Une accélération de la fréquence cardiaque (FC) au repos est observée chez les femmes enceintes. Au dernier trimestre, la FC accélère en moyenne de 15%, ce qui représente un facteur de risque dans le développement d’arythmies de novo ou dans l’exacerbation d’arythmies cardiaques préexistantes. Ceci est dangereux pour la mère ainsi que pour le fœtus. Cependant, les mécanismes responsables de ce changement cardiovasculaire restent peu connus. Notre laboratoire a récemment démontré que la grossesse était associée à une augmentation de la densité du courant pacemaker (If) et du courant calcique de type L (ICaL), ainsi qu’à des changements de l’homéostasie calcique dans les cellules de nœud sinusal (NS) de souris. Sachant que les concentrations plasmatiques en œstrogènes sont significativement augmentées pendant la grossesse et que ces hormones sexuelles féminines ont la capacité de modifier les propriétés électrophysiologiques du cœur, l’hypothèse de ce projet de recherche est que les œstrogènes jouent un rôle important dans l’augmentation de la FC associée à la grossesse et régulent les propriétés électrophysiologiques du NS. Les objectifs de ce projet de recherche sont de déterminer le rôle du 17β-œstradiol (E2) dans l’augmentation de la FC, d’examiner si ces effets sont régulés par les récepteurs aux œstrogènes alpha (ERα) et/ou bêta (ERβ) ainsi que d’évaluer les différents mécanismes de régulation de l’E2 sur l’électrophysiologie du NS. Des souris femelles adultes non-gestantes (2-4 mois) déficientes en ERα (ERKOα) ou en ERβ (ERKOβ) ont reçu un traitement chronique à l’E2 (30 μg deux fois par jour pendant quatre jours) simulant les concentrations plasmatiques en E2 retrouvées en fin de grossesse (23,3 ± 5,0 nM) chez la souris. L’analyse des électrocardiogrammes de surface montrent que la FC des souris ERKOβ (ERKOβ : 511 ± 15 bpm; ERKOβ +E2 : 580 ± 10 bpm, n = 10, p < 0,001) est significativement accélérée suivant le traitement à l’E2. Toutefois, la FC demeure inchangée chez les souris ERKOα (ERKOα : 520 ± 16 bpm; ERKOα +E2 : 530 ± 21 bpm, n = 7, p = 0,114). La méthode du patch-clamp en mode courant-imposé a permis de démontrer une accélération de l’automaticité des cellules du NS des souris ERKOβ suivant le traitement à l’E2, se traduisant par une augmentation de la fréquence des potentiels d’action spontanés (ERKOβ : 284 ± 24 bpm, n = 8; ERKOβ +E2 : 354 ± 23 bpm, n = 15, p = 0,0395) et par une pente de dépolarisation diastolique plus rapide (ERKOβ : 82 ± 12 mV/s, n = 8; ERKOβ +E2 : 140 ± 14 mV/s, n = 15, p < 0,003). En lien avec ces résultats, le patch-clamp en mode voltage-imposé a permis de démontrer que la densité de If est augmentée suivant un traitement à l’E2 (à -90 mV : ERKOβ : -6,6 ± 0,7 pA/pF, n = 12-15; ERKOβ +E2 : -11 ± 1 pA/pF, n = 9-11, p < 0,05). Cependant, If est similaire chez les souris ERKOα traitées ou non à l’E2. De plus, des cardiomyocytes humains dérivés de cellules souches pluripotentes induites de type nodal (N-hiPSC-CM) ont une accélération de la fréquence des potentiels d’action (CTL : 69 ± 5 bpm, n = 12; +E2 : 99 ± 6 bpm, n = 14, p < 0,001) ainsi qu’une augmentation de la densité de If (à -90 mV : CTL : -0,95 ± 0,14 pA/pF, n = 7-10; +E2 : -1,62 ± 0,17 pA/pF, n = 13-14, p < 0,05) suivant le traitement à l’E2. L’administration d’E2 ne modifie pas la fréquence des transitoires calciques des cellules de NS des souris ERKOα (139 ± 15, n = 13-14; +E2 : 142 ± 14, n = 15-16, p = ns) et ERKOβ (142 ± 11, n = 14-15; +E2 : 147 ± 13, n = 15-16, p = ns). En lien avec ces résultats, le courant ICaL des N-hiPSC-CM est inchangé suivant le traitement d’E2 (à 0 mV : CTL : -14,0 ± 1,3 pA/pF, n = 12-13; +E2 : -14,5 ± 1,4 pA/pF, n = 22, p = ns). En conclusion, l’accélération de l’automaticité cardiaque associée à la grossesse est, entre autres, expliquée par une augmentation de la densité de If, régulée par la voie de signalisation E2-ERα. Cependant, les changements