Three dimensional flow regimes are encountered in many types of industrial flow processes such as filtration, mixing, reaction engineering, polymerization and polymer forming as well as environmental systems. Thus, the analyses of phenomena involved fluid flow are of great importance and have been subject of numerous ongoing research projects. The analysis of these important phenomena can be conducted in laboratory through experiments or simply by using the emerging computational fluid dynamics (CFD) techniques. But when dealing with three dimensional fluid flow problems, the complexities encountered make the analysis via the traditional experimental techniques a daunting task. For this reason, researchers often prefer to use the CFD techniques which with some care taken, often produce accurate and stable results while maintaining cost as low as possible. Many CFD codes have been developed and tested in the past decades and the results have been successful and thus encouraging researchers to develop new codes and/or improve existing codes for the solutions of real world problems. In this present project, CFD techniques are used to simulate the fluid flow phenomena of interest by solving the flow governing equations numerically through the use of a personal computer. The aim of this present research is to develop a robust and reliable technique which includes a novel aspect for the solution of three dimensional generalized Newtonian fluids in domains including obstructions, and this must be done bearing in mind that both accuracy and cost efficiency have to be achieved. To this end, the finite element method (FEM) is chosen as the CFD computational method. There are many existing FEM techniques namely the streamline upwind Petrov-Galerkin methods, the streamline diffusion methods, the Taylor-Galerkin methods, among others. But after a thorough analysis of the physical conditions (geometries, governing equations, boundary conditions, assumptions …) of the fluid flow problems to be solve in this project, the appropriate scheme chosen is the UVWP family of the mixed finite element methods. It is scheme originally developed to solve two dimensional fluid flow problems but since the scheme produced accurate and stable results for two dimensional problems, then attempt is made in this present study to develop a new version of the UVWP scheme for the numerical analysis of three dimensional fluid flow problems. But, after some initial results obtained using the developed three dimensional scheme, investigations were made during the course of this study on how to speed up solutions' convergence without affecting the cost efficiency of the scheme. The outcomes of these investigations yield to the development of a novel scheme named the modified three dimensional UVWP scheme. Thus a computer model based on these two numerical schemes (UVWP and the Modified UVWP) is developed, tested, and validated through some benchmark problems, and then the model is used to solve some complicated tests problems in this study. Results obtained are accurate, and stable, moreover, the cost efficiency of the computer model must be mentioned because all the simulations carried out are done using a simple personal computer.

In everyday situations individuals make decisions. For example, a tourist usually chooses a crowded or recommended restaurant to have dinner. Perhaps it is an individual decision, but the observed pattern of decision-making is a collective phenomenon. Collective behaviour emerges from the local interactions that give rise to a complex pattern at the group level. In our example, the recommendations or simple copying the choices of others make a crowded restaurant even more crowded. The rules of interaction between individuals are important to study. Such studies should be complemented by biological experiments. Recent studies of collective phenomena in animal groups help us to understand these rules and develop mathematical models of collective behaviour. The most important communication mechanism is positive feedback between group members, which we observe in our example. In this thesis, we use a generic experimentally validated model of positive feedback to study collective decision-making. The first part of the thesis is based on the modelling of decision-making associated to the selection of feeding sites. This has been extensively studied for ants and slime moulds. The main contribution of our research is to demonstrate how such aspects as "irrationality", speed and quality of decisions can be modelled using differential equations. We study bifurcation phenomena and describe collective patterns above critical values of a bifurcation points in mathematical and biological terms. In the second part, we demonstrate how the primitive unicellular slime mould Physarum Polycephalum provides an easy test-bed for theoretical assumptions and model predictions about decision-making. We study its searching strategies and model decision-making associated to the selection of food options. We also consider the aggregation model to investigate the fractal structure of Physarum Polycephalum plasmodia. / <p>Fel serie i tryckt bok /Wrong series in the printed book</p>

