronary artery disease (CAD) which can impair myocardial blood flow and may result in myocardial infarction. Mathematical modelling of cardiac DCE-MRI data can provide quantitative assessment of myocardial blood flow. Quantitative assessment of myocardial blood flow may have merit in further stratification of patients with obstructive CAD and to improve the diagnosis and prognostication of the disease in the clinical setting. This thesis investigates the development of a quantitative analysis protocol for cardiac DCE-MRI data. In the first study presented in this thesis, Fermi and distributed parameter (DP) modelling are compared in single bolus versus dual bolus analysis. For model-based myocardial blood flow quantification, the convolution of a model with the arterial input function (i.e. contrast agent concentration-time curve extracted from the left ventricular cavity) is fitted to the tissue contrast agent concentration-time curve. In contrast to dual bolus DCE-MRI protocols, single bolus protocols reduce patient discomfort and acquisition protocol duration/complexity but, are prone to arterial input function saturation caused in the left ventricular cavity by the high concentration of contrast agent during bolus passage. Saturation effects can degrade the accuracy of quantification using Fermi modelling. The analysis presented in this study showed that DP modelling is less dependent on arterial input function saturation than Fermi modelling in eight healthy volunteers. In a pilot cohort of five patients, DP modelling detected for the first time reduced myocardial blood flow in all stenotic vessels versus standard clinical assessments. In the second study, it was investigated whether first-pass DP modelling can give accurate myocardial blood flow, against ideal values generated by numerical simulations. Unlike Fermi modelling which is convolved with only the first-pass range of the arterial input function, DP modelling is convolved with the entire contrast agent concentration-time course. In noisy and/or dual bolus data, it can be particularly challenging to identify the end point of the first-pass in the arterial input function. This study demonstrated that contrary to Fermi modelling, myocardial blood flow analysis using DP modelling does not depend on the number of time points used for fitting. Furthermore, this data suggests that DP modelling can reduce the quantitative variability caused by subjectivity in selection of the first-pass range in cardiac MR data. This in turn may help to facilitate the development of more automated software algorithms for myocardial blood flow quantification. In the third study, Fermi and DP modelling were compared against invasive clinical assessments and visual MR estimates, to assess their diagnostic ability in detecting obstructive CAD. A single bolus DCE-MRI protocol was implemented in twentyfour patients. In per vessel analysis, DP modelling reached superior sensitivity and negative predictive value in detecting obstructive CAD compared to Fermi modelling and visual estimates. In per patient analysis, DP modelling reached the highest sensitivity and negative predictive value in detecting obstructive CAD. These studies show that DP modelling analysis of cardiac single bolus DCE-MRI data can provide important functional information and can establish haemodynamic biomarkers to non-invasively improve the diagnosis and prognostication of obstructive CAD.

Durante a solidificação de ligas metálicas, a decantação de grãos equiaxiais pode causar: macrossegregação, mudança na posição da transição colunar-equiaxial e alteração no tamanho de grão equiaxial. O objetivo do presente trabalho é a implementação e análise de um modelo matemático para simular a solidificação sob efeito da decantação de grãos. Este modelo combina: (a) a técnica do autômato celular bi-dimensional em escala microscópica considerando a decantação de grãos, (b) um submodelo microscópico baseado em equações de conservação para simular os processos internos aos grãos e (c) um submodelo macroscópico também baseado em equações de conservação para simular os processos importantes da escala de tamanho macroscópica. Os submodelos macroscópico e microscópico compartilham informações correspondentes às suas escalas características de tamanho através de um método de acoplamento. O modelo matemático completo foi examinado inicialmente através da simulação de diversas situações idealizadas como: a decantação de uma esfera sólida, a decantação de um conjunto de esferas porosas e a decantação e solidificação simultânea de um grão dendrítico isolado e imerso em um líquido super-resfriado. Posteriormente, compararam-se os resultados do modelo para a solidificação isotérmica e para a solidificação unidirecional com resultados disponíveis na literatura obtidos por outros modelos numéricos e por técnicas experimentais. Os resultados do modelo mostraram que a decantação de grãos resulta nos seguintes efeitos no caso da solidificação unidirecional: variação de tamanho médio de grãos e macrossegregação ao longo do lingote e alteração ou até eliminação na posição da transição colunar-equiaxial. / During solidification of metallic alloys, the settling of equiaxed grains can cause macrosegregation, change the position of the columnar-to-equiaxed transition, and change the grain size of equiaxed grains. The objective of the present work is to implement and analyze a mathematical model to simulate the solidification under the effect of grain settling. The present model combines: (a) the cellular automaton technique in two dimensions applied in the microscopic lengthscale to account for the movement of grains; (b) a microscopic submodel based on conservation equations to simulate important phenomena occurring within the grains, and (c) a macroscopic submodel, also based on conservation equations, to simulate important phenomena of the macroscopic lengthscale. Using a strong coupling scheme, the macroscopic and microscopic submodels share important information specific to their typical lengthscales. The complete mathematical model was initially examined in several idealized conditions: the settling of a single solid sphere; the settling of a group of porous spheres; and the growth of a single dendritic grain settling in an undercooled liquid. The model was also used to simulate the isothermal solidification and the unidirectional solidification. For these cases, the outcome of the model was compared with experimental and calculated results available in the literature. For the unidirectional solidification, the model results showed that the settling of grains can cause a variation in the macrosegregation and grain size along the ingot and can change the position or even eliminate the columnar-to-equiaxed transition region.