de l’homéostasie calcique observés pendant la grossesse sont indépendants des niveaux élevés en œstrogènes. Les résultats obtenus sur les N-hiPSC-CM concordent avec ce qui est observé dans les cellules de NS de souris, ce qui démontre l’applicabilité humaine des résultats. Notre étude contribue à élucider l’influence de la grossesse et le rôle des hormones sexuelles féminines sur la fonction du NS et l’automaticité cardiaque. Ultimement, notre travail pourrait aider à développer une meilleure gestion des arythmies associées aux fluctuations hormonales féminines et/ou à la grossesse. / An increased heart rate (HR) is observed in pregnant women. In fact, in the last trimester, in average, the HR increases by 15%, which is a known risk factor to developing cardiac arrhythmias or exacerbating pre-existing arrhythmias. This can lead to major consequences for both the mother and fetus. However, the mechanisms underlying this increased HR remain largely unexplored. Our laboratory recently demonstrate that pregnancy is associated with an increased density of the pacemaker current (If) and the L-type calcium current (ICaL) as well as changes in calcium homeostasis of mouse sinoatrial node (SAN) cells. Knowing that estrogens are increased during pregnancy and that these sex hormones can modify cardiac electrophysiological properties, we hypothesized that estrogens play a key role in the pregnancy-induced increased HR and regulate the SAN electrophysiological properties. Our research project aims to determine the role of 17β-estradiol (E2) on the pregnancy-induced increased HR, to determine if these effects are regulated through estrogen receptor alpha (ERα) and/or beta (ERβ) and to study the E2 underlying mechanisms on SAN electrophysiology. Non-pregnant female mice (2-4 months) lacking ERα (ERKOα) or ERβ (ERKOβ) received a chronic E2 treatment (30 μg twice daily for four days) mimicking E2 concentrations found in late pregnancy (23.3 ± 5.0 nM). Surface electrocardiogram analysis showed a significant increased HR in ERKOβ mice (ERKOβ: 511 ± 15 bpm; ERKOβ +E2: 580 ± 10 bpm; n = 10; p<0.001) following E2 administration. However, the HR remains unchanged in ERKOα mice (ERKOα: 520 ± 16 bpm; ERKOα +E2: 530 ± 21 bpm, n = 7, p = 0.114). Following E2 treatment, current-clamp method demonstrates an increase SAN cells automaticity in ERKOβ mice, resulting in an increase in the spontaneous action potential frequency (ERKOβ : 284 ± 24 bpm, n = 8; ERKOβ +E2 : 354 ± 23 bpm, n = 15, p = 0.0395), associated with a steeper diastolic depolarization slope (ERKOβ : 82 ± 12 mV/s, n = 8; ERKOβ +E2 : 140 ± 14 mV/s, n = 15, p < 0.003), a major determinant of cardiac automaticity. In line with these results, voltage-clamp data showed an increased If density in SAN cells of ERKOβ mice treated with E2 (at -90 mV: ERKOβ: -6.6 ± 0.7 pA/pF, n = 12-15; ERKOβ +E2: -11.0 ± 1.3 pA/pF, n = 9-11, p < 0.05). Nevertheless, If density was similar in E2-treated ERKOα mice. E2-treated nodal-like human-induced pluripotent stem cell-derived cardiomyocytes (N-hiPSC-CM) also showed an increased spontaneous action potential frequency (CTL : 69 ± 5 bpm, n = 12; +E2 : 99 ± 6 bpm, n = 14, p < 0.001) and If density (at -90 mV: CTL: -0.95 ± 0.14 pA/pF, n = 7-10; +E2: -1.62 ± 0.17 pA/pF, n = 13-14, p < 0.05). Following E2 administration, the rate of calcium transient was similar in SAN cells from ERKOα (139 ± 15, n = 13-14; +E2 : 142 ± 14, n = 15-16, p = ns) and ERKOβ (142 ± 11, n = 14-15; +E2 : 147 ± 13, n = 15-16, p = ns) mice. In line with these results, no modification was seen on ICaL density in E2-treated N-hiPSC-CM (at 0 mV: CTL: -14.0 ± 1.3 pA/pF, n = 12-13; +E2: -14.5 ± 1.4 pA/pF, n = 22, p = ns). In conclusion, the increased cardiac automaticity observed during pregnancy is, in part, explained by an increased If density. This mechanism is mediated by the E2-ERα pathway. In the other hand, calcium homeostasis changes detected during pregnancy appear to be mediated by an E2-independent mechanism. Finally, results obtained on N-hiPSC-CM are consistent with our observations on mouse SAN cells, demonstrating the human applicability of our results. This study provides novel insight on the effects of female sex hormones on the SAN functions. Ultimately, this information can lead to improved management of arrhythmias associated with female hormone fluctuations and/or pregnancy-induced arrhythmias.