L'objectif primordial de cette thèse est la recherche de modèles mathématiques qui sont à mieux de décrire le processus d'absorption gaz-liquide dans un contacteur membranaire à fibres creuses poreuses ou denses. La configuration géométrique de ces contacteurs combinée à leur compacité, et de leur faible consommation d'énergie leur permet de se substituer progressivement aux procédés conventionnels tels les colonnes à garnissage et autres tours d'absorption. Notre but est d'étudier la performance de ces processus novateurs par l'élaboration de modèles mathématiques de plus en plus rigoureux. Pour cela, nous avons étudié plusieurs cas de figures où l'hydrodynamique d'écoulement des fluides, la nature du soluté et/ou du solvant ont été changées. Dans un premier temps, il n'a été tenu compte que de l'hydrodynamique du compartiment côté fibre pour deux types de processus d'absorption avec et sans réaction chimique. Par la suite, l'hydrodynamique d'écoulement des fluides dans le côté fibre comme côté calandre a été prise en considération. Des modèles ont été développés pour l'absorption classique de gaz carbonique dans des solutions de monoéthanolamine (liquide d'absorption de référence) où l'écoulement du fluide côté calandre est assimilé à un écoulement piston dans un premier cas, obéissant au modèle dit de surface libre "modèle de Happel" dans un deuxième cas, et enfin caractérisé par des équations de moments de Navier-Stokes dans un troisième cas. La comparaison des résultats numériques de ces modèles a montré que ceux du troisième cas de figure sont les plus proches des résultats d"essais expérimentaux / The overarching objective of this thesis is the research of mathematical models which are better to describe the process of gas-liquid absorption in a membrane contactor with porous or dense hollow fibers. The geometric configuration of these contactors, combined with their low energy consumption and their compactness, allows them to gradually replace conventional processes such as packing towers and absorption columns. Our goal is to study the performance of these innovative processes by developing more rigorous mathematical models. In this scope, we studied several cases where the hydrodynamics of fluid flow, the nature of the solute or solvent have been changed. First, only the hydrodynamics of the fibre side compartment has been taken into account for two types of an absorption process with and without chemical reaction. Subsequently, the hydrodynamics of fluid flow in both the fiber side as shell side were taken into consideration. Models have been developed for classical carbon dioxide absorption in monoéthanolamine solutions (liquid absorption of reference) where the flow fluid in the shell were is assumed to obey a plug-flow in a first case, described by the surface free model known as "Happel model" in a second case, and finally characterized by the momentum Navier-Stokes equations in a third case. The comparison of the numerically simulated results collected from the three models showed that those of the third case matched very closely with the laboratory experimental results

Le présent manuscrit de thèse présente l'étude de différents phénomènes dans un convertisseur d?acier, grâce au développement de deux modèles distincts. Le premier modèle décrit la cavité produite à la surface libre du bain de métal par l'impact du jet d'oxygène supersonique. Il est basé sur le découpage du domaine de calcul en deux régions. Les effets de compressibilité du gaz sont pris en compte uniquement dans la région du jet où la vitesse est élevée, alors que partout ailleurs, le gaz est considéré comme incompressible. La méthode Volume Of Fluid (VOF) est utilisée pour suivre la déformation de la surface libre du bain. Les résultats de simulations sont présentés pour des systèmes bi- et triphasés et comparés à des données expérimentales obtenues dans diverses maquettes froides. L'influence sur la taille et la forme de la cavité de différents paramètres (parmi lesquels les conditions aux limites en sortie de la lance d'injection, le schéma d'advection de la méthode VOF et le modèle de turbulence) est étudiée. Le modèle est ensuite utilisé pour simuler l'interaction entre un jet supersonique d'oxygène et la surface libre d'un bain d'acier liquide dans un convertisseur de taille pilote. Le second modèle se focalise sur l'écoulement du gaz, le transfert de chaleur et la réaction de postcombustion dans la phase gazeuse au-dessus du bain de métal. Il utilise l'algorithme Simple Chemical Reaction Scheme pour décrire le transport des espèces chimiques, et prend en compte l'absorption d'oxygène dans le bain et les transferts