A presente pesquisa buscou resolver o problema de planejamento de operações submarinas através das perspectivas de programação de tarefas e dimensionamento de frota. O problema consistiu em estabelecer a melhor sequência de tarefas a serem atendidas por embarcações levando em consideração sua compatibilidade, regras de sequenciamento e o tamanho da frota. O problema é uma extensão do modelo clássico de roteirização com janelas de tempo com o objetivo de minimizar os custos associados à roteirização e as perdas econômicas associadas às interrupções de produção. A resolução do trabalho concentrou-se no curto e longo prazo, utilizando como principal método de solução a heurística Simulated Anneling por meio de um algoritmo de simulação-otimização. / This research aimed at solving the problem of planning underwater operations that involves job scheduling and fleet sizing decisions. The problem consisted in establish the best sequence of tasks to be atended by vessels taking into account compatibility constraints, sequencing rules and the size of the fleet. The problem is an extension of the classical vehicle routing problem with time windows. The objective is to minimize the routing costs and the economic losses associated with production losses. The solution procedure focused on short and long-term decisions based on the heuristic Simulated Anneling through a simulation-optimization algorithm.

In this thesis, we consider four different problems in membrane filtration, using a different mathematical approach in each instance. We account for the fluid-driven deformation of a filtercake using nonlinear poroelasticity in Chapter 2. By considering feeds with very high and very low particle concentrations, we introduce a quasi-static caking model that provides a suitable approximation to the full model for the physically realistic concentration regimes. We illustrate the agreements and differences between our model and the existing conventional cake-filtration law. In Chapter 3, we introduce a stochastic model for membrane filtration based on the quantised nature of the particles and show how it can be applied for feeds with different particle types and membranes with an interconnected pore structure. This allows us to understand the relation between the effects of clogging on the level of an individual pore and on the macroscopic level of the entire membrane. We conclude by explaining the transition between the discrete and continuous model based on the Fokker--Planck equation. In Chapter 4, we consider the inverse problem of determining the underlying filtration law from the spreading speed of a particle-laden gravity current. We first couple the theory of gravity currents with the stochastic model developed in Chapter~3 to determine a filtration law from a given set of experiments. We then generalise this idea for the porous medium equation, where we show that the position of the front follows a power law for the conventional filtration laws, which allows us to infer the clogging law in certain instances. We conclude the thesis by showing in Chapter 5 how we can combine experimental measurements for the clogging of a depth filter and simple fluid dynamics to accurately predict the pressure distribution in a multi-capsule depth filter during a filtration run.