La présente thèse porte sur différentes questions émanant de la géométrie spectrale. Ce domaine des mathématiques fondamentales a pour objet d'établir des liens entre la géométrie et le spectre d'une variété riemannienne. Le spectre d'une variété compacte fermée M munie d'une métrique riemannienne $g$ associée à l'opérateur de Laplace-Beltrami est une suite de nombres non négatifs croissante qui tend vers l’infini. La racine carrée de ces derniers représente une fréquence de vibration de la variété. Cette thèse présente quatre articles touchant divers aspects de la géométrie spectrale. Le premier article, présenté au Chapitre 1 et intitulé « Superlevel sets and nodal extrema of Laplace eigenfunctions », porte sur la géométrie nodale d'opérateurs elliptiques. L’objectif de mes travaux a été de généraliser un résultat de L. Polterovich et de M. Sodin qui établit une borne sur la distribution des extrema nodaux sur une surface riemannienne pour une assez vaste classe de fonctions, incluant, entre autres, les fonctions propres associées à l'opérateur de Laplace-Beltrami. La preuve fournie par ces auteurs n'étant valable que pour les surfaces riemanniennes, je prouve dans ce chapitre une approche indépendante pour les fonctions propres de l’opérateur de Laplace-Beltrami dans le cas des variétés riemanniennes de dimension arbitraire. Les deuxième et troisième articles traitent d'un autre opérateur elliptique, le p-laplacien. Sa particularité réside dans le fait qu'il est non linéaire. Au Chapitre 2, l'article « Principal frequency of the p-laplacian and the inradius of Euclidean domains » se penche sur l'étude de bornes inférieures sur la première valeur propre du problème de Dirichlet du p-laplacien en termes du rayon inscrit d’un domaine euclidien. Plus particulièrement, je prouve que, si p est supérieur à la dimension du domaine, il est possible d'établir une borne inférieure sans aucune hypothèse sur la topologie de ce dernier. L'étude de telles bornes a fait l'objet de nombreux articles par des chercheurs connus, tels que W. K. Haymann, E. Lieb, R. Banuelos et T. Carroll, principalement pour le cas de l'opérateur de Laplace. L'adaptation de ce type de bornes au cas du p-laplacien est abordée dans mon troisième article, « Bounds on the Principal Frequency of the p-Laplacian », présenté au Chapitre 3 de cet ouvrage. Mon quatrième article, « Wolf-Keller theorem for Neumann Eigenvalues », est le fruit d'une collaboration avec Guillaume Roy-Fortin. Le thème central de ce travail gravite autour de l'optimisation de formes dans le contexte du problème aux valeurs limites de Neumann. Le résultat principal de cet article est que les valeurs propres de Neumann ne sont pas toujours maximisées par l'union disjointe de disques arbitraires pour les domaines planaires d'aire fixée. Le tout est présenté au Chapitre 4 de cette thèse. / The main topic of the present thesis is spectral geometry. This area of mathematics is concerned with establishing links between the geometry of a Riemannian manifold and its spectrum. The spectrum of a closed Riemannian manifold M equipped with a Riemannian metric g associated with the Laplace-Beltrami operator is a sequence of non-negative numbers tending to infinity. The square root of any number of this sequence represents a frequency of vibration of the manifold. This thesis consists of four articles all related to various aspects of spectral geometry. The first paper, “Superlevel