Des modèles spécifiques de gravitation quantique suggèrent l’existence d’une Violation de l’Invariance de Lorentz (LIV en anglais) à l’échelle de Planck. Une des signatures de cette violation est la modification de la propagation des photons dans le vide, induisant des décalages temporels dépendant de l’énergie des photons observés sur Terre. De tels décalages dans le temps d’arrivée de rayons γ sont recherchés avec l’expérience H.E.S.S. (High Energy Stereoscopic System), grâce aux émissions de très hautes énergies en provenance de sources lointaines telles que les blazars. Néanmoins, l’origine du décalage temporel doit être comprise en détails. En effet, un décalage intrinsèque à la source pourrait venir biaiser les contraintes sur les modèles de gravitation quantique. Cette thèse propose dans un premier temps de s’intéresser à la modélisation temporelle des éruptions de blazars, pour étudier les possibles décalages intrinsèques liés aux processus d’émissions de ces éruptions. Grâce à l’élaboration d’un modèle simple, cette étude met en relief les différentes caractéristiques de ces décalages intrinsèques sur les scénarios d’éruptions de blazar afin d’essayer de les distinguer des décalages potentiellement dus à un effet de LIV et aussi de proposer de nouvelles contraintes basées sur ces décalages temporels. Dans un deuxième temps, la méthode de recherche de décalages temporels dépendant de l’énergie avec H.E.S.S. est présentée ainsi qu’une application sur l’éruption du blazar Markarian 501 ayant eu lieu en juillet 2014. Cette analyse a permis d’établir la meilleure limite obtenue sur le terme quadratique de la signature de la LIV avec l’utilisation d’éruption de blazars. / Specific models of quantum gravity suggest the existence of a Lorentz Invariance Violation (LIV) at the Planck scale. One signature of that violation is a modification the propagation of photons in vacuum which induces energy dependent delays in the arrival time of photons on Earth. The H.E.S.S. (High Energy Stereoscopic System) experiment can search for such delays in the arrival time of gamma rays, thanks to the very high energy emission coming from distant blazars. However, the time delay origin have to be fully understood. Indeed, an intrinsic time delay coming from the source can bias the constraints made on quantum gravity models. In the first part of this thesis, a time dependent blazar flare model is considered to search for the presence of intrinsic time delays related to the emission mechanisms of flares. With the elaboration of a simple scenario, this study highlights the different characteristics of intrinsic time delays in order to investigate how to disentangle them from delays due to LIV as well as to provide new constraints on blazar modeling. In the second part of this thesis, the method used to search for LIV signatures in blazar light curves at very high energy is presented as well as an application to the flare of Markarian 501 which occurred in July 2014. This analysis provides in particular the best upper limit on the quadratic term of LIV signature.

In this thesis, we are interested in damped wave models with time-dependent propagation speed and time-dependent damping term both having a time-dependent oscillation term. The main goal of this thesis is to understand the influence of strong time-dependent oscillations on Sobolev solutions to the linear models and consequently, to the semilinear models. Especially, due to the deteriorating influence of oscillations on solutions, a stabilization condition and higher-order regularity of the time-dependent coefficients may compensate 'bad behaviors' arising from oscillations.:1. Introduction 2. The influence of oscillations on linear damped wave equation with time-dependent coefficients 3. Global in time existence results for damped wave models with power nonlinearity 4. Global in time existence results for damped wave models with different power nonlinearities 5. Lp-Lq estimates for wave equations with strong time-dependent oscillations 6. Further research topics A. Basic tools B. List of symbols and abbreviations Bibliography

