No contexto do método MAC e baseado em esquemas de diferenças finitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre. Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretiza ção explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável. Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção. Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para fluidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres. Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW. A eficiência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado / In the context of the MAC method and based on finite difference schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface flows. In the stability analysis, the main result shows a precise stability restriction on the Crank-Nicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable. In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure fields; hence new projection methods for free surface flows need to be developed. The developed projection methods result in new methodologies for low Reynolds number free surface flows. It is also shown that the proposed methods can be applied for viscoelastic fluids. New strategies are derived for obtaining second-order accurate projection methods for free surface flows. In addition to the theoretical results on the stability of numerical schemes, implicit techniques and projection methods, computational tests are carried out and the results compared to consolidate the theory. The numerical results are obtained by the FREEFLOW system. The eficiency and robustness of the techniques in this work are demonstrated by solving complex tridimensional problems involving free surface and low Reynolds numbers, including the jet buckling and the extrudate swell problems

Ocean submesoscales are the subject of increasing focus in the oceanographic literature; with instrumentation now more capable of observing them in situ and numerical models now able to reach the resolution required to more fully capture them. Submesoscales are typified by horizontal spatial scales of O(1 − 10) km, vertical scales O(100) m and time-scales of O(1) day and are known to be associated with regions of high vertical velocity and vorticity. Occurring most commonly at density fronts at the ocean surface they can control mixed layer restratification and provide an important control on fluxes between the atmosphere and the deep ocean. This thesis sets out to better understand the fundamental physical processes underpinning submesoscale instabilities using a number of idealised process models. Linear stability analysis complemented by non-linear, high-resolution simulations will be used initially to explore the ways in which submesoscale instabilities in the mixed layer may compete and interact with one another. In particular, we will investigate the way in which symmetric and ageostrophic baroclinic instabilities interact when simultaneously present in a flow, with focus on the growth rates and energetic pathways of previously unexplored dynamic instabilities that arise in this paradigm; three-dimensional, mixed symmetric-baroclinic instabilities. Further, these non-linear simulations will allow us to investigate the transition to dissipative scales that can occur in the classical Eady model via a multitude of small-scale secondary instabilities that result from primary submesoscale instabilities. Finally, observational data, taken aboard the SMILES project cruise to the Southern Ocean, helps to motivate the consideration of a new dynamical paradigm; the Eady model with superimposed high amplitude barotropic jet. Non-linear simulations investigate the extent to which the addition of such a jet is capable of damping submesoscale growth. The causes of this damping are then investigated using linear analysis. With this approach eventually demonstrated as being unable to fully explain growth rate reductions, we introduce a new framework combining potential vorticity mixing by submesoscale instabilities with geostrophic adjustment, which relaxes the flow back to a geostrophic balanced state. This framework will help to explain, conceptually, how non-linear eddies control the linear stability of the flow.

This study presents Computer-Aided Fixture Design Verification (CAFDV) - the methods and implementations to define, measure and optimize the quality of fixture designs. CAFDV verifies a fixture for its locating performance, machining surface accuracy, stability, and surface accessibility. CAFDV also optimizes a fixture for its locator layout design, initial clamping forces, and tolerance specification. The demand for CAFDV came from both fixture design engineers and today's supply chain managers. They need such a tool to inform them the quality of a fixture design, and to find potential problems before it is actually manufactured. For supply chain managers, they will also be able to quantitatively measure and control the product quality from vendors, with even little fixture design knowledge. CAFDV uses two models - one geometric and one kinetic - to represent, verify and optimize fixture designs. The geometric model uses the Jacobian Matrix to establish the relationship between workpiece-fixture displacements, and the kinetic model uses the Fixture Stiffness Matrix to link external forces with fixture deformation and workpiece displacement. Computer software for CAFDV has also been developed and integrated with CAD package I-DEAS TM. CAD integration and a friendly graphic user interface allows the user to have easy interactions with 3D models and visual feedback from analysis results.

L’objectif de cette thèse est d’étudier, à l’aide de modèles mathématiques, le mécanisme de régulation qui permet au corps de maintenir une quantité optimale de plaquettes sanguines. Le premier chapitre présente le contexte biologique et mathématique. Dans un second chapitre, un modèle pour la mégacaryopoïèse est introduit qui suppose une régulation ponctuelle par le nombre de plaquettes du taux de différentiation des cellules souches vers la lignée mégacaryocytaire et du nombre de plaquettes produites par mégacaryocyte. Nous montrons que la dynamique de ce modèle est régie par une équation différentielle à retard x'(t) = -?x(t)+f(x(t))g(x(t-t)), et nous obtenons ensuite de nouvelles conditions suffisantes pour la stabilité et l’oscillation des solutions de cette équation. Dans le troisième chapitre, nous analysons un second modèle pour la mégacaryopoïèse qui considère cette fois-ci une régulation opérée en continu uniquement via la vitesse de maturation des mégacaryoblastes. L’analyse de stabilité nécessite d’adapter un cadre pré-existant aux cas où le paramètre de bifurcation n’est pas le retard, et permet de montrer que l’augmentation du taux de mort des mégacaryoblastes conduit à l’apparition de solutions périodiques, en accord avec les observations cliniques de la thrombopénie cyclique amégacaryocytaire. Le dernier chapitre est consacré l’analyse de stabilité d’une équation différentielle à deux retards qui apparait notamment dans le cadre de la mégacaryopoïèse lorsque l’on considère que les plaquettes ont une durée de vie limitée / The object of this thesis is the study, using mathematical models, of the regulation mechanism maintaining an optimal quantity of blood platelets. The first chapter presents the biological and mathematical context of the thesis. In a second chapter, we introduce a model for megakaryopoiesis assuming a regulation by the platelet quantity of both the differentiation rate of stem cells to the platelet cell line and the amount of platelets produced by each megakaryocyte. We show that the dynamic of this model corresponds to a delay differential equation x'(t) = -?x(t) + f(x(t))g(x(t - t)), and we obtain for this equation new sufficient conditions for stability and for the oscillation of solutions. In a third chapter, we analyze a second model for megakaryopoiesis in which the regulation is continuous through the maturation speed of megakaryocyte progenitors. The stability analysis requires to adapt a pre-existing framework to problems where the bifurcation parameter is not the delay, and allows to show that increasing the death rate of megakaryocyte progenitors leads to the onset of periodic solutions, in agreement with clinical observation of amegakaryocytic cyclical thrombocytopenia. The last chapter covers a differential equation with two delays that appears among others in a model of platelet production which considers that platelet death can both age-independent and age-dependent

Tightly regulated power converters behave as constant power loads which may introduce instability in power systems. Prior to this work, the design-oriented stability criteria of DC and three-phase AC systems has been extensively studied, while the stability of single-phase AC power systems has received less attention. In this research, the modeling and stability analysis of single-phase AC power systems is studied. In particular, this research focuses on a system architecture where loads are connected in series and powered by a current source. Based on the proposed current source and load power electronic based topologies, which are typically used in airfield lighting systems, three types of system characterization are developed: waveform-level model, average-value <i>qd</i> model, and <i>qd</i> impedance/admittance measurement. Each approach has its own advantages and drawbacks, but the result - a frequency-domain (s-domain) representation of the system, is identical. Applying the generalized Nyquist stability criterion, the small-signal stability criteria of the system is developed. It is shown that the predictions of the system stability using these three approaches are consistent.