sets and nodal extrema of Laplace eigenfunction”, is presented in Chapter 1. Nodal geometry of various elliptic operators, such as the Laplace-Beltrami operator, is studied. The goal of this paper is to generalize a result due to L. Polterovich and M. Sodin that gives a bound on the distribution of nodal extrema on a Riemann surface for a large class of functions, including eigenfunctions of the Laplace-Beltrami operator. The proof given by L. Polterovich and M. Sodin is only valid for Riemann surfaces. Therefore, I present a different approach to the problem that works for eigenfunctions of the Laplace-Beltrami operator on Riemannian manifolds of arbitrary dimension. The second and the third papers of this thesis are focused on a different elliptic operator, namely the p-Laplacian. This operator has the particularity of being non-linear. The article “Principal frequency of the p-Laplacian and the inradius of Euclidean domains” is presented in Chapter 2. It discusses lower bounds on the first eigenvalue of the Dirichlet eigenvalue problem for the p-Laplace operator in terms of the inner radius of the domain. In particular, I show that if p is greater than the dimension, then it is possible to prove such lower bound without any hypothesis on the topology of the domain. Such bounds have previously been studied by well-known mathematicians, such as W. K. Haymann, E. Lieb, R. Banuelos, and T. Carroll. Their papers are mostly oriented toward the case of the usual Laplace operator. The generalization of such lower bounds for the p-Laplacian is done in my third paper, “Bounds on the Principal Frequency of the p-Laplacian”. It is presented in Chapter 3. My fourth paper, “Wolf-Keller theorem of Neumann Eigenvalues”, is a joint work with Guillaume Roy-Fortin. This paper is concerned with the shape optimization problem in the case of the Laplace operator with Neumann boundary conditions. The main result of our paper is that eigenvalues of the Neumann boundary problem are not always maximized by disks among planar domains of given area. This joint work is presented in Chapter 4.

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Ce travail porte sur le problème des partitions minimales, à l'interface entre théorie spectrale et optimisation de forme. Une introduction générale précise le problème et présente des résultats, principalement dûs à B. Helffer, T. Hoffmann-Ostenhof et S. Terracini, qui sont utilisés dans le reste de la thèse.Le premier chapitre est une étude spectrale asymptotique du laplacien de Dirichlet sur une famille de domaines en dimension deux qui tend vers un segment. L'objectif est d'obtenir une localisation des lignes nodales dans la limite des domaines minces. En appliquant les résultats de Helffer, Hoffmann-Ostenhof et Terracini, on montre ainsi que les domaines nodaux des premières fonctions propres forment des partitions minimales.Le deuxième chapitre étudie les valeurs propres de certains opérateurs de Schrödinger sur un domaine plan avec condition au bord de Dirichlet. On considère des opérateurs qui ont un potentiel électrique nul et un potentiel magnétique d'un type particulier, dit d'Aharonov-Bohm, avec des singularités en un nombre fini de points appelés pôles. On démontre que les valeurs propres dépendent continuement des pôles. Dans le cas de pôles distincts et éloignés du bord, on prouve que cette dépendance est analytique lorsque la valeur propre est simple. On exprime de plus une condition suffisante pour que la fonction qui aux pôles associe une valeur propre présente un point critique. On utilise alors la caractérisation magnétique des partitions minimales pour montrer que l'énergie minimale est une valeur critique d'une de ces fonctions.Le troisième chapitre est un article écrit en collaboration avec Virginie Bonnaillie-Noël. Il porte sur une famille d'exemples, les secteurs angulaires de rayon unité et d'ouverture variable, dont on