This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>

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Le Modèle standard de la physique de particules explique avec beaucoup de succès comment les particules fondamentales interagissent entre elles. Néanmoins, ce modèle n’est pas capable d’expliquer certains défis contemporains du domaine, comme la grande quantité de paramètres libres, le problème de la hiérarchie ou l’identité de la matière sombre. Pour expliquer ces phénomènes, il faut chercher la physique au-delà du Modèle standard. De sorte à satisfaire les contraintes provenant des mesures expérimentales, on peut considérer l’addition d’une seule nouvelle particule au Modèle standard qui se couple à deux quarks, le diquark. Sa contribution aux processus hadroniques offre une opportunité d’obtenir des limites dans ses paramètres à partir des données expérimentales contemporaines. Ceci nous permettrait d’évaluer son potentiel et d’identifier les processus auxquels cette particule peut contribuer. Parmi les états de diquarks possibles, on trouve les diquarks scalaires Dᵘ et Dᵈ, qui possèdent un couplage antisymétrique à des paires de quarks droitiers du type up ou du type down, respectivement. L’obtention des contraintes sur les valeurs de leur masse Mᴰ et leurs couplages aux quarks (x^q, y^q), où q = u, d, est l’objectif central de ce travail. Pour cela, on considère tout d’abord des recherches directes dans la production de dijet, la signature expérimentale des désintégrations de ces particules. Ensuite, on sonde l’influence indirecte du diquark Dᵘ dans les mesures expérimentales de la section efficace de production d’un seul quark top. Les données expérimentales obtenues dans le Grand collisionneur d’hadrons (LHC) pour ces processus à haute énergie sont utilisées pour comparer les prédictions théoriques de ces modèles et quantifier leur viabilité en fournissant de nouvelles contraintes sur ses paramètres. On est capable d’améliorer les contraintes trouvées dans la littérature de |xᵘ| ≤ 14,4 à |xᵘ| ≤ 0,13–0,15 pour Dᵘ et de |xᵈyᵈ| ≤ 0,022 avec |yᵈ| ≤ 0,17 à |xᵈ| ≤ 0,15–0,17 pour Dᵈ, les deux avec une masse de Mᴰ = 600 GeV. De plus, l’analyse des données pour la production d’un seul quark top montre que la réduction de l’espace de phase des pᵀ peut améliorer encore plus ces contraintes. / The Standard Model of particle physics explains with great success how fundamental particles interact. However, this model cannot explain some contemporary challenges of the domain, such as the large number of free parameters, the hierarchy problem or the identity of dark matter. To explain these phenomena, we need to search for physics beyond the Standard Model. In order to satisfy the existing constraints from experimental measurements, we can consider the addition of a single new particle to the Standard Model that couples to two quarks, a diquark. Its contribution to hadronic processes offers an opportunity to set limits on its parameters from contemporary experimental data. This would allow us to evaluate their potential and identify processes to which they can contribute. Among the possible diquark states, we find the scalar diquarks Dᵘ and Dᵈ, which have an antisymmetric coupling to pairs of right-handed up-type or down-type quarks, respectively. To obtain constraints on their mass Mᴰ and on their couplings to quarks (x^q, y^q), where q = u, d, is the main goal of this work. In order to do so, we start by considering direct searches in the production of dijet, the experimental signature of the decay of these particles. Afterwards, we probe the indirect influence of the Dᵘ diquark to the experimental measurements of the single-top-production cross section. Recent data for both of these processes from the Large Hadron Collider (LHC) is used to compare the theoretical predictions of these models and quantify their viability by providing new constraints on its parameters. We are able to improve the constraints found in the literature from |xᵘ| ≤ 14.4 to |xᵘ| ≤ 0.13–0.15 for Dᵘ and from |xᵈyᵈ| ≤ 0.022 to |yᵈ| ≤ 0.17 to |xᵈ| ≤ 0.15–0.17 for Dᵈ, both with masses of Mᴰ = 600 GeV. Other than that, the analysis of the data from single top production shows that the reduction of the pᵀ space can further improve these constraints.

The master’s thesis deals with design and realization of three-phase inverter for experimental high speed asynchronous motor with a mechanical power of 6 kW. The thesis deals with the design of the individual components of the DC link. The thesis describes the selection of suitable capacitors in the DC link. There is also a complete simulation of the inverter in the Matlab Simulink program. Part of the thesis is also the design and realization of printed circuit boards of this inverter.

