With the introduction of a computational design environment, architectural design and representation processes witness a radical transition from the analog to the digital medium, that may be asserted to initiate a paradigm shift affecting both. In this new design environment, extending the instrumentality of computer-aided processes to the generative use of computational tools and procedures, architectural design and representation processes are subject to mutual alterations, challenged with computational design strategies such as parametric design, associative geometry, generative diagrams, scripting and algorithmic procedures. Computational design approaches proceed with the definition of a mathematical model based on the numeric definition of relations and equations, substituting the conventional visual/orthographic representation. This thesis aims to inquire the outcomes of assuming non-visual/numeric representation as a strategy in the therefore redefined process of architectural representation. Through the generative logic embedded in the mathematical model, attention shifts from form to process. This emphasis on process rather than the formal outcome, aids the experimentation of a desired indeterminacy, coming forth in dynamic, non-linear design processes, blurring the boundaries between different phases of design, and of representation. The intentional search for a generative design process liberated from the visual/formal determinism of the conventional design approach, initiates a conscious delay in the definition of form, and thus of visual representation. The thesis discusses the potentials presented by generative mathematical models defined with the aid of computational design tools, and the ways in which they alter and inform architectural design and representation.

The worldwide increase in antibiotic resistance is a concern for public health. When the appropriate antibiotic dosage is determined, the priorities are efficacy and toxicity. The aim of this thesis was to gain knowledge about the most efficient dosing regimens in order to minimize the emergence and selection of antibiotic-resistant mutants. We also wanted to assess the impact of antibiotic selective pressure and host to host transmission for the dissemination of resistance. Escherichia coli bacteria with different levels of cefotaxime susceptibility were competed in an in vitro kinetic model, demonstrating a complex selection of low-level resistance influenced e.g. by the time duration of selective concentrations and the rise of new mutants. We also constructed a mathematical model incorporating biologically relevant parameters and showed its usefulness when assessing the risks of resistance development. When E. coli populations with pre-existing fluoroquinolone-resistant mutants were exposed to simulated serum concentrations, several currently used doses of fluoroquinolones clearly enhanced the development and selection of resistance. The mutant prevention concentration (MPC) was measured for several E. coli isolates with different fluoroquinolone susceptibilities, and because of fluctuating antibiotic concentrations in the human body, the pharmacokinetics was considered when evaluating MPC. Results indicate that the area under the serum concentration time curve in relation to the MPC may be a useful predictor for emergence of resistance. In the commensal flora of healthy human couples we noted a high frequency of trimethoprim-resistant E. coli. There was also an extensive sharing and transmission of E. coli clones. Treating the female with trimethoprim reduced the number of intestinal E. coli which might have facilitated the transmission from the male partner. These findings suggest that the rate of transmission is high and effectively contributes to the spread of both susceptible and antibiotic-resistant E. coli in intrafamilial settings.

Articular cartilage is the translucent, heterogeneous three-component biological load processing gel that overlays the end of the articulating bones of mammalian joints. Normally, healthy intact articular cartilage performs two biomechanical functions very effectively. These are (i) redistribution of stresses due to loads acting on the joint; (ii) act as a near-frictionless interface between contacting bone ends. These principal functions are enabled by its highly elastic properties. Under normal physiological conditions, these essential biomechanical functions are provided over the lifetime of a mammalian joint with little or no degenerative changes. However, certain levels of physiological and traumatic loads and degenerative processes induced by activities such as running, walking, extreme sport, and aging can alter the composition and structure of the tissue, leading to changes in its biomechanical properties. This, inturn, influences its functional characteristics. The most common degenerative change in articular cartilage is osteoarthritis and the management and treatment of this disease is pivotal to all research targeted toward articular cartilage. Several scientific groups around the world have developed models of articular cartilage to predict its fundamental and functional responses to load and altered biochemical conditions through both in vivo and in vitro studies. The most predominant of these models are the biphasic and triphasic models, which are based on the conceptualisation of articular cartilage as a dispersed mixture of its three main components namely collagen fibrils proteoglycan aggregates and water. The triphasic model is an extension of the biphasic model and incorporates swelling as a separate identifiable component of the tissue's biomechanical response. While these models are capable of predicting the elastic and viscoelastic behaviour and certain aspects of the swelling characteristics of articular cartilage, they are incapable of accounting for its short-term responses where the fluid component is the main carrier of the applied pressure. The hydrostatic and swelling components of the fluid content determine the manner of stress-sharing and hence transient load processing within the matrix as stress is transmitted to the underlying structure. Furthermore, the understanding of the nature of this stress-sharing between fluid and solid components of the tissue is fundamental to the comprehension of the nature of degeneration and its biomechanical consequence in the function of the articulating joint. The inability of the biphasic and triphasic theories to predict, in accordance with experimental results, the transient behaviour of the loaded matrix fluid requires a more representative model. This imperative therefore forms the basis for the research work presented in this thesis. In this thesis, a new mathematical model of articular cartilage load carriage is presented which can predict the transient load-induced responses. The model is based on a continuum framework invoking the principle of mechanical consolidation of fluid-saturated, swollen porous elastic materials. The cartilage matrix is conceptualised as a heterogeneous anisotropic fluid-saturated porous material in which its solid component responds to load as a hyperelastic material and whose interaction with the swelling component produces a partially distributed time-varying permeability. In accordance with the principle of consolidation, a phenomenological approach is adopted for developing both analogue/engineering models and mathematical models for the tissue. The models are then used to predict both bulk matrix responses and the properties of the hypothetical layers of the tissue when subjected to physiological loading conditions. Ultimately, the generalized mathematical model is used to analyse the effect of superficial layer laceration on the stress-processing or stress-sharing characteristic of normal healthy articular cartilage. Finally, predicted results are shown to compare with experimental data demonstrating that the new models for swelling deformation, the hyperelastic law for solid skeletal structure and the distributed, time-dependent permeability are representative of the articular cartilage.