tente de déterminer les partitions minimales. On applique pour cela les théorèmes généraux rappelés dans l'introduction afin de déterminer les partitions nodales qui sont minimales. On s'intéresse plus particulièrement aux partitions minimales en trois domaines. En appliquant les idées du deuxième chapitre, on montre que pour certaines valeur de l'angle, il n'existe aucune partition minimale qui soit symétrique par rapport à la bissectrice du domaine. D'un point de vue quantitatif, on obtient des encadrements précis de l'énergie minimale.Le quatrième chapitre consiste en l'étude des partitions minimales de tores plats dont on fait varier le rapport entre longueur et largeur. On utilise une méthode numérique très différente de celle du troisième chapitre, basée sur un article de B. Bourdin, D. Bucur et É. Oudet. Elle consiste en une relaxation suivie d'une optimisation par un algorithme de gradient projeté. On peut ainsi tester des résultats théoriques antérieurs. Les résultats présentés suggèrent de plus la construction explicite de familles de partitions (en liaison avec des pavages du tore) qui donnent une nouvelle majoration de l'énergie minimale.Un dernier chapitre de perspectives présente plusieurs applications possibles des méthodes décrites dans la thèse. / This work is concerned with the problem of minimal partitions, at the interface between spectral theory and shape optimization. A general introduction gives a precise statement of the problem and recall results, mainly due to B. Helffer, T. Hoffmann-Ostenhof and S.Terracini, that are used in the rest of the thesis.The first chapter is an asymptotic spectral study of the Dirichlet Laplacian on a familly of two-dimensional domains converging to a line segment. The aim is to localize the nodal lines when the domains become very thin. With the help of the results of Helffer, Hoffmann-Ostenhof, and Terracini, we then show that the nodal domains of the first eigenfunctions give minimal partitions.The second chapter studies the eigenvalues of some Schrödinger operators on a domain with Dirichlet boundary conditions. We consider operators that have no electric potential and a so-called Aharonov-Bohm magnetic potential, which has singularities at a finite number of points called poles. We prove that the eigenvalues are continuous functions of the poles. When the poles are distinct and far from the boundary, we prove that this function is analytic, assuming the eigenvalue is simple. We also give a sufficient condition for the function to have a critical point. Using the magnetic characterization of minimal partitions, we show that the minimal enery is a critical value for one of these functions.The third chapter in an article written in collaboration with Virginie Bonnaillie-Noël. It studies minimal partitions for sectors of unit radius with a variable angular opening. We apply the general results presented in the introduction, together with numerical computations, to determine nodal partitions that are minimal. We focus on partitions into three domains. Using ideas from the second chapter, we show that, for some values of the angle, there is no minimal partition that is symmetric with respect to the bisector. Form a quantitative point of view, we obtain precise bounds on the minimal energy.The fourth chapter studies the minimal partitions of flat tori in function of the ratio between width and length. We use a numerical method that is quite different from chapter three, and is based on an article by B. Bourdin, D. Bucur, and É. Oudet. It consists in a relaxation of the problem, followed by optimization with the help of a projected gradient algorithm. The results shown here additionally suggest explicit families of partitions, which consist in tilings of tori by polygons, that give upper bounds on the minimal energy. In the last chapter we consider several possible applications of the methods described in the thesis.