The non-adiabatic quantum molecular dynamics (NA-QMD) method couples self-consistently classical nuclear motion with time-dependent density functional theory (TDDFT) in basis expansion for the electron dynamics. It has become a versatile approach to study the dynamics of atoms, molecules and clusters in a wide range of scenarios. This work presents applications of the NA-QMD method to important benchmark systems and its systematic extension to include quantum effects in the nuclear motion. Regarding the first objective, a complete study of the strong-field ionization and dissociation dynamics of nature’s simplest molecule H2+ is performed. By including all electronic and nuclear degrees of freedom and all reaction channels, molecular rotation is shown to play an important role in the ionization process. In addition, strong orientation effects in the energy deposition process of the Buckminster fullerene C60 in short intense laser pulses are surprisingly found in full dimensional calculations. Their consequences on the subsequent nuclear relaxation dynamics shed new light on available experimental data and future experiments are proposed to confirm the detailed predictions. Regarding the second objective, the NA-QMD formalism is basically extended to take electron-nuclear correlations into account. This extension is achieved by means of a trajectory surface hopping scheme in the adiabatic Kohn-Sham framework. First studied examples from collision physics and photochemistry illustrate the relevance and importance of quantum effects in the nuclear dynamics.

Viele Problemstellungen der Naturwissenschaften führen zur Betrachtung von nichtlinearen Wellengleichungen. Dabei ist von großem Interesse, ob zu vorgegebenen kleinen Daten Lösungen eindeutig existieren und ob diese stetig von den Daten abhängen. Hilfsmittel für diese Probleme sind Aussagen über lineare Wellengleichungen. In der vorliegenden Arbeit werden lineare Klein-Gordon Gleichungen, also Wellengleichungen mit Potentialterm, mit zeitabhängiger Masse bzgl. des Verhaltens ihrer Lösungen untersucht. Von speziellem Interesse sind Resultate mit Bezug auf verallgemeinerte Energieerhaltung und sogenannte Lp – Lq decay-Abschätzungen. Aus der Arbeit geht hervor, dass man eine Klassifizierung für Gleichungen mit fallendem Masseterm finden kann. Für Gleichungen vom Wellentyp ist der Einfluss des Potentialterms gering und die Lösungen verhalten sich wie Lösungen der Wellengleichung. Dem gegenüber stehen Gleichungen vom Klein-Gordon-Typ mit erkennbarem Einfluss des Masseterms. Ausgangspunkt für die Klassifizierung ist das kritische Verhalten der Lösungen einer skaleninvarianten Gleichung mit speziellem Masseterm.

The analysis of the immensity of data in space and time is a challenging task. For this thesis, the time-dependent data has been explored in various directions. The studies focused on data visualization, feature extraction, and data classification. The data that has been used in the studies comes from various well-recognized archives and has been the basis of numerous researches. The data characteristics ranged from the univariate time series to multivariate time series, from hand gestures to unconstrained views of general human movements. The experiments covered more than one hundred datasets. In addition, we also discussed the applications of visual analytics to video data. Two approaches were proposed to create a feature vector for time-dependent data classification. One is designed especially for a bio-inspired model for human motion recognition and the other is a subspace-based approach for arbitrary data characteristics. The extracted feature vectors of the proposed approaches can be easily visualized in two-dimensional space. For the classification, we experimented with various known models and offered a simple model using data in subspaces for light-weight computation. Furthermore, this method allows a data analyst to inspect feature vectors and detect an anomaly from a large collection of data simultaneously. Various classification techniques were compared and the findings were summarized. Hence, the studies can assist a researcher in picking an appropriate technique when setting up a corresponding model for a given characteristic of temporal data, and offer a new perspective for analyzing the time series data. This thesis is comprised of two parts. The first part gives an overview of time-dependent data and of this thesis with its focus on classification; the second part covers the collection of seven publications.

The diploma thesis deals with the design of a road bridge on the I/57 expressway over the relocation of the cycle path, the Opavice river and the local road, which involves the relocation of the access to the waterworks. The bridge structure is located in the territory of the town of Krnov. A study of the area's bridges is part of the project and three studies have been prepared. Study A was chosen for detailed processing. It is a continuous box girder bridge with three spans. The superstructure is designed as a monolithic, post-tensioned structure. A sliding girder is being investigated for the structure's construction. Scia Engineer 18.1 is used to do the load effects computation. Only the consequences of vertical load effects have been addressed, with no consideration of horizontal load effects. The structure was evaluated using limit states, taking into account the impact of construction on its design.

