Soit $p in N^*$. On définit une famille d'idempotents (et de nilpotents) des algèbres de Temperley-Lieb aux racines $4p$-ième de l'unité qui généralise les idempotents de Jones-Wenzl usuels. Ces nouveaux idempotents sont associés aux représentations simples et indécomposables projectives de dimension finie du groupe quantique restreint $Uq$, où $q$ est une racine $2p$-ième de l'unité. A l'instar de la théorie des champs quantique topologique (TQFT) de [BHMV95], ils fournissent une base canonique de classes d'écheveaux coloriés pour définir des représentations des groupes de difféotopie des surfaces. Dans le cas du tore, cette base nous permet d'obtenir une correspondance partielle entre les actions de la vrille négative et du bouclage, et la représentation de $SL_2(Z)$ de [LM94] induite sur le centre de $Uq$, qui étend non trivialement de la représentation de $SL_2(Z)$ obtenue par la TQFT de [RT91]. / Let $p in N^*$. We define a family of idempotents (and nilpotents) in the Temperley-Lieb algebras at $4p$-th roots of unity which generalizes the usual Jones-Wenzl idempotents. These new idempotents correspond to finite dimentional simple and projective indecomposable representations of the restricted quantum group $Uq$, where $q$ is a $2p$-th root of unity. In the manner of the [BHMV95] topological quantum field theorie (TQFT), they provide a canonical basis in colored skein modules to define mapping class groups representations. In the torus case, this basis allows us to obtain a partial match between the negative twist and the buckling actions, and the [LM94] induced representation of $SL_2(Z)$ on the center of $Uq$, which extends non trivially the [RT91] representation of $SL_2(Z)$.

L'objectif ultime de ce travail est de fournir des méthodologies robustes et efficaces sur le plan des calculs pour la modélisation et la résolution des problèmes de contact adhésifs basés sur le potentiel de Lennard-Jones (LJ). Pour pallier les pièges théoriques et numériques du modèle LJ liés à ses caractéristiques nondéfinies et non-bornées, une méthode d'adaptativité en modèle est proposée pour résoudre le problème purement-LJ comme limite d'une séquence de problèmes multiniveaux construits de manière adaptative. Chaque membre de la séquence consiste en une partition modèle entre le modèle microscopique LJ et le modèle macroscopique de Signorini. La convergence de la méthode d'adaptativité est prouvée mathématiquement sous certaines hypothèses physiques et réalistes. D'un autre côté, la méthode asymptotique numérique (MAN) est adaptée et utilisée pour suivre avec précision les instabilités des problèmes de contact à grande échelle et souples. Les deux méthodes sont incorporées dans le cadre multiéchelle Arlequin pour obtenir une résolution précise, tout en réduisant les coûts de calcul. Dans la méthode d'adaptativité en modèle, pour capturer avec précision la localisation des zones d'intérêt (ZDI), une stratégie en deux résolutions est suggérée : une résolution macroscopique est utilisée comme une première estimation de la localisation de la ZDI. La méthode Arlequin est alors utilisée pour obtenir une résolution microscopique en superposant des modèles locaux aux modèles globaux. En outre, dans la stratégie MAN, la méthode Arlequin est utilisée pour supprimer les oscillations numériques, améliorer la précision et réduire le coût de calcul. / The ultimate goal of this work is to provide computationally efficient and robust methodologies for the modelling and solution of a class of Lennard-Jones (LJ) potential-based adhesive contact problems. To alleviate theoretical and numerical pitfalls of the LJ model related to its non-defined and nonbounded characteristics, a model-adaptivity method is proposed to solve the pure-LJ problem as the limit of a sequence of adaptively constructed multilevel problems. Each member of the sequence consists of a model partition between the microscopic LJ model and the macroscopic Signorini model. The convergence of the model-adaptivity method is proved mathematically under some physical and realistic assumptions. On the other hand, the asymptotic numerical method (ANM) is adapted to track accurately instabilities for soft contact problems. Both methods are incorporated in the Arlequin multiscale framework to achieve an accurate resolution at a reasonable computational cost. In the model-adaptivity method, to capture accurately the localization of the zones of interest (ZOI), a two-step strategy is suggested: a macroscopic resolution is used as the first guess of the ZOI localization, then the Arlequin method is used there to achieve a fine scale resolution. In the ANM strategy, the Arlequin method is also used to suppress numerical oscillations and improve accuracy.

Thesis advisor: Corey Creekmur, Kim Marra. Includes bibliographic references (p. 330-356).