thermiques par rayonnement. Les prédictions numériques sont en assez bon accord avec les mesures recueillies dans une expérience de laboratoire et dans un four à l'échelle pilote / The present thesis treats different phenomena taking place in a steelmaking converter through the development of two separate models. The first model describes the cavity produced at the free surface of the metal bath by the high speed impinging oxygen jet. It is based on a zonal approach, where gas compressibility effects are taken into account only in the high velocity jet region while elsewhere the gas is treated as incompressible. The Volume Of Fluid (VOF) method is employed to follow the deformation of the bath free surface. Calculations are presented for two- and three-phase systems and compared against experimental data obtained in various cold model experiments. The influence on the size and shape of the cavity of various parameters (including the jet inlet boundary conditions, the VOF advection scheme and the turbulence modelling) is studied. Next, the model is used to simulate the interaction of a supersonic oxygen jet with the surface of a liquid steel bath in a pilot-scale converter. The second model concentrates on fluid flow, heat transfer and the post-combustion reaction in the gas phase above the metal bath. It uses the Simple Chemical Reaction Scheme approach to describe the transport of the chemical species and takes into account the consumption of oxygen by the bath and thermal radiative transfer. The numerical predictions are in reasonable agreement with measurements collected in a laboratory experiment and in a pilot-scale furnace

Les Néandertaliens, dont l'évolution a eu lieu en Europe sur environ 300kans, disparaissent vers 30kans. Les déterminants de cette disparition restent encore aujourd'hui très discutés et plusieurs hypothèses tentent d'en expliquer les causes. Parmi celles privilégiées à ce jour on peut citer l'influence du climat, d'une compétition avec Homo sapiens, d'une épidémie ou de modifications démographiques. Cette recherche doctorale revisite ces différentes hypothèses par le biais de la modélisation mathématique. Cette approche originale synthétise et potentialise les données de la paléontologie classique afin de mieux comprendre les phénomènes associés à l'extinction des Néandertaliens. Après avoir réalisé une étude démographique à l'aide de modèle classiques, nous avons conçu des modèles déterministes spécifiques pour analyser les Néandertaliens et la chaine alimentaire à laquelle ils sont associés. Une fois ces modèles testés et validés, nous les avons utilisés pour analyser l'évolution démographique de la population néandertalienne au cours du stade isotopique 3 et nous avons comparés nos résultats avec les données des études préhistoriques, archéozoologiques ou encore paléoanthropologiques. Suite à notre analyse, nous suggérons d'exclure certaines hypothèses souvent avancées comme la compétition pour la ressource, les oscillations climatiques ou encore les épidémies. Une modification des caractéristiques intrinsèques de la population (fécondité et/ou vitesse de maturation) nous semble être une hypothèse bien plus plausible pour expliquer la disparition des Néandertaliens. / The Neanderthal population lived and thrived in Europe during about 300ky in Middle Pleistocene. The causes of their disappearance about 30ky ago are strongly debated. Among the current hypotheses developed to explain this demographical crisis, competition with Modern humans, climate changes, epidemic diseases or demographical changes have often been evoked. The aim of this thesis was to re-analyse these assumptions and their determinants by using mathematical modelling. Models are used here to synthesize the data obtained by classical paleoanthropological studies and try to understand the complex and unknown phenomenon relative to the dramatic demographic fluctuation observed in Neanderthal populations during OIS3. Classical mathematical models are firstly used to analyse the influence of both demographical parameters and environmental stresses on the Neanderthal population. Next, we created new deterministic models more specified to the Neanderthal population. After checking the relevance of these models, we used them to analyse the demographical crisis of OIS3 and the information given by modelling have been checked with the information supplied by classical paleoanthropological, zooarchaeological and prehistorical studies. Our results allowed us to exclude the assumption of an epidemic disease or a climate change or even a resource competition as a cause of Neanderthal extinction whereas competition in a broad sense and above all demographic change could have led, under specific conditions, to Neanderthal demise. A demographic modification in the Neanderthal population across the time, in terms of fecundity or maturation speed, could be the reason of Neanderthals disappearance.