O objetivo central deste trabalho é implementar modelos constitutivos hiperelásticos não lineares em um código computacional que faz análise não linear geométrica de cascas. São necessários, para este propósito, conceitos sobre álgebras linear e tensorial, cinemática, deformação, tensão, balanços, princípios variacionais, métodos numéricos e hiperelasticidade. Tal programa usa a formulação Lagrangiana posicional, o método dos elementos finitos, o princípio dos trabalhos virtuais e o método iterativo de Newton-Raphson para solução das equações não lineares. O elemento finito de casca possui dez nós, sete parâmetros por nó e variação linear da deformação ao longo da espessura. Para dedução dos novos modelos usou-se a decomposição multiplicativa do gradiente da função mudança de configuração, o tensor deformação de Green-Lagrange e o tensor da tensão de Piola-Kirchhoff de segunda espécie. O código desenvolvido foi usado em simulações de diversos exemplos e apresentou boa precisão na análise mecânica de polímeros naturais altamente deformáveis. A ocorrência do fenômeno travamento não se manifestou nas análises realizadas. A presente pesquisa confirmou outros trabalhos, reforçou a necessidade de se usar modelos hiperelásticos não lineares para simular o comportamento mecânico de polímeros naturais e apresentou resultados condizentes com dados experimentais existentes na literatura científica e às respectivas soluções analíticas. / The main objective of this work is to implement nonlinear hyperelastic constitutive models in a computational code of geometrically nonlinear analysis of shells. For this purpose, concepts of linear and tensor algebras, kinematics, strain, stress, balances, variational principles, numerical methods and hyperelasticity are necessary. Such program uses the positional Lagrangian formulation, the finite element method, the principle of virtual work and the iterative method of Newton-Raphson for the solution of the nonlinear equations. The shell finite element has ten nodes, seven parameters per node and presents linear variation of the strain along the thickness. To achieve the new constitutive models the multiplicative decomposition of the deformation gradient, the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor are used. The developed code is tested for simulations of various examples and presents good accuracy in the mechanical analysis of highly deformable natural rubber. The locking phenomena didn\'t appear in the proposed analysis. The present research confirms other works, corroborates the need of using nonlinear hyperelastic models to simulate the mechanical behavior of natural rubber and presents suitable results when compared to existent experimental data of the scientific literature and to the respective analytical solutions.

Thesis submitted in fulfilment of the requirements for the degree Master of Technology: Horticultural Sciences in the Faculty of Applied Sciences at the CAPE PENINSULA UNIVERSITY OF TECHNOLOGY Supervisor: Dr L Kambizi Co-supervisor: Dr NP Makunga Cape Town December 2013 / Agathosma betulina (Berg.) Pillans, previously known as Barosma betulina, is a member of the Rutaceae family, and indigenous to the fynbos botanical biome of the Western Cape of South Africa. It is commonly known as buchu. Extracts as well as powdered leaves have traditionally been used for the treatment of various ailments. The increase in the international demand for A. betulina for health as well as food and beverage benefits, have raised concerns over exploitation of wild populations and the lack of horticultural information necessitates this study to evaluate the propagation of this economical important species. The main objective of this study was to establish a simple and highly productive micropropagation protocol for A. betulina through experimenting with nodal explants. Testing of the effect of various treatments (physical scarification, chemical scarification, GA, stratification, smoke and combinations thereof) on the in vitro germination of A. betulina seeds was done to elucidate the factors which control seed germination. The study revealed that the physical scarification and smoke-induced germination had a significant effect on germination percentages. In terms of germination rate, the radical generally started to appear after approximately 10 days in the physical scarification with smoke treatment. Initial decontamination methods with the exposure of various concentrations of NaOCl gave fatal results, however 1.5% NaOCl had more phenolic reactions rather than fungal or bacterial contamination. Interestingly, contamination rates of explants were influenced by the stage of maturity of the explant material. This plant material was used to test different strengths of regeneration media, to ensure that the explants receive ample nutrients. Results made exhibited that ½ MS was the best strength for growing A. betulina nodal explants. Compared comparison between in vitro derived explants and ex vitro collected explants showed that the ex vitro derived explants had significant results, but the explants lost vigour soon after the initial exponential growth leading to the explants dying off. Furthermore, ex vitro decontaminated plant material was not economically viable to continue with. Seedlings derived from germinated seeds appeared to be the preferred method of propagation as this spent the least time in culture and produced a stable plant with an established root system, which is essential during the hardening off process after in vitro growth. When exposing nodal explants to phytohormone 2,4-D it responds best to dosages 0.5mg Lˉ¹ and 1mg Lˉ¹. Phytohormone BA was very effective in producing soft friable callus. The best results were shown when 0.5mg Lˉ¹ BA was applied to ½ MS media. For both shoot length and multiple shoot production, a combination of phytohormones BA-NAA (1: 0.5mgLˉ¹) had the most significant results. Interestingly, a higher phytohormone concentration of NAA is necessary to develop multiple adventitious roots. The effect of 3mg Lˉ¹ was significant in that it resulted in multiple adventitious roots, but fewer calli was observed in this treatment. Micropropagation becomes valuable as little attention between subcultures is needed; making it less labour intensive compared to conventional nursery propagation systems where weeding watering and spraying of plants are labour intensive. In the traditional world of medicine, more so in Southern Africa, extracts are prepared by adding boiling water to the plant material; however commercial ethanol is used as an extractant. Establishment of the essential oil quality of the in vitro cultures post exposure to various treatments was done. Analysis of essential oils from A. betulina resulted in the identification of twenty one compounds. The results showed qualitative as well as quantitative differences amongst the samples used in the study. The highest relative concentration of limonene was observed in the callus of nodal explants after it was exposed to 0.5mg lˉ¹ NAA. No pulegone was found in this treatment making it ideal for limonene production. This suggests that liquid culture with the same treatment may produce more calli making it ideal for the production of limonene.