Engine manufacturers are constantly seeking avenues to build cleaner and more ef cient engines to meet ever increasing stringent emission legislations. This requires a closer under- standing of the in-cylinder physical and chemical processes, which can be obtained either through experiments or simulations. The advent of computational hardware, methodologies and modelling approaches in recent times make computational uid dynamics (CFD) an important and cost-effective tool for gathering required insights on the in-cylinder ow, combustion and their interactions. Traditional Reynolds-Averaged Navier-Stokes (RANS) methods and emerging Large Eddy Simulation (LES) techniques are being used as a reli- able mathematical framework tools for the prediction of turbulent ow in such conditions. Nonetheless, the combustion submodels commonly used in combustion calculations are developed using insights and results obtained for atmospheric conditions. However, The combustion characteristics and its interaction with turbulence at Internal combustion (IC) engine conditions with, high pressure and temperatures can be quite different from those in conventional conditions and are yet to be investigated in detail. The objective here is to apply FlaRe (Flamelets revised for physical consistencies) model for IC engines conditions and assess its performance. This model was developed in earlier studies for continuous combustion systems. It is well accepted that the laminar burning velocity, SL, is an essential parameter to determine the fuel burn rate and consequently the power output and ef ciency of IC engines. Also, it is involved in almost all of the sophisticated turbulent combustion models for premixed and partially premixed charges. The burning velocities of these mixtures at temperatures of 850 ≤ T ≤ 950 decrease with pressure up to about 3 MPa as it is well known, but it starts to increase beyond this pressure. This contrasting behaviour observed for the rst time is explained and it is related to the role of pressure dependent reaction for iso-octane and involving OH and the in uence of this radical on the fuel consumption rate. The results iv seem to suggest that the overall order of the combustion reaction for iso-octane and gasoline mixture with air is larger than 2 at pressures higher than 3 MPa. The FlaRe combustion is used to simulate premixed combustion inside a spark-ignition engine. The predictive capabilities of the proposed approach and sensitivity of the model to various parameters have been studied. FlaRe approach includes a parameter βc representing the effects of ame curvature on the burning rate. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities may be stronger in IC engines and thus this parameter is less likely to be constant. The sensitivity of engine simulation results to this parameter is investigated for a range of engine speed and load conditions. The results indicate some sensitivity and so a careful calibration of this parameter is required for URANS calculation which can be avoided using dynamic evaluations for LES. The predicted pressure variations show fair agreement with those obtained using the level-set approach. DNS data of a hydrogen air turbulent premixed ame in a rectangular constant volume vessel has been analysed to see the effect of higher pressure and temperature on the curvature parameter βc. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities are expected to be stronger in IC engines and thus the parameter βc may not be constant. To shed more light on this, two time steps from the DNS data has been analysed using dynamic βc procedure. The results show that the effect of higher pressure and temperature need to be considered and taken into account while evaluating βc. When combustion takes place inside a closed vessel as in an IC engine the compression of the un-burnt gases by the propagating ame causes the pressure to rise. In the nal part of this thesis, the FlaRe combustion model is implemented in a commercial computational uid dynamics (CFD) code, STAR-CD, in the LES framework to study swirling combustion inside a closed vessel. Different values of βc has been tested and the need for dynamic evaluation is observed.

It has been shown that prolonged systemic presence of a drug can cause a build up of that drug in the skin. This drug ‘reservoir’, if properly understood, could provide useful and important information about the recent drug-taking history of a patient. In this thesis we create three mathematical models which combine to explore the potential for a drug reservoir to form in the skin and be collected as a method of monitoring compliance. The first model is used to characterise timedependent drug concentrations in plasma and tissue following a customisable drug regimen. Outputs from this model provide boundary conditions for the second, spatio-temporal model of drug build-up and concentration profile in the skin. This then provides initial conditions for the final model which predicts the extraction. These models are then used to identify the scenarios which have the greatest potential for successfully monitoring patient compliance via the skin. We focus in particular on drugs that are highly bound as this will restrict their potential to move freely into the skin but which are lipophilic so that, in the unbound form, they would demonstrate an affinity to the outer layers of the skin (which are built around a lipid matrix). We highlight how this study might be used to inform future experimental design and data collection in order to provide relevant parameter estimates for reservoir formation and its potential to contribute to enhanced drug monitoring techniques.