The work deals with a theoretical description of mathematical model and practical aspects of model simulation. Subsequently, it solves the current flow and the two design versions of the flowing debris trap profile. For the original channel and for the two designed versions two simulations were done for the flows of Q2 and Q5. As part of the work the theoeretical calculation of velocity in two cross sections of the existing channel was realized for the existing channel, which were due to calibration of the model. Results were compared at the same cross sections in the existing channel simulation solutions. Simulations are created in FLOW-3D. The purpose of this thesis is to determine whether the construction of trap profile is feasible.

Matematisk modellering är en av de förmågor eleverna ska ges möjlighet att utveckla på gymnasiet. Det är dock inte helt självklart bland lärare vad modellering innebär och frågan är om de undervisningsaktiviteter som används i relation till undervisning av modellering idag verkligen är ändamålsenliga. Denna studie undersöker elevernas potentiella utveckling i att modellera inom en lektionsserie, en så kallad modelleringsmodul, riktad mot kursen Matematik 5 på gymnasiet. Elevernas potentiella utveckling studeras utifrån deras involvering i de olika delprocesser som anses utgöra modelleringsprocessen i sin helhet. Resultatet indikerar att modelleringsmodulen tycks involvera eleverna i samtliga dessa delprocesser. Samtidigt visar resultatet att detta inte är en självklarhet och att vissa delprocesser tycks vara svårare att involvera eleverna i än andra. / Mathematical modelling is one of the competences students will have the possibility to develop in upper secondary school. However, it is not entirely obvious among teachers what modelling really means and it is questionable if the learning activities that are being used in relation to modelling education today really are effective. This study focuses on the students’ potential development within a series of lessons, a so-called modelling module, adapted for the course Mathematics 5 in upper secondary school. The students’ potential development is studied based on their involvement in the various sub-processes that are considered to be the modelling process as a hole. The result indicates that the modelling module involves students in all of these sub-processes. At the same time, the results show this is not self-evident and some of the subprocesses seem to be harder to involve the students in than others.

O problema de empacotamento de cilindros em níveis é comumente encontrado nas indústrias de cerâmica. Solucionar este problema significa encontrar o posicionamento ideal dos itens cerâmicos cilíndricos dentro do forno de modo que o menor número de fornos seja utilizado e os itens não se sobreponham e obedeçam aos limites do recipiente. Também é considerado o uso de prateleiras para que haja uma melhor ocupação do espaço do forno. Propomos uma formulação matemática não-linear inteira mista e métodos de resolução heurísticos e exato para o problema. Os métodos heurísticos consistem em escolher uma estratégia de ordenação, posicionar os itens em cada nível por meio da heurística Bottom-Left e posicionar os níveis no recipiente utilizando as estratégias Best-Fit, First-Fit ou Worst-Fit. Ao total, propomos seis variações heurísticas para resolução do problema. O método exato consiste em estimar o número de níveis e recipientes necessários e resolver o problema por meio de um solver de otimização global. Os experimentos computacionais foram realizados para um conjunto de instâncias que criamos. Os resultados mostraram que o método exato é capaz de encontrar a solução ótima em um curto período de tempo para instâncias de pequeno porte e que as heurísticas são capazes de resolver o problema em um tempo computacional baixo, para instâncias de pequeno, médio e grande porte, sendo que algumas heurísticas apresentam melhor desempenho que outras. / The cylinder packing problem in levels is commonly found in ceramic industries. Solving this problem consists in finding the ideal position of items inside furnaces so that the minimum number of furnaces is used and the items do not overlap and obeying furnaces size. In this case, it is possible to add levels to the furnace. We proposed a non-linear integer mixed mathematical model for the problem and heuristic and exact resolution methods. Heuristic methods consist of choosing a sorting strategy, packing the items at each level by a Bottom-Left heuristic, and positioning the levels in the furnace using Best-Fit, First- Fit or Worst-Fit strategy. In total, it is proposed six heuristic variations to solve the problem. The exact method consists in solving the problem by a global optimization solver. The computational experiments were run over a set of new proposed instances. The results have shown that the exact method is able to find an optimal solution in a short period of time for small instances and that the proposed heuristics are capable of solving the problem in a low computational time for small, medium and large instances. Furthermore, some of them have performed better than others.