Mes travaux de thèse portent sur le développement de schémas numériques d'ordre élevé en temps et en espace pour la simulation de propagation des ondes. Nous avons proposé de discrétiser dans un premier temps l'équation des ondes par rapport au temps, en utilisant une technique de type équation modifiée. Puis nous avons utilisé une méthode d'éléments finis de type Galerkine discontinue pour la discrétisation en espace. En modifiant l'ordre de la discrétisation, nous avons construit des schémas tout aussi précis que ceux déjà existants pour un coût de mise en oeuvre très intéressant. Après avoir validé numériquement la nouvelle méthode, nous nous sommes intéressés à sa stabilité ainsi qu'à son adaptivité en temps et en espace. Pour arriver à cela, nous avons dû faire une étude précise de la stabilité de la méthode de Galerkine discontinue et nous avons proposé des améliorations à cette technique entraînant des gains de temps significatifs. / My work consists in developing some high order numerical schemes in time and space for the modeling of the wave propagation. We have proposed to first discretize the wave equation with respect to the time using the so called Modified Equation Technique. Then, we have used a Discontinuous Galerkine Finite Element method for the space discretization. Switching the classical discretization process, we have constructed schemes as accurate as the classical ones with a numerical cost very interesting. After the numerical validation of this method, we have focused on its stability and on its adaptibility in time and space. To reach these objectives, we have performed a stability analysis of the Discontinuous Galerkin method and we have proposed some improvements to this technique which imply very important gain in terms of computationnal time.

Os escorregamentos de taludes de corte rodoviários verificados na região entre as cidades de Jarinu e Campo Limpo Paulista, ambas no estado de São Paulo, são derivados da atuação conjunta do intemperismo, da presença de estruturas reliquiares, e sua geometria, e das técnicas construtivas. Dentre estes fatores, as estruturas reliquiares (foliação e fraturas) desempenham o papel mais importante, pois os escorregamentos ocorrem quando há incompatibilidade entre as atitudes das estruturas e a geometria dos taludes de corte facilitando os escorregamentos, principalmente quando a face de taludes é paralela ou subparalela à foliação e esta mergulha na direção da estrada. O levantamento destas estruturas, utilizando-se em conjunto produtos de sensoriamento remoto, que possibilita a elaboração de uma análise geométrica regional, que também se aplica em escala de afloramento, pois as estruturas geológicas, em qualquer escala, apresentam feições em comum. Os produtos gerados são mapas de forma estrutural, de traços de fraturas e o estabelecimento de setores homogêneos baseados nas diferentes direções da foliação. Nos vários taludes estudados, são elaborados estereogramas que permitem a visualização espacial das descontinuidades. Com base nestes produtos, são feitas previsões de instabilidades, através de uma simulação de três direções de traçados rodoviários, onde são avaliadas as possibilidades de ocorrência de instabilidades. Os resultados obtidos em dados regionais são confrontados com os dados extraídos em campo nos vários taludes estudados, para a obtenção da aplicabilidade da metodologia utilizada. / The sliding of highways cut slopes verified between Jarinu and Campo Limpo Paulista, both in São Paulo state, region are originated of action ensemble of weathering, relicts structures presence, geometric and the constructive characteristics. Among them, the relict structures (foliation and fractures) perform the very important hole, because the sliding is effective when there is incompatibility between spacial attitudes of structures and the geometry of cut slopes. In the great number, the geometry of cut slopes facility the sliding, mainly when the slopes surface is parallel or sub parallel to foliation, diverging to the highway bed. The investigation of structures together with remote sensing images enables the elaboration of a geometrical analysis, applicable in outcrop scale, as geological structures in any scale, ranging from microscopical up to regional, have common features. The mapping of joints and foliation were made and well-defined sectors were separated, on the basis of different foliation attitudes. Stereographic nets were made for all slopes studied and the efficiency of graphical stability analysis in saprolitos was estimated, where there is a significant action of erosion processes. Lastly, the possibility of slides and erosional processes within the several sectors is evaluated, along three possible different highway directions. The predicted results, based on regional data, are compared to field data, obtained in the slopes, in order to confirm the applicability of the method under investigation.