Author also know as S M Loveday / Fresh bakery products have a very short shelf life, which limits the extent to which manufacturing can be centralised. Frozen doughs are relatively stable and can be manufactured in large volumes, distributed and baked on-demand at the point of sale or consumption. With appropriate formulation and processing a shelf life of several months can be achieved.Shelf life is limited by a decline in proofing rate after thawing, which is attributed to a) the dough losing its ability to retain gas and b) insufficient gas production, i.e. yeast activity. The loss of shelf life is accelerated by delays between mixing and freezing, which allow yeast cells the chance to ferment carbohydrates.This work examined the reasons for insufficient gas production after thawing frozen dough and the effect of pre-freezing fermentation on shelf life. Literature data on yeast metabolite dynamics in fermenting dough were incomplete. In particular there were few data on the accumulation of ethanol, a major fermentation end product which can be injurious to yeast.Doughs were prepared in a domestic breadmaker using compressed yeast from a local manufacturer and analysed for glucose, fructose, sucrose, maltose and ethanol. Gas production after thawing declined within 48 hours of frozen storage. This was accelerated by 30 or 90 minutes of fermentation at 30;C prior to freezing.Sucrose was rapidly hydrolysed and yeast consumed glucose in preference to fructose. Maltose was not consumed while other sugars remained. Ethanol, accumulated from consumption of glucose and fructose, was produced in approximately equal amounts to CO2, indicating that yeast cells metabolised reductively.Glucose uptake in fermenting dough followed simple hyperbolic kinetics and fructose uptake was competitively inhibited by glucose. Mathematical modelling indicated that diffusion of sugars and ethanol in dough occurred quickly enough to eliminate solute gradients brought about by yeast metabolism.

Master of Science / In vivo many forms of glia utilise both intercellular and extracellular pathways in the form of IP3 permeable gap junctions and cytoplasmic ATP diffusion to produce calcium waves. We introduce a model of ATP and Ca2+ waves in clusters of glial cells in which both pathways are included. Through demonstrations of its capacity to replicate the results of existing theoretical models of individual pathways and to simulate experimental observations of retinal glia the validity of the model is confirmed. Characteristics of the waves resulting from the inclusion of both pathways are identified and described.

We introduce new methods based on the L2 Optimal Transport (OT) problem and the Navier-Stokes equations to approximate a fluid velocity field from images obtained with Particle Image Velocimetry (PIV) measurements. The main idea is to consider two successive images as the initial and final densities in the OT problem, and to use the associated OT flow as an estimate of the underlying physical flow. We build a simple but realistic model for PIV data, and use it to analyze the behavior of the transport map in this situation. We then design and implement a series of post-processing filters created to improve the quality of the numerical results, and we establish comparisons with traditional cross-correlation algorithms. These results indicate that the OT-PIV procedure performs well on low to medium seeding densities, and that it gives better results than typical cross-correlation algorithms in some cases. Finally, we use a variational method to project the OT velocity field on the space of solutions of the Navier-Stokes equations, and extend it to the rest of the fluid domain, outside the particle locations. This extension provides an effective filtering of the OT solution beyond the local post-processing filters, as demonstrated by several numerical experiments. / Graduate