O presente trabalho tem por objetivo definir o modal de transporte ótimo para componentes comprados que abastecem a linha de produção de uma empresa aeronáutica, ao menor custo logístico. Devido a característica do material e das exigências de órgãos e entidades responsáveis pelo ambiente industrial aeronáutico, os fornecedores são especializados e de origem internacional, pois as indústrias nacionais ainda não têm a certificação exigida para produzir tais materiais, salvo algumas poucas exceções, o que onera e torna a cadeia de suprimentos muito mais complexa. Portanto, para atingir o objetivo proposto utilizou-se um modelo heurístico, que decide o modal de transporte ótimo para transportar estes materiais de sua origem, EUA ou Europa, até seu destino que é o Brasil. / The present paper aims to define an optimum modal of transportation for acquired components used to supply the production line in a Aeronautical Company, based on the lowest logistic cost. Due to the caracteristics of such material and the special requirements of the Governamental agencies as well as the specific agencies that rule the aeronautical industrial environment, the suppliers which are in its vast majority of this net are from abroad. It happens due to the fact that the local Industry do not hold the required certification to manufacture or assemble such materials which throws the costs and its complexity much more present. Some few isolated companies constitute a exception of this general frame. Based on the exposed, to achieve the proposed goal a heuristic model was used, which defines that the best modal of transportation to transport those specific materials from its origin, USA or Europe, to your final destination in Brazil.

O milho é uma das culturas mais importantes do mundo, pois os produtos dele oriundos são largamente utilizados na indústria de amidos, na alimentação animal e humana, e também na produção de energia proveniente de biomassa. Por esse motivo, há sempre um grande interesse em conhecer a potencialidade de uso dos principais materiais genéticos disponíveis em relação aos ambientes em que serão inseridos. Este trabalho teve como objetivo central caracterizar, para o genótipo DKB-390 conduzido sob condição irrigada, atributos ecofisiológicos como área foliar, eficiência de uso da radiação, coeficiente de extinção, coeficientes de cultura, consumo hídrico e componentes de espiga; bem como conceitualizar modelos norteadores de manejo e de planejamento para cultura do milho, no intuito de obter a produtividade de grãos contemplada pelas incertezas climáticas diárias dos principais elementos do clima e suas correlações, para posteriormente se obter as correspondentes necessidades de água e de nitrogênio pela cultura. Para tanto, um experimento de campo foi conduzido, informações da literatura foram revisadas e levantadas, e modelos de previsão foram concebidos para a produtividade de grãos e para as demais variáveis de interesse. Como principais resultados, obteve-se: (i) sob condições adequadas de suprimento hídrico e de nitrogênio, o híbrido DKB-390 requer cerca de 573 litros de água para kg de grão que produz; (ii) o genótipo responde significativamente à segunda cobertura com nitrogênio, caso a cultura seja conduzida sob elevada população de plantas e adequado suprimento hídrico; (iii) a segunda cobertura com nitrogênio promoveu melhor manutenção da área foliar durante a fase de enchimento de grãos; (iv) o incremento da segunda cobertura de nitrogênio promoveu maior eficiência de uso da água pela cultura, bem como um leve aumento nos valores modais do número de grãos por fileira (da espiga) e da massa de 1000 grãos; (v) sob condições de adequado suprimento hídrico, o coeficiente de extinção médio, generalizado para todo o ciclo, é da ordem de 0,4267; valor que tende a ser maior na medida em que o suprimento de nitrogênio é menor; (vi) a eficiência de uso da radiação foi calculada em 3,52 g (fitomassa seca de parte aérea) MJ-1 (radiação solar fotossinteticamente ativa interceptada), tendo sido menor em função do emprego do regime de nitrogênio mais restritivo; (vii) os coeficientes de cultura obtidos do experimento podem ser utilizados para o manejo da irrigação do híbrido DKB-390, para os principais subperíodos, para que a produtividade não seja penalizada por déficit hídrico; (viii) o índice de colheita (expresso em relação à parte aérea) foi da ordem de 