L'intégration des sources d'énergies renouvelables sur le réseau électrique est complexe en raison de leur nature intermittente et décentralisée. Le micro-réseau est une approche prometteuse pour interconnecter des générateurs distribués (DGs) locaux, alimenter des charges locales et également échanger de l'énergie avec le réseau électrique de manière contrôlée. Ce mode de production/consommation locales permet d'éviter la transmission d'électricité sur de longues distances, et implique donc une plus grande efficacité. Ces travaux se concentrent sur l'analyse et le contrôle du micro-réseau continu afin que les DGs se répartissent l'alimentation des charges et qu'ils maintiennent également la tension du bus continu. À l'équilibre, les contraintesde la commande du statisme classique (droop control) pour un système comportant de multiples DGs sont analysés, et une méthode de compensation mixte est proposée pour améliorer simultanément le maintien en tension et le partage du courant de charge. En dynamique, le modèle global du système est construit en introduisant une inductance virtuelle dans le circuit équivalent du DG, puis plusieurs modèles d'ordre réduit sont examinés pour vérifier leur efficacité dans l'analyse de la stabilité du système. Un modèle multi-échelle d'ordre réduit (RMM) est proposé afin de conserver les contraintes temporelles ainsi que de réduire la complexité du système. Enfin, une méthode basée sur le contrôle de rejet de perturbation active (ADRC) est présentée afin de mettre en oeuvre le contrôle local de la tension des DG en prenant en compte l'échelle de temps. Cette méthode permet d'améliorer la dynamique du système de contrôle en ajustant la largeur de bande passante de la commande et de l'observateur. Les analyses et les méthodes de contrôle proposées sont vérifiées par des essais expérimentaux dans notre plateforme au laboratoire. / The direct integration of renewable energy resources to the utility grid is pretty tough due to their intermittent feature and dispersed nature. Microgrid is one promising approach to gather the local distributed generators (DGs), supply local loads as well as exchange power with the utility grid as a controllable unit. This local-generation-localconsumption mode is able to avoid the long distance power transmission, thus can benefit a higher efficiency. The control aim of DC microgrids is to make the multiple DGs share the load properly as well as maintain the DCbus voltage stable. In steady state, the constrains of the classic droop control in multiple DGs environment are analyzed, and a mixed compensation method using common current is proposed to improve the voltage and load sharing performance simultaneously. In dynamic state, the system comprehensive model is constructed by the introduction of virtual inductor in the equivalent circuit of the DG, then several reduced-order models are examined to check their effectiveness for the system stability analysis. A reduced-order multi-scale model (RMM) is proposedto keep major time scale information as well as reduce the system complexity. Finally, an active disturbance rejection control (ADRC) based control method is proposed to realize the time scale droop control. It can effectively adjust the dynamic of the local control by adjusting the bandwidth of the Linear Extend State Observer or/and the controller. The proposed analysis and control methods are verified by experimental tests in our laboratory platform.

Phase behaviour information is essential for the development and optimization of hydrocarbon resource production, transport and refining technologies. Experimental data sets for mixtures containing heavy oil and bitumen are sparse as phase behaviour data are difficult to obtain and cost remains prohibitive for most applications. A computational tool that predicts phase behaviours reliably for mixtures containing such ill-defined components, over broad temperature, pressure and composition ranges would play a central role in the advancement of bitumen production and refining process knowledge and would have favourable impacts on the economics and environmental effects linked to the exploitation of such ill-defined hydrocarbon resources. Prior to this work, predictive computational methods were reliable for dilute mixtures of ill-defined constituents. To include a much wider range of conditions, three major challenges were addressed. The challenges include: creation of a robust and accurate numerical approach, implementation of a reliable thermodynamic model, and speciation of ill-defined constituents like Athabasca Bitumen Vacuum Residue (AVR). The first challenge was addressed by creating a novel computational approach based on a global minimization method for phase equilibrium calculations. The second challenge was tackled by proposing a thermodynamic model that combines the Peng-Robinson equation of state with group contribution and related parameter prediction methods. The speciation challenge was addressed by another research group at the University of Alberta. Pseudo components they proposed were used to assign groups and estimate thermodynamic properties. The new phase equilibrium computational tool was validated by comparing simulated phase diagrams with experimental data for mixtures containing AVR and n-alkanes. There is good qualitative and quantitative agreement between computed and experimental phase diagrams over industrially relevant ranges of compositions, pressures and temperatures. Mismatch was only observed over a limited range of compositions, temperatures and pressures. This computational breakthrough provides, for the first time, a platform for reliable phase behaviour computations with broad potential for application in the hydrocarbon resource sector. The specific computational results can be applied directly to solvent assisted recovery, paraffinic deasphalting, and distillation and refining processes for Athabasca bitumen a strategic resource for Canada. / Chemical Engineering