Orientador: Helenice de Oliveira Florentino Silva / Resumo: A escassez de combustíveis fósseis e a demanda por fontes alternativas de energia renovável e limpa são impulsionadores para o desenvolvimento de biocombustíveis, tais como o biohidrogênio. Este gás é conhecido por seu alto valor calorífico, extrema leveza e baixa densidade, além de, ao ser queimado, produzir apenas vapor d'água e calor. Dentre os modos de produção, destaca-se a fermentação escura, a qual gera biohidrogênio e subprodutos através do tratamento microbiológico de resíduos agroindustriais. O objetivo deste trabalho foi modelar matematicamente este bioprocesso, estudar suas propriedades à luz da teoria de estabilidade, além de propor um modelo de otimização que determine uma combinação das concentrações de substrato e bactérias, tais que maximizem o rendimento da produção de biohidrogênio. Foram propostas duas heurísticas para a resolução do modelo, Algoritmo de Busca em Vizinhança Variável e Algoritmo Memético. Os resultados das simulações numéricas mostraram que o modelo obtido corrobora com a dinâmica bioquímica e microbiológica do bioprocesso. / Abstract: The lack of fossil fuels and the demand of alternative, renewable and clean energy sources promote development in biofuels, as biohydrogen. It is known by its high heat, extreme lightness and low density and also when it burns, the products are only steam and energy. Among the productions ways, we highlight dark fermentation, which generates biohydrogen and subproducts through organic waste microbiological treatment. The aim of this work was to mathematical model this bioprocess, to study its properties via stability analysis, besides to propose a optmization model to determine a combination of substract and bacteria concentrations, in order to maximize biohydrogen production yield. To solve the mathematical model have been proposed two heuristics: Variable Neighboor Search Algorithm and Memetic Algorithm. Numeric simulations showed that the mathematical model corroborates with the bioprocess microbial and biochemical dynamics. / Mestre

Cardiac disease is the most common cause of death among the adult population worldwide and atrial fibrillation (AF) is the most common cardiac arrhythmia. The state of the art in AF treatment involves creating lesions of heart tissue through radiofrequency ablation. In this thesis, mathematical modelling techniques are developed to design decision support tools that could help a cardiologist determine the best location to ablate in clinic. Firstly, parameter optimisation methods are explored to adapt a model designed for the ventricles to the atria, and a novel technique is introduced to characterise pathways through parameter space from a healthy state to a diseased state using a multi-objective genetic algorithm. Next, I reproduce clinical signals recorded during AF ablation through the use of a phenomenological model of the cardiac action potential on a cylinder and show how this model can enable us to recover information lost in clinic to improve clinical decision. This is followed by introducing a more simplistic approach to the same problem, by characterising the electrical activity on the recording by a sine wave. Finally, the effectiveness of these two approaches is compared in the clinical setting by testing both as decision support tools. The emphasis of the approaches throughout the thesis is on developing techniques with clinical applicability. We demonstrate that lost information in clinic can affect the decision made by an experienced clinician, and that the mathematical modelling approaches developed in the thesis can significantly reduce the impact that this information loss can have on clinical decision making.

Esta dissertação apresenta o desenvolvimento de uma pesquisa, acompanhada de experimentação, no curso de Costureira que faz parte do programa Mulheres Mil - PRONATEC no Instituto Federal Sul-rio-grandense sobre Matemática Básica por meio de tarefas de Modelagem Matemática. O objetivo deste trabalho é investigar como é possível despertar o senso crítico das educandas, buscando encontrar a importância da Matemática na sociedade a partir de tarefas que lhes permitam refletir e interferir na realidade em que vivem. Os referenciais teóricos são a Educação Matemática Crítica segundo Skovsmose (2012) e a Modelagem Matemática em uma perspectiva Sócio-crítica de Barbosa (2001). Para analisar as contribuições/ reflexões das alunas, nos apoiamos na Análise do Conteúdo de Bardin (2006). A análise dessas contribuições aponta indicativos de reflexões e reações das alunas alinhadas com os interesses da Educação Matemática Crítica. / This dissertation shows the development of a research, followed by experimentation, in the Seamstress Course which is part of Mulheres Mil - PRONATEC Program offered by Sul-rio-grandense Federal Institute about Financial Mathematics using mathematical modeling tasks. The aim of this study is to investigate how it is possible to awake the students‟ critical sense, seeking to find the importance of Mathematics in the society using tasks that allow to think and interfere in the reality where they live. The theoretical frameworks are Critical Mathematic Education according to Skovsmose (2012) and the Mathematical Modelling by Barbosa‟s Socio-critical perspective (2001). To analyze the students‟ contribuitions/reflections, we were based on the Content Analysis, according to the model of Bardin (2006). The analysis of theses contribuitions shows indicatives of the students‟ reflections and reactions aligned with the Critical Mathematics Education‟s interest.