The growth of electricity markets around the world has introduced new challenges in which one of the challenges is the uncertainty that has become a structural element in this new environment. Market players have to deal with it to guarantee the appropriate power system planning and operation as well as its own economical liquidity. Under an open access environment in a deregulated power system, transmission management holds a vital role in supporting transactions between suppliers and customers. Nevertheless, a transmission network has some constraints that should be addressed in order to ensure sufficient control to maintain the security level of a power system while maximizing market efficiency. The most obvious drawback of transmission constraints is a congestion problem that becomes an obstacle of perfect competition among the market participants since it can influence spot market pricing. The system becomes congested when the supplier and customer agree to produce and consume a particular amount of electric power, but this can cause the transmission network to exceed its thermal limits. Congestion can cause the market players to exercise market power that can result in price volatility beyond the marginal costs. Thus, it is important to manage congestion efficiently in the design of a power market. One mechanism that has direct correlation with transmission management is market clearing price (MCP). Under an open access environment, energy prices throughout the network will be different and measured based on transmission constraint and network losses. When network losses are ignored and there is no congestion on the transmission lines, the power price will be the same at all nodes. This is known as uniform marginal pricing (UMP). However, as the power flow violates transmission constraints, redispatching generating units is required and this will cause the price at every node to vary. This phenomenon is defined as locational marginal pricing (LMP). Therefore, the market clearing price has a strong relationship with transmission management, which is needed to be assessed in order to obtain an efficient and transparent price but satisfying all market participants. This project investigates an alternative solution to the dispatch mechanism, and then formulates a new Locational Marginal Price scheme using optimization technique that may well control congestion as the main issue. The model will vary and be improved, to be distilled into energy price, congestion revenue, cost of losses, as well as transmission usage tariff. The objective of the project is to support developing standard market design (SMD) in managing transmission systems which promotes economic efficiency, lowers delivered energy costs, maintains power system reliability and mitigates exercising market power.

DYN3D is an best estimate advanced code for the three-dimensional simulation of steady-states and transients in light water reactor cores with quadratic and hexagonal fuel assemblies. Burnup and poison-dynamic calculations can be performed. For the investigation of wide range transients, DYN3D is coupled with system codes as ATHLET and RELAP5. The neutron kinetic model is based on the solution of the three-dimensional two-group neutron diffusion equation by nodal expansion methods. The thermal-hydraulics comprises a one- or two-phase coolant flow model on the basis of four differential balance equations for mass, energy and momentum of the two-phase mixture and the mass balance for the vapour phase. Various cross section libraries are linked with DYN3D. Systematic code validation is performed by FZR and independent organizations.

Les travaux de recherche présentés dans ce document portent sur le dimensionnement de machines synchrones pour des applications de véhicules hybrides. L'utilisation de la machine électrique au sein du véhicule hybride est caractérisée par des appels de puissance de courtes durées. Cette thèse propose donc une stratégie de dimensionnement permettant de minimiser considérablement le volume de l'actionneur par la prise en compte des limites thermiques réelles lors du cycle de conduite. La stratégie de dimensionnement est composée de deux étapes. La première étape est l'optimisation du dimensionnement de l'actionneur à partir des points de fonctionnement du cycle. Nous autorisons des niveaux d'induction dans le fer élevés et des niveaux de densité de courant dans les conducteurs dépassant les niveaux habituellement autorisés pour un fonctionnement en régime permanent thermique. Ces deux points ont un impact réel sur le volume de la machine. Cela-dit, à ce stade, la thermique de la machine n'est prise en compte qu'indirectement en fixant une densité de courant dans les conducteurs. La seconde étape permet alors de vérifier la thermique par une simulation sur cycle pour ensuite réajuster si besoin la densité de courant et reprendre la première étape d'optimisation de la machine. Des modèles adaptés au processus d'optimisation ont alors été mis en place et offrent un bon compromis entre le temps de calcul et la précision requise. Par conséquent, un modèle magnétique prenant en compte la saturation croisée dans la machine utilisant la méthode nodale a été développé ; un modèle permettant une meilleure prise en compte des pertes fer notamment dans le zone de défluxage a également été développé ainsi qu'un modèle thermique en transitoire utilisant également la méthode nodale. Le modèle thermique étant la clé de la stratégie de dimensionnement, une grande attention y a été portée. Ce modèle permet de prendre en compte la direction des flux dans les trois dimensions et fournit de bonnes estimations des températures dans la machine notamment aux endroits les plus chauds comme les encoches et les têtes de bobines. Ces résultats ont été corroborés par des essais expérimentaux réalisés dans les bancs IFPEN sur une machine spécialement instrumentée en thermocouples. Cela a permis de valider le comportement thermique en régime permanent thermique et en régime transitoire thermique. Ces modèles ont ensuite été implantés dans une modélisation multi-physique pour l'outil d'optimisation et pour l'outil de simulation. Une étude de cas a été présentée pour un véhicule hybride Kangoo où la machine doit pouvoir assurer son fonctionnement pour un cycle Artémis urbain. Les résultats de la stratégie de dimensionnement permettent alors de conclure que sur cycle, le volume extérieur des parties actives de la machine électrique peut-être réduit de 40 % par rapport à un dimensionnement établi par les règles de l'art en régime permanent. De plus, la réduction du volume de fer dans la machine induit également une réduction des pertes fer ce qui nous permet de conclure que, toujours sur cycle, son rendement moyen reste élevé.

The growth of electricity markets around the world has introduced new challenges in which one of the challenges is the uncertainty that has become a structural element in this new environment. Market players have to deal with it to guarantee the appropriate power system planning and operation as well as its own economical liquidity. Under an open access environment in a deregulated power system, transmission management holds a vital role in supporting transactions between suppliers and customers. Nevertheless, a transmission network has some constraints that should be addressed in order to ensure sufficient control to maintain the security level of a power system while maximizing market efficiency. The most obvious drawback of transmission constraints is a congestion problem that becomes an obstacle of perfect competition among the market participants since it can influence spot market pricing. The system becomes congested when the supplier and customer agree to produce and consume a particular amount of electric power, but this can cause the transmission network to exceed its thermal limits. Congestion can cause the market players to exercise market power that can result in price volatility beyond the marginal costs. Thus, it is important to manage congestion efficiently in the design of a power market. One mechanism that has direct correlation with transmission management is market clearing price (MCP). Under an open access environment, energy prices throughout the network will be different and measured based on transmission constraint and network losses. When network losses are ignored and there is no congestion on the transmission lines, the power price will be the same at all nodes. This is known as uniform marginal pricing (UMP). However, as the power flow violates transmission constraints, redispatching generating units is required and this will cause the price at every node to vary. This phenomenon is defined as locational marginal pricing (LMP). Therefore, the market clearing price has a strong relationship with transmission management, which is needed to be assessed in order to obtain an efficient and transparent price but satisfying all market participants. This project investigates an alternative solution to the dispatch mechanism, and then formulates a new Locational Marginal Price scheme using optimization technique that may well control congestion as the main issue. The model will vary and be improved, to be distilled into energy price, congestion revenue, cost of losses, as well as transmission usage tariff. The objective of the project is to support developing standard market design (SMD) in managing transmission systems which promotes economic efficiency, lowers delivered energy costs, maintains power system reliability and mitigates exercising market power.