The diploma thesis deals with the design of the supporting structure of a road bridge over a reservoir. Two variants of bridging were processed. The selected variant is a three span continuous beam. It is made of box girder cross section with a variable height. The structure has a total length of 156,8 m and is built using balanced cantilever method. The bridge is designed and assessed according to the limit states for temporary and permanent design situations. Structural analysis, drawing documentation and visualization of the bridge is part of the work.

This work is concerned with the theoretical analysis of the space-time discontinuous Galerkin method applied to the numerical solution of nonstationary nonlinear convection-diffusion problem in a time- dependent domain. At first, the problem is reformulated by the use of the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convection term. Then the problem is discretized with the use of the ALE space-time discontinuous Galerkin method. On the basis of a technical analysis we obtain an unconditional stability of this method. An important step in the analysis is the generalization of a discrete characteristic function associated with the approximate solutionin a time-dependentdomainand the derivationof its properties. Further we derive an a priori error estimate of the method in terms of the interpolation error, as well as in terms of h and tau. Finally, some practical applications of the ALE space-time discontinuos Galerkin method in a time-dependent domain are given. We are concerned with the numerical solution of a nonlinear elasticity benchmark problem and moreover with the interaction of compressible viscous flow with elastic structures. The main attention is paid to the modeling of flow induced vocal fold...

[pt] Durante a gelificação por parafina, a rede de cristais de parafina modifica o comportamento do óleo cru. Ele muda de um material newtoniano de baixa viscosidade para um material com dependência temporal e de alta viscosidade com tensão limite do escoamento. Com isto, é totalmente desafiador descobrir a pressão minima de início do fluxo de petróleo gelificado com uma microestrutura tão complexa. Através da minha dissertação de mestrado, investigamos dois materiais viscoplásticos: um gel de cabelo com uma tixotropia desprezível e uma suspensão aquosa tixotrópica 2 por cento de laponita para imitar o início de fluxo de óleos gelificados. Para ambos os materiais, o gradiente de pressão axial mínimo necessário para o início do fluxo foi medido e os valores medidos estavam de acordo com a previsão do balanço de força convencional. Por outro lado, os casos da indústria exibiram que o balanço de força mencionado acima leva a uma superestimação da pressão mínima inicial. Em alguns estudos, uma explicação elicitada é o comportamento tixotrópico do petróleo gelificado, mas nossos resultados acima mencionados serviram para refutá-lo. Durante a primeira parte da minha tese de doutorado, buscamos verificar por laboratório porque o balanço de força não se aplica ao petróleo gelificado, em seguida, buscamos uma explicação fisicamente adequada para essa discrepância e também uma maneira confiável de prever a pressão mínima de início do escoamento. Nesta linha, mostramos o efeito do encolhimento do petróleo gelificado na discordância entre a tensão limite estática de escoamento e o gradiente de pressão mínimo necessário para iniciar o fluxo, através da reometria e do fluxo de fluido em um tubo. Em seguida, introduzimos uma equação de balanço de força modificada com o efeito de encolhimento incluído para obter o melhor estimação da pressão minima de início de escoamento. Outro elemento essencial sobre o início de escoamento de petróleo gelificado é descobrir uma estratégia confiável para modelar matematicamente a reologia do material. Na maioria dos modelos que visam prever o comportamento reológico de petróleo gelificado, as mudanças da microestrutura durante o fluxo são consideradas tixotrópicas; dependência temporal reversível. Porém, observamos em nossos experimentos com histórias de fluxo e térmicas bem controladas que o caráter irreversível da dependência temporal é bastante evidente. Assim, na segunda parte da tese, propomos um modelo baseado no desenvolvimentos anteriores de Souza Mendes e colaboradores que considera a dependência temporal irreversível observada experimentalmente para petróleo gelificado. A capacidade preditiva do modelo proposto é então avaliada através de comparações com dados experimentais. / [en] Throughout the wax gelation, the network of parafinn crystals modifies the behavior of waxy crude oil. It changes from a low viscosity Newtonian to a high viscosity time-dependent material with yield strength. Now, it is totally challenging to find out the restart pressure for gelled crude oil ow with such a complex microstructure. Through my Master s dissertation, we investigated two viscoplastic materials, namely a hair gel with a negligible thixotropy and a quite thixotropic 2 percent aqueous suspension of Laponite to mimic the startup flow of waxy crude oils. For both materials, the minimum axial pressure gradient required for the onset of flow was measured, and the measured values were in good agreement with the prediction of a conventional force balance. On the other hand, industry cases have exhibited that the just mentioned force balance leads to an overestimation of the minimum startup pressure gradient. In some studies, an elicited explanation is the thixotropic behavior of the gelled crude, but our results above-mentioned served to falsify it. Over the first part of my PhD thesis, we aimed to verify in the laboratory that why the force balance does not hold for gelled crude oil and then we sought a physically proper explanation for this discrepancy and also a reliable way to predict the minimum startup pressure gradient. Along these lines, we show the role of gelled crude oil s shrinkage in the discordance between static yield strength and required minimum pressure gradient to onset the flow, through rheometry and fluid flow in a tube. Then, we introduce a modified force balance equation with the role of shrinkage included to best estimate the minimum restart pressure gradient. Another essential element through the restart flow of gelled waxy crude is to find out a reliable strategy to mathematically model the material s rheology. In most models that aim at predicting the rheological behavior of gelled waxy crude oil, the microstructure changes during ow are assumed to be thixotropic (reversible time dependent). But, we observed in our experiments with well-controlled flow and thermal histories that the irreversible character of time dependence is quite evident. Thus, in the second part of thesis we propose a model based on previous developments by Souza Mendes and co-workers that accounts for the irreversible time dependence observed experimentally in a waxy crude oil. The predictive capability of the proposed model is then assessed via comparisons with experimental data.

Les services de livraison express font face au défi d’optimiser les routes de leurs véhicules alors que ceux-ci circulent dans un réseau routier où les temps de parcours varient en fonction du moment de la journée et où ils doivent répondre à l’arrivée dynamique de requêtes consistant à récupérer et livrer des colis. Notre but ici est de proposer une modélisation et une méthode de type heuristique pour résoudre ce problème. Nous commençons par explorer les travaux menés précédemment au sujet de l’arrivée dynamique des requêtes, des temps de parcours variables selon le moment de la journée et des collectes et livraisons dans les problèmes de tournées de véhicules. Ensuite, nous décrivons le problème de manière formelle sur le graphe du réseau routier avec des requêtes deux-points où l’objectif est de minimiser le temps total de parcours des véhicules et les temps de retard aux points de service et au dépôt. Par la suite, nous détaillons l’implémentation d’une méthode de résolution basée sur la recherche tabou utilisant une structure de voisinage basée sur la réinsertion d’une requête. Cette méthode utilise également la structure Dominant Shortest Path (DSP) qui considère plusieurs chemins alternatifs entre chaque paire de sommets, contrairement à l’approche traditionnelle où un chemin unique est fixé a priori. Finalement, nous testons notre méthode à l’aide de 390 instances générées de manière synthétique afin d’évaluer son efficacité ainsi que l’impact de certains aspects du problème et de la méthode de résolution. Les résultats démontrent une amélioration particulièrement importante due à l’utilisation de la structure DSP. / Express delivery services face the challenge of optimizing the routes of their vehicles while they are moving in a road network where the travel times vary according to the time of day in order to serve dynamic requests which consist in collecting and delivering parcels. Our goal here is to propose a model and a heuristic method to solve this problem. We begin by exploring previous work on the topic of the dynamic arrival of requests, timedependent travel times and pickups and deliveries in vehicle routing problems. Afterwards, we describe the problem formally on the graph of the road network with the objective of minimizing the total travel time of the vehicles and lateness at the service points and at the depot. Then, we detail the implementation of a solving method based on tabu search using a neighbourhood structure based on the reinsertion of a request. This method also uses the Dominant Shortest Path (DSP) structure which considers multiple alternative paths between each pair of vertices, unlike the traditional approach where a single path is fixed a priori. Finally, we test our method using 390 instances generated synthetically in order to evaluate its efficiency as well as the impact of certain aspects of the problem and solution method. The results show a particularly significant improvement due to the use of the DSP structure.