This diploma thesis deals with a design modification of detection part of the laboratory instrument for measuring the topography of rough surfaces – laser goniometric scatterometer (SM II). Design modification is based on replacement of so far used detector instead for the detector of higher quality with better measurement parameters. The first part of the diploma thesis contains theoretical basics, which are necessary to understand the relationship between scalar diffraction theory and scattering measurements of monochromatic light. The emphasis is on the importance of choosing appropriate detection coordinates, which are affecting the aberrations of detected diffracted light. The practical part is dedicated to improving the sensitivity of the detection part of the scatterometer SM II that is used in The laboratory of coherence optics at IFE FME BUT. This part justifies the choice of the detector which predetermines both the use of optical elements and the overall design of the detection part as the goniometer.

This master's thesis is interested in concept of frequency converter for induction machine to power 2 kW. Control of this converter is wirelessly or via PC. The solution is based on execution with integrated circuits and microprocesors to control them.

This thesis is about visualizing a kind of data that is trivial to process by computers but difficult to imagine by humans because nature does not allow for intuition with this type of information: high-dimensional data. Such data often result from representing observations of objects under various aspects or with different properties. In many applications, a typical, laborious task is to find related objects or to group those that are similar to each other. One classic solution for this task is to imagine the data as vectors in a Euclidean space with object variables as dimensions. Utilizing Euclidean distance as a measure of similarity, objects with similar properties and values accumulate to groups, so-called clusters, that are exposed by cluster analysis on the high-dimensional point cloud. Because similar vectors can be thought of as objects that are alike in terms of their attributes, the point cloud\''s structure and individual cluster properties, like their size or compactness, summarize data categories and their relative importance. The contribution of this thesis is a novel analysis approach for visual exploration of high-dimensional point clouds without suffering from structural occlusion. The work is based on implementing two key concepts: The first idea is to discard those geometric properties that cannot be preserved and, thus, lead to the typical artifacts. Topological concepts are used instead to shift away the focus from a point-centered view on the data to a more structure-centered perspective. The advantage is that topology-driven clustering information can be extracted in the data\''s original domain and be preserved without loss in low dimensions. The second idea is to split the analysis into a topology-based global overview and a subsequent geometric local refinement. The occlusion-free overview enables the analyst to identify features and to link them to other visualizations that permit analysis of those properties not captured by the topological abstraction, e.g. cluster shape or value distributions in particular dimensions or subspaces. The advantage of separating structure from data point analysis is that restricting local analysis only to data subsets significantly reduces artifacts and the visual complexity of standard techniques. That is, the additional topological layer enables the analyst to identify structure that was hidden before and to focus on particular features by suppressing irrelevant points during local feature analysis. This thesis addresses the topology-based visual analysis of high-dimensional point clouds for both the time-invariant and the time-varying case. Time-invariant means that the points do not change in their number or positions. That is, the analyst explores the clustering of a fixed and constant set of points. The extension to the time-varying case implies the analysis of a varying clustering, where clusters appear as new, merge or split, or vanish. Especially for high-dimensional data, both tracking---which means to relate features over time---but also visualizing changing structure are difficult problems to solve.

In dieser Arbeit werden zwei Klassen von Evolutionsgleichungen in einem Matrixraum-Setting studiert: Hyperbolische Erhaltungsgleichungen und aktive skalare Gleichungen. Für erstere wird untersucht, wann man Oszillationen mit Hilfe polykonvexen Maßen ausschließen kann; für Zweitere wird mit Hilfe von Oszillationen gezeigt, dass es unendlich viele periodische schwache Lösungen gibt.