Made available in DSpace on 2016-12-12T20:15:52Z (GMT). No. of bitstreams: 1 Graziele Bortolini.pdf: 3189488 bytes, checksum: 6e8f5c11b189fb8f0ee4624270ebcee3 (MD5) Previous issue date: 2015-03-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Nosé-Hoover dynamics is deterministic and time-reversible and performs a statistical sampling of the canonical ensemble of a many-body system directly from the system dynamics. This system is coupled to one extra degree of freedom (extended system) acting as a heat reservoir. In this work, we study the dynamical of the prototype system: the harmonic oscillator thermalized in the Nosé-Hoover dynamics. We observe periodic and quasi periodic regular trajectories in the phase space for different initial conditions. However, the oscillator is non-ergodic and non-canonical in the Nosé-Hoover dynamics, when we add one reservoir degree of freedom (thermostats chain), the momentum distribution tends to the canonical one. The second system studied is an Argonne gas with 4000 particles which interact by means of a Lennard-Jones potential. For this system, we observe phase transitions, momentum distributions in agreement of canonical ensemble, as well, the thermostat efficiency to keep constant the average temperature. / A dinâmica de Nosé-Hoover é determinística e reversível no tempo e realiza uma amostragem estatística de um sistema de muitos corpos no ensemble canônico diretamente a partir da dinâmica do sistema. Esse sistema é acoplado a um grau de liberdade extra (sistema estendido) que desempenha o papel de um reservatório térmico. Neste trabalho, estudamos a dinâmica do sistema protótipo mínimo: o oscilador harmônico na dinâmica de Nosé-Hoover. Observamos trajetórias regulares periódicas e quase periódicas no espaço de fase para diferentes condições iniciais. Embora, o oscilador não seja ergódico e não reproduza as médias do ensemble canônico na dinâmica de Nosé-Hoover, ao adicionarmos mais um grau de liberdade ao reservatório (cadeia de termostatos), a distribuição de momentos tende a canônica. O segundo sistema estudado é um gás de Argônio constituído de 4000 partículas que interagem segundo um potencial de Lennard-Jones. Para esse sistema, observamos transições de fase, distribuições de momento em concordância com o ensemble canônico, assim como a eficiência do termostato de Nosé-Hoover em manter a temperatura média constante.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Devido à sua importância, o chamado problema de Lennard-Jones tem atraído pesquisadores de diversos campos da ciência pura e aplicada. Tal problema resume-se em achar as coordenadas de um sistema no espaço Euclidiano tridimensional, as quais correspondem a um mínimo de um potencial de energia. Esse problema desempenha um papel de fundamental importância na determinação da estabilidade de moléculas em arranjos altamente ramificados, como das proteínas. A principal dificuldade para resolver o problema de Lennard-Jones decorre do fato de que a função objetivo é não-convexa e altamente não-linear com várias variáveis, apresentando, dessa forma, um grande número de mínimos locais. Neste trabalho, foram utilizados alguns métodos de otimização global estocástica, onde procurou-se comparar os resultados numéricos dos algoritmos, com o objetivo de verificar quais se adaptam melhor à minimização do referido potencial. No presente estudo, abordou-se somente micro agrupamentos possuindo de 3 a 10 átomos. Os resultados obtidos foram comparados também com o melhores resultados conhecidos atualmente na literatura. Os algoritmos de otimização utilizados foram todos implementados em linguagem C++. / Because of its importance, the so-called Lennard-Jones problem has attracted researchers from various fields of pure and applied science. This problem boils down to find the coordinates of a system with three-dimensional Euclidean space, which correspond to minimum potential energy. This problem plays a fundamental role in determining the stability of molecules in highly branched arrangement, such as proteins. The main difficulty in solving the problem of Lennard-Jones from the fact that the objective function is non-convex and highly nonlinear with several variables, thus presenting a large number of local minima. Here, we used some methods of stochastic global optimization, where we seek to compare the results of the numerical algorithm, in order to see which are better suited to the minimization of the potential. In this study, we addressed only micro groups having 3-10 atoms. The results were also compared with the currently best known results in literature. The optimization algorithms were all implemented in C + +.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Devido à sua importância, o chamado problema de Lennard-Jones tem atraído pesquisadores de diversos campos da ciência pura e aplicada. Tal problema resume-se em achar as coordenadas de um sistema no espaço Euclidiano tridimensional, as quais correspondem a um mínimo de um potencial de energia. Esse problema desempenha um papel de fundamental importância na determinação da estabilidade de moléculas em arranjos altamente ramificados, como das proteínas. A principal dificuldade para resolver o problema de Lennard-Jones decorre do fato de que a função objetivo é não-convexa e altamente não-linear com várias variáveis, apresentando, dessa forma, um grande número de mínimos locais. Neste trabalho, foram utilizados alguns métodos de otimização global estocástica, onde procurou-se comparar os resultados numéricos dos algoritmos, com o objetivo de verificar quais se adaptam melhor à minimização do referido potencial. No presente estudo, abordou-se somente micro agrupamentos possuindo de 3 a 10 átomos. Os resultados obtidos foram comparados também com o melhores resultados conhecidos atualmente na literatura. Os algoritmos de otimização utilizados foram todos implementados em linguagem C++. / Because of its importance, the so-called Lennard-Jones problem has attracted researchers from various fields of pure and applied science. This problem boils down to find the coordinates of a system with three-dimensional Euclidean space, which correspond to minimum potential energy. This problem plays a fundamental role in determining the stability of molecules in highly branched arrangement, such as proteins. The main difficulty in solving the problem of Lennard-Jones from the fact that the objective function is non-convex and highly nonlinear with several variables, thus presenting a large number of local minima. Here, we used some methods of stochastic global optimization, where we seek to compare the results of the numerical algorithm, in order to see which are better suited to the minimization of the potential. In this study, we addressed only micro groups having 3-10 atoms. The results were also compared with the currently best known results in literature. The optimization algorithms were all implemented in C + +.

Cette thèse s’inscrit dans le contexte de l’ANR ISABEAU (Innovating for Structural Adhesive Bonding Evaluation and Analysis with Ultrasounds, associant des physico-chimistes et des acousticiens) et cherche à apporter des connaissances nouvelles sur l’évaluation par ultrasons du niveau d’adhésion d’un collage structural par ondes de Lamb. La première partie porte sur l’aspect cohésif et particulièrement sur l’influence du paramètre de réticulation de réseaux époxys sur les courbes de dispersion des ondes de Lamb. La deuxième partie est consacrée à la caractérisation de niveaux d’adhésion dans une structure bicouche Aluminium Epoxy en tenant compte aussi bien des aspects cohésifs qu’adhésifs. Des échantillons à niveau d’adhésion connus et maîtrisés sont réalisés avec l’aide de physico-chimistes, où l’époxy est partiellement ou totalement réticulé, et où l’interface substrat adhésif a subit différents traitements chimiques et/ou mécaniques. Les résultats expérimentaux sont confrontés à ceux issus du modèle rhéologique de Jones résolu par éléments finis. Enfin, la troisième partie porte sur l’étude d’un assemblage tricouche Aluminium/Epoxy/Aluminium et cherche à qualifier différents niveaux d’adhésion à l’aide du modèle de Jones par ondes guidées et également par l’étude des fréquences de coupure des modes verticaux de la structure. / This thesis is in the context of the ANR ISABEAU (Innovating for Structural Adhesive Bonding Evaluation and Analysis with Ultrasounds, with the association of physico-chemists and acousticians) and seeks to bring new knowledge of the ultrasonic evaluation of the level of adhesion of structural bonding using Lamb waves. The first part focuses on the cohesive aspect, in particular on the influence of the crosslinking parameter of the polymer on the Lamb waves dispersion curves. The second part is dedicated to the evaluation of the adhesion level of a bi-layer Aluminum Epoxy taking into account the both cohesive and adhesive aspects. Samples of controlled and known adhesion levels are manufactured with the help of physico-chemists, where the crosslinking of the epoxy is partial or total, and the interface substrate-adhesive have been treated chemically and/or mechanically. The experimental results are compared to those obtained from a predictive model based on the rheological model of Jones solved by finite elements method. Finally, the third part focuses on the study of tri-layers Aluminum/Epoxy/Aluminum, looking for the qualification of different levels of adhesion with the Jones model using guided waves as well as the cut-off frequencies of the structure.

Ce travail de thèse présente la modélisation théorique de l'expérience FORCA-G. L'objectif de cette expérience est la mesure des interactions à courte portée entre des atomes piégés dans un réseau optique et une surface massive à une grande précision. Nous nous sommes intéressés plus particulièrement à l'effet Casimir-Polder induit par la surface sur les atomes. Le but était de fournir la prédiction la plus précise possible des états atomiques. Ceci a consisté à considérer les effets de la température sur l'interaction Casimir-Polder et modéliser la surface de la manière la plus réaliste possible. Afin de résoudre le problème de divergence qu'impliquait un traitement perturbatif de l'interaction atome-surface, nous avons développé une méthode numérique pour un traitement non-perturbatif de l'interaction Casimir-Polder et modélisé l'interaction atome-surface à très courte distance par un potentiel de Lennard-Jones. Chaque effet et incertitude sur les états atomiques ont été évalués afin de déterminer s'ils seraient observables ou un facteur limitant en regard de la précision visée par l'expérience. Enfin nous nous sommes intéressés au cas d'un déséquilibre thermique entre la température du miroir et la température de l'environnement qui pourrait être induit par les lasers en présence ou un laser de chauffage. Nous avons calculé la correction du potentiel Casimir-Polder due au déséquilibre et évalué l'effet sur les niveaux d'énergie atomiques pour déterminer si cet effet pouvait être mesuré. / This thesis presents the theoretical modeling of the experiment FORCA-G. The purpose of this experiment is to measure short-range interactions between trapped atoms in an optical lattice and a massive surface with a high precision. We are focused on Casimir-Polder effect induced by the surface on the atoms. The aim was to give the most possible precise prediction of atomic states. This work took the temperature effects on Casimir-Polder interaction into account, modelled the surface of the experiment. In order to solve the divergence problem due to the perturbative