The convective drying of thin layers of multicomponentliquid mixtures into an inert gas, and the influence ofdifferent process controlling mechanisms on drying selectivityis studied. Drying experiments under gas-phase-controlledconditions are performed by low intensity evaporation, fromfree liquid surfaces, of ternary mixtures without non-volatilesolutes. Liquid-side-controlled experiments are carried out bydrying a multicomponent polymeric solution containing twovolatile components, one non-volatile polymer and an optionalnonvolatile softening substance. Mathematical models to describe gas- andliquid-side-controlled drying based on interactive diffusion inboth liquid and gas phases as the main mechanisms for masstransfer are developed. For gas-phase-controlled drying, astability analysis of the ordinary differential equations thatdescribes the evaporation process is performed. Isothermal andnon-isothermal drying processes are considered in batch andcontinuous modes. The mathematical model to describe thecomposition profiles during batch drying of the polymeric film,considering liquid resistance, is solved numerically. Due tothe lack of experimental data, properties for this polymericsystem are estimated by using established methods. Ananalytical solution of the diffusion equation, by assuming anisothermal drying process and a constant matrix ofmulticomponent diffusion coefficients is developed. For thecontinuous case, liquid-side resistance is studied by modellingevaporation of a multicomponent falling liquid film into aninert gas including indirect heating. The results of the gas-phase-controlled model are in goodagreement with experimental results. For the polymeric film,the agreement is only qualitative since the model does notaccount for a membrane that develops on the film surface. Thestability analysis permits the prediction of trajectories andfinal state of a liquid mixture in a gas-phase-controlleddrying process. For isothermal evaporation of ternary mixturesinto pure gas, the solutions are trajectories in the phaseplane represented by a triangular diagram of compositions. Thepredicted ternary dynamic azeotropic points are unstable orsaddle. On the other hand, binary azeotropes are stable whenthe combination of the selectivities of the correspondingcomponents is negative. In addition, pure component singularpoints are stable when they are contained within theirrespective isolated negative selectivity zones. Undernon-isothermal conditions, maximum temperature valuescharacterise stable azeotropes. Incremental loading of the gaswith one or more of the components leads to a node-saddlebifurcation, where a saddle azeotrope and a stable azeotropecoalesce and disappear. For continuous drying, the singularpoints are infinite and represent dynamic equilibrium pointswhose stability is mainly dependent on the ratio of inletgas-to-liquid flow rates. As long as the process isgas-phasecontrolled, these results also apply to a porous solidcontaining a liquid mixture. In general, liquid-side control makes the drying processless selective but it is difficult to maintain this conditionduring the whole process. Under the influence of its owndynamics, a process starting as liquid-side-controlled tendstowards a gas-phase-controlled process. The presence ofnon-volatile components and indirect heating may delay thisdevelopment. Considering the evolution of the processcontrolling steps and its influence on selectivity, a modelaimed at describing the complete trajectory of a drying orevaporation process must include the coexistence of allrelevant mechanisms. Keywords:ternary mixture, falling film, diffusionequation, gas-phase control, liquid-phase control, selectivity,stability analysis, polymeric solution, evaporation, azeotrope,batch drying, continuous drying.