Cette thèse porte sur la gravitation et certains de ses liens avec la théorie des champs. Le point de départ de cette recherche a été l’étude de la limite newtonienne de la relativité générale. Très vite, notre intérêt s’est porté sur l’effet du temps retardé et son rôle dans l’absence d’aberration. Ce manque d’aberration est la raison pour laquelle la force pointe dans la direction instantanée (extrapolée) pour des sources sans accélération, malgré la vitesse finie de la gravitation (c’est aussi le cas pour l’électromagnétisme). Ceci nous a conduit à calculer le champ résultant entre deux masses accélérées avec la présence d’aberration. Nous avons en particulier considéré le mouvement de deux masses de telle façon que la force totale de Newton à une position s’annule alors que les effets du temps retardé soient bien différents de zéro. Nous avons pu calculer ces derniers et proposer deux situations où ils pourraient être observés dans le futur. L’étude de la linéarisation de la relativité générale a naturellement porté notre intérêt sur la physique du graviton, la version quantifiée de la théorie classique linéaire. Plusieurs travaux sur l’impossibilité d’observer directement ce graviton [1,2] ainsi que des expériences de pensée sur la possibilité de le quantifier ou non [3] ont piqué notre curiosité. C’est ce qui a lancé la recherche de la section efficace (et du potentiel) dans le cas d’une diffusion gravitationnelle sur une particule initialement dans une superposition spatiale. En parallèle de ces recherches, des discussions avec mon collègue Kévin Nguyen et la lecture de son article [4], ont attiré mon attention sur le problème de la constante cosmologique et l’élégante solution proposée. Cette dernière est basée sur l’ajout d’un scalaire couplé non minimalement avec la gravité et permet d’expliquer la valeur minuscule de la constante cosmologique par certains très petits paramètres du champ scalaire. Leur solution était cependant encore très théorique, car elle n’était valable que dans un univers sans matière. Nous avons donc analysé l’effet de la matière sur l’évolution du champ scalaire et montré que dans une partie de l’espace des paramètres, la théorie considérée résolvait le problème de la constante cosmologique tout en restant indistinguable de la relativité générale. / This thesis concerns gravitation and some of its connections with field theory. The starting point of this research was the study of the Newtonian limit of general relativity. Our interest was focused on the effect of retarded time and its role in the absence of aberration. Lack of aberration is the reason why the gravitational force points in the instantaneous (extrapolated) direction for unaccelerated sources, despite the finite speed of propagation of gravity (this also holds true for electromagnetism). Naturally this led us to compute the resulting gravitational field of accelerating masses, where aberration is not absent. In particular, we considered the motion of two masses such that their total Newtonian force at a position vanished but the retarded gravitational effects were non-zero. We were able to calculate these retarded effects and to propose two situations where they could be observed in the future. The study of the linearization of general relativity naturally arouse our interest toward the physics of gravitons, the quantized version of the linear classical theory. In particular, there has been much thought and literature on the impossibility of directly observing a graviton [1, 2] as well as thought experiments on the possibility of quantizing gravity or not [3]. This led to the calculation of the cross section (and gravitational potential) in the case of the gravitational scattering off a massive particle that is in a spatially non-local quantum superposition. In parallel with this research, some discussions with my colleague Kévin Nguyen about his article [4] on the problem of the cosmological constant, focussed my interest on this problem and the elegant solution proposed. The solution is based on the addition of a nonminimally coupled scalar and makes it possible to explain the tiny value of the cosmological constant through some small parameters of the scalar field. The solution is however very theoretical as it was only done in a matter free universe. We therefore examined at the effect of different kinds of matter on the evolution of the scalar field. We show that in one part of the parameter space, the theory we considered resolved the cosmological constant problem while being indistinguishable from general relativity.

This thesis proposes, validates, and compares low-complexity algorithms for the fast-and-safe charge and balance of Li-ion batteries both for the single cell case and for the case of a serially-connected string of battery cells. The proposed algorithms are based on a reduced-order electrochemical model (Equivalent Hydraulic Model, EHM), and make use of constrained-control strategies to limit the main electrochemical degradation phenomena that may accelerate aging, namely: Lithium plating in the anode and solvent oxidation inthe cathode. To avoid the computational intensiveness of solving an online optimization as in the Model Predictive Control (MPC) framework, this thesis proposes the use of Reference Governor schemes. Variants of both the Scalar Reference Governors (SRG) and the Explicit Reference Governors (ERG) are developed to deal with the non-convex admissible region for the charge of a battery cell, while keeping a low computational burden. To evaluate the performance of the proposed techniques for the single cell case, they are experimentallyvalidated on commercial Turnigy LCO cells of 160 mAh at four different constant temperatures (10, 20, 30 and 40 °C). In the second part of this thesis, the proposed charging strategies are extended to take into account the balance of a serially-connected string of cells. To equalize possible mismatches, a centralized policy based on a shunting grid (active balance) connects or disconnects the cells during the charge. After a preliminary analysis, a simple mixed-integer algorithm was proposed. Since this method is computationally inefficient due to the high number of scenarios to be evaluated, this thesis proposes a ratio-based algorithm based on a Pulse-Width Modulation (PWM) approach. This approach can be used within both MPC and RG schemes. The numerical validations of the proposed algorithms for the case of a string of four battery cells are carried out using a simulator based on a full-order electrochemical model. Numerical validations show that the PWM-like approach charges in parallel all the cells within the pack, whereas the mixed-integer approach charges the battery cells sequentially from the battery cell with the lowest state of charge to the ones with the highest states of charge. On the basis of the simulations, an algorithm based on a mixed logic that allows to charge in a “sequential parallel” approach is proposed. Some conclusions and future directions of research are proposed at the end of the thesis. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished