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.

Das Verständnis der komplexen Interaktionen innerhalb des weltweiten Transportnetzes ist ein essentieller Schritt auf dem Weg zur Vorhersage der Krankheitsausbreitung und Entwicklung von effektiven Gegenmaßnahmen. Ungeachtet der weltweiten Vernetzung werden die politischen Entscheidungen oft von nationaler, regionaler und egozentrischen Denkweise geleitet. Die Ebola-Epidemie in 2014 demonstrierte deutlich, dass solche Herangehensweise modernen Epidemien nicht gerecht werden kann. In dieser Dissertation werden mehrere Methoden entwickelt, welche es ermöglichen während einer Epidemie die globalen Teilnehmer entsprechend ihrer Rolle einzustufen und das Risiko des Krankheitsexports zu berechnen. Die Methodik wird analytisch und numerisch ausführlich diskutiert. Darüber hinaus werden Lösungen für hypothetische und reale Epidemien auf dem Flugverkehrsnetz vorgestellt. Im zweiten Teil wird mit Hilfe eines vereinfachten spieltheoretischen Modells der Prozess der Ressourcenverteilung zur Epidemieeindämmung untersucht. Dabei erfolgt die Verteilung der Ressourcen von den Knoten und kann in egozentrischer oder altruistischer Weise erfolgen. Im Rahmen der Modells liegen die Optima für das altruistische und egozentrische System eng beieinander, solange der ausbruch räumlich konzentriert ist. In diesem Fall ist es optimal alle Ressourcen in den Ausbruchsknoten zu investieren. Bei lokal getrennten Ausbrüchen streben die Systeme verschiedene Gleichgewichte an. In allen Aspekten der Arbeit wird netzwerkbasierte Repräsentation des Systems verwendet, so dass die Orte durch Knoten innerhalb eines Transportnetzwerkes abgebildet werden. Die vorliegende Arbeit vereint mehrere Vorteileder etablierten Methoden: während der Schwerpunkt auf der Topologie des Netzwerkes liegt, berücksichtigt die vorgestellte Methodik den Ursprungsort der Epidemie. / The growing complexity of the global mobility is a key challenge for the understanding of the worldwide spread of emergent infectious diseases and the design of effective containment strategies. Despite global connectivity, containment policies are often based on national, regional and ’egocentric’ assessments of outbreak situations that are no longer effective or meaningful, as recently demonstrated by 2014 Ebola outbreak in West Africa, where months passed before a concerted, international effort followed. Despite the importance of the matter, optimal strategies in highly connected non-local settings are poorly understood. In the work at hand we propose a set of methods for more informed decision making during and prior to a pandemic. All of the studied systems are represented by networks in analogz the traffic networks, which play a dominant role during the global disease spreading. We introduce methods to calculate the risk of disease importation in a specific location and to determine the role of a node during an outbreak. Using the world aviation network, we demonstrate how the methods can be applied on real and hypothetical pandemics. We show that the airports can be divided into two distinct groups according to the role they take on in distributing the disease. Further, investigate the allocation of resources as a game theoretic dilemma. We embrace a bottom-up approach to this question, allowing the nodes of the network to distribute the resourses. We investigate egocentric and altruistic strategies and conclude that the optimal state of both systems are very similar if the outbreak is spacially confined. In this case allocation of resources ti the affected nodes is the optimal strategy. When there are multiple independent outbreaks, the optima diverge substantially. To foster the benefits of multiple approaches, the work at hand combines the information on the network topology but also regard some specifics of the outbreak at hand outbreak.

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.