Orientador: Helenice de Oliveira Florentino Silva / Banca: Adriana Cristina C.Nicola / Banca: Antonio Roberto Balbo / Resumo: A cana-de-açúcar possui grande importância social e econômica para o brasileiro. O Brasil é maior produtor de cana-de-açúcar do mundo, na safra de 2009/2010 a produção foi de 597,8 milhões de toneladas, uma alta de 4,4% em relação às 571,40 milhões de toneladas colhidas em 2008/2009. O país possui 420 Usinas e Destilarias, as quais movimentam cerca de 51 bilhões de reais, o que representa 1,5% do PIB Brasileiro, gerando 4,5 milhões de empregos diretos e indiretos, exportando 23,2 milhões toneladas de açúcar e 3,3 bilhões de litros de etanol, e um investimento médio no país de 6 bilhões de reais ao ano, o que mostra a grande importância da cana-de-açúcar para a economia brasileira. Por outro lado, o crescimento acelerado deste setor tem trazido problemas de grandes dimensões e dificultado o gerenciamento das empresas, estes problemas são de ordens estruturais e ambientais. Por isso é importante conhecer todo processo de cultivo da cana, que vai desde o preparo do solo até processo industrial, que ocorre da recepção da cana até a saída dos produtos, e buscar formas de minimizar os custos de produção. Assim, surge a necessidade de ferramentas que auxiliem os gestores das empresas nas tomadas de decisões. Desta forma, a modelagem matemática pode ser utilizada como uma importante fonte de produção de estimativas para este setor, facilitando cálculos e auxiliando as decisões. O objetivo deste trabalho foi estudar toda a cadeia produtiva de álcool e açúcar e investigar modelos matemáticos para estimar quantitativamente o balanço de energia e o custo de produção, considerando todo o processo de produção de álcool e açúcar, deste o plantio da cana, até a venda destes produtos / Abstract: The sugarcane has great social and economic importance for the Brazilian. Brazil is the largest producer of sugarcane in the world, in 2009/2010 crop production was 597.8 million tons, up 4.4% compared to 571.40 million tonnes harvested in 2008 / 2009. That season the country had 420 mills and distilleries, which handle about 51 billion reais, representing 1.5% of Brazilian GDP, generating 4.5 million direct and indirect jobs, exporting 23.2 million tonnes of sugar and 3.3 billion liters of ethanol, generating an average investment in the country of 6 billion reais a year, which shows the great importance of sugarcane to the Brazilian economy. The accelerated growth of this sector has brought large problems and complicating the management of enterprises these problems are structural and environmental. Therefore it is important to know the whole process of sugar cane cultivation, ranging from soil preparation until industrial process, which occurs in the reception of the cane to the output of products, and seek ways to minimize production costs. Thus it, arises the need for tools that help business managers in making decisions. Thus, mathematical modeling can be used as an important source to estimates the production for this sector, making calculations and aiding decisions. The objective of this work was to study the entire production chain of sugar and alcohol and to investigate mathematical models to quantitatively estimate the cost of production, considering the whole process of producing alcohol and sugar cane, since the plantation until the sale of these products / Mestre

O presente trabalho apresenta a análise térmica do fenômeno de fermentação de cerveja com o objetivo de quantificar a energia liberada durante o processo e avaliar o comportamento do campo de temperaturas do fermentando. É adotada uma metodologia que reúne abordagens teóricas e experimentais, aplicadas a um processo completo de fermentação. O calor dissipado durante a fermentação é calculado por equações presentes na literatura, tendo como entrada a taxa de conversão de glicose e produção de CO2. Essas taxas são calculadas pelas concentrações de glicose medidas de amostras retiradas durante ensaios planejados. A dissipação é usada como entrada em dois modelos térmicos para o cálculo do campo de temperaturas do fermentando. As temperaturas calculadas são superiores àquelas monitoradas experimentalmente, com diferenças de até 78%. Esse comportamento embasa a proposta de uma equação de ajuste do calor liberado durante a fermentação. A equação proposta indica que é liberado 38 kJ por mol de glicose convertido, neste estudo a taxa de dissipação térmica atinge valor máximo de 11,41 Wm-3 e a energia total dissipada é de 385 kJ para produzir 40 litros de cerveja. O ajuste mostrou-se satisfatório, as temperaturas máximas e os campos de temperaturas calculados apresentaram valores equivalentes aos valores experimentais. / The present study carry out a thermal analysis of beer fermentation process which aims to quantify the energy released during the process and evaluate the temperature field, using a methodology that brings together theoretical and experimental approaches. The heat dissipated during the fermentation is calculated by equations reported in the literature, with the conversion rates of glucose and CO2 production as input. These rates are calculated using the glucose concentrations measured of samples taken during tests. The dissipation is used as input in two thermal models for the calculation of temperature field. The calculated temperatures are higher than those monitored experimentally, with differences up to 78%. It supports the proposal of an adjusted equation for heat release of beer fermentation. The proposed equation indicates that 38 kJ per mol of converted glucose is released. In this study, the thermal dissipation rate reaches a maximum value of 11.41 Wm-3 and the total energy dissipated is 385 kJ for producing 40 liters of beer. The adjustment is satisfactory, the maximum temperatures and the temperature fields calculated are equivalent to the experimental values.

Philosophiae Doctor - PhD / Malaria is most prevalent in tropical climates, where there are sufficient rainfall for mosquitoes to breed and conducive temperatures for both the mosquito and protozoa to live. A slight change in temperature can drastically affect the lifespan and patterns of mosquitoes, and moreover, the protozoan itself can only survive in a certain temperature range. With higher temperatures, mosquitoes can mature faster, and thus have more time to spread the disease. The malaria parasite also matures more quickly at warmer temperatures. However, if temperatures become too high, neither mosquitoes nor the malaria pathogen can survive. In addition, stagnant water is also a major contributor to the spread of malaria, since most mosquito species breed in small pools of water. The correct amount and distribution of rainfall increases the possible breeding sites for mosquito larvae, which eventually results in more vectors to spread the disease. With little rainfall, there are few places for the mosquitoes to breed. For these reasons, and in order to control mosquito population, it is important to examine the weather parameters such as temperature and rainfall which are imperative in determining the disease epidemics. Accurate seasonal climate forecasts of these variables, together with malaria models should be able to drive an early warning system in endemic regions. These models can also be used to evaluate the possible change in regions under climate change scenarios, and the spread of malaria to new regions. In this study, we develop and analyse a mosquito model to study the population dynamics of mosquitoes. Ignoring the impact of climate, the model is further developed by introducing human compartments into the model. We perform both analytical and numerical analyses on the two models and verify that both models are epidemiological and mathematical well-posed. Using the next generation matrix method, the basic reproduction number of each system is calculated. Results from both analyses confirm that mosquito- and disease-free equilibria are locally asymptotically stable whenever R0 < 1 and unstable whenever R0 > 1. We further establish the global stability of the mosquito-free equilibrium using a Lyapunov function. In order to examine the effectiveness of control measures, we calculate the sensitivity coefficients of the reproductive number of the mosquito-human malaria model and highlight the importance of mosquito biting rate on malaria transmission. In addition, we introduce climate dependent parameters of Anopheles gambiae and climate data of Limpopo province into the malaria model to study malaria transmission over the province. Climate variables and puddle dynamics are further incorporated into the mosquito model to study the dynamics of Anopheles arabiensis. The climatedependent functions are derived from the laboratory experiments in the study of Maharaj [114], and we further verify the sensitivity of the model to parameters through sensitivity analysis. Running the climate data of Dondotha village in Kwazulu-Natal province over the mosquito model, it is used to simulate the impact of climate variables on the population dynamics of Anopheles arabiensis over the village. Furthermore, we incorporate human compartments into the climate-based mosquito model to explore the impact of climate variability on malaria incidence over KwaZulu-Natal province over the period 1970-2005. The outputs of the climate-based mosquito-human malaria model are further analysed with Principal Component Analysis (PCA), Wavelet Power Spectrum (WPS) and Wavelet Cross-coherence Analysis (WCA) to investigate the relationship between the climate variables and malaria transmission over the province. The results from the mosquito model fairly accurately quantify the seasonality of the population of Anopheles arabiensis over the study region and also demonstrate the influence of climatic factors on the vector population dynamics. The model simulates the population dynamics of both immature and adult Anopheles arabiensis and increases our understanding on the importance of mosquito biology in malaria models. Also, the simulated larval density produces a curve which is similar to observed data obtained from another study. In addition, the mosquito-malaria models produce reasonable fits with the observed data over Limpopo and KwaZulu Natal provinces. In particular, they capture all the spikes in malaria prevalence. Our results further highlight the importance of climate factors on malaria transmission and show the seasonality of malaria epidemics over the provinces. The results of the PCA on the model outputs suggest that there are two major process in the model simulation. One of the processes indicate high loadings on the population of Susceptible, Exposed and Infected humans, while the other is more correlated with Susceptible and Recovered humans. However, both processes reveal the inverse correlation between Susceptible-Infected and Susceptible-Recovered humans respectively. Through spectrum analysis, we notice a strong annual cycle of malaria incidence over the province and ascertain a dominant periodicity of one year. Consequently, our findings indicate that an average of 0 to 120-day lag is generally noted over the study period, but the 120-day lag is more associated with temperature than rainfall. The findings of this study would be useful in an early warning system or forecasting of malaria transmission over the study areas.

O efeito da heterose na produção de leite é de suma importância nos cruzamentos obtidos entre animais de raças europeias e zebuínas. Contudo, são inexistentes pesquisas que comprovem o efeito da heterose sobre os componentes da curva de lactação nos diferentes grupos genéticos da raça Girolando. Objetivou-se utilizar diferentes modelos matemáticos para melhor descrever a curva de lactação a fim de avaliar o efeito de heterose sobre os componentes da curva de lactação dessa população, bem como avaliar o impacto da inclusão do efeito da heterose no modelo sobre as estimativas de parâmetros genéticos para produção de leite até 305 dias obtidas via método REML. Os modelos linear e não linear de Wood, Wilmink e Ali e Shaeffer foram ajustados aos registros produtivos de controles mensais, para posterior estimar forma individual e conjunta (média), o pico de lactação, tempo ao pico, persistência, produção total de leite até 305 dias e os parâmetros específicos dos modelos relacionados com curva de lactação (produção inicial e taxa de decréscimo da produção). Na comparação de todos esses modelos matemáticos quanto à qualidade de ajustamento foram utilizados os critérios RMSE, AIC e BIC No geral, observou-se que a qualidade de ajuste dos modelos diferiu conforme o grupo genético. Foi observado efeito de heterose (P<0,001) para a maioria dos componentes que compõem a curva de lactação, com exceção de algumas medidas de persistência. Dentre os componentes da curva de lactação, o pico de lactação foi o que apresentou efeito de heterose mais expressivo, explicando parcialmente a heterose (20% a 23%) observada na produção de leite até 305 dias. As estimativas de herdabilidade para a produção de leite até 305 dias ajustada ou não pelos modelos matemáticos não lineares quase não variaram (0,14 à 0,20). Verificou-se ainda que a maioria dos grupos genéticos apresentaram efeito de heterose para a produção de leite até 305 dias, porém os maiores efeitos ocorreram em vacas 1/2H com 1112,73 kg a mais em relação à média de seus pais puros. Assim, pode se concluir que os benefícios da heterose para a raça Girolando são evidentes e mostram ser mais relacionados com os componentes da fase inicial da curva da lactação refletindo na expressão da heterose para a produção de leite até 305 dias, principal característica da atividade leiteira. / The effect of heterosis on milk yield is fundamental in cross breeding between European breeds and zebu. However, there is a lack of studies on the heterosis effect of the components of lactation curve in the different crossbred genetic groups of Girolando Cattle. The objective was to use different mathematical models to better describe the lactation curve in order to evaluate the effect of heterosis on the components of the lactation curve of this population, as well as to evaluate the impact of the inclusion of the heterosis effect in the model on the estimation of the genetic parameters for 305-day milk yield obtained by REML method. Wood’s, Wilmink’s, and Ali and Shaeffer’s models were fitted to the monthly test day milk yield records, to estimate individual and joint (average) shape, peak yield, time to peak, persistency, 305-day milk yield and the specific parameters of the models associated to the lactation curve (initial stage of lactation and rate of decrease of production). RMSE, AIC, and BIC criteria were used in order to compare the quality of fit of the different mathematical models. In general, the quality of fit of the models differed in the genetic groups The effect of heterosis was significant (P <0.001) for most of the components that of the lactation curve, with the exception of some measures of persistency. Among the components of the lactation curve, the peak of lactation presented the most expressive heterosis effect, which partially could explain the heterosis (20% to 23%) on 305-day milk yield. Estimates of heritability for 305-day milk yield presented a low variation (0.14 to 0.20). Most of the groups presented heterosis effect for 305-day milk yield, but the highest effects were on 1/2H cows. The 305-day milk yield of 1/2H was 1112.73 kg higher than that in the average between parental pure breeds. Thus, it can be concluded that the benefits of heterosis to the Girolando breed are evident. The heterosis is associated to the components of the initial stage of the lactation curve, which is reflected in the expression of heterosis for 305-day milk yield, the most important trait of economic interest in Brazil.