40% (variando entre 37% e 43%) sob condições de suprimento adequado de água e nitrogênio, valores que tenderam a ser maiores quando da restrição da segunda cobertura; (ix) o modelo determinístico proposto simulou adequadamente a evolução da produtividade de fitomassa de parte aérea do híbrido empregado, bem como sua produtividade de grãos sob adequadas condições de suprimento hídrico e de nitrogênio; (x) o modelo determinístico simulou adequadamente as evapotranspirações diárias o consumo hídrico através do método de Penman-Monteith; (xi) o modelo estocástico sugerido mostrou-se satisfatório, mediante o uso da distribuição normal bivariada das variáveis radiação solar e temperatura média do ar, para simular a produtividade de grãos sob condições de suprimento hídrico adequado e sob déficit moderado; e (xii) aparentemente, o modelo estocástico necessita ser melhorado quanto à capacidade de previsão das necessidades hídricas e de nitrogênio, pois tende claramente a subestimar as primeiras e superestimar as segundas. / Maize is on of the world most important crops, given that the products generated from this cereal are largely used by sectors like starch industry, animal and human nutrition, as well as biomass energy production and refineries. For these reasons, there is frequently a huge interest in knowing the potential adoption of the main available genotypes in relation to the environment in which they will be supposedly subjected. Considering the hybrid DKB-390 under full irrigated conditions, this work has as the central objective to characterize the most important ecophysiological attributes such as leaf area, radiation use efficiency, extinction coefficient, crop coefficients, water use and ear yield components. Additionaly, specif goals were to conceptualize models applicable for both management and planning of maize crops in order to predict the grain productivity contemplated by daily climate incertainties of the driven climate variables (i.e. radiation and temperature) and their correlation, then to achieve the water and nitrogen requirement corresponding to the predicted productivity. A field experiment was carried out, useful information from literature were obtained and reviewed, and models were created towards to support the prediction tools. The following outcomes might be highligthed: (i) under suitable conditions of both nitrogen and water supply, hybrid DKB-390 requires about 573 litters of water per each kilogram of produced grain; (ii) the genotype is significantly responsive to the second nitrogen covering when growing under high plant population and suitable water supply; (iii) the second nitrogen covering has enhanced better leaf area maintainance during grain filling stage; (iv) the second nitrogen covering has led to a better water use efficiency, as well as slightly increased modal values of the number of kernels per row (of ear) and the mass of a thousand kernels; (v) under suitable water supply, averaged extinction coefficient might be generalized as 0.4267 throughout the whole cycle, whereas tending to be higher as the nitrogen supply is restricted; (vi) the radiation use efficiency as calculated as 3.52 g (above-ground dry matter) MJ-1 (intercepted photossyntheticaly active radiation), being smaller as the nitrogen supply is restricted; (vii) some crop coefficients were found for the main phenological stages and may be adopted for irrigation management of hybrid DKB-390, when one aims to not deplet the productivity; (viii) the harvest index (above-ground based) was found about 40% (varying from 37% to 43%) if water and nitrogen are added sufficiently, and is likely to be higher provided that the second covering is not done; (ix) the proposed determinist model has performed well when simulating above-ground dry matter time course and its corresponding grain productivity under full and moderated water deficit conditions; (x) by using Penman-Montheit method, the deterministic model apparently simulates well both daily evapotranspiration and water uses; (xi) through bivariate normal distribution of averaged daily solar radiation and air temperature, the suggested stochastic model has simulated grain productivity in a satisfactory way; and (xii) the suggested stochastic model need to be improved in terms of its water and nitrogen requirement predictability, given that it clearly tends to underestimate the former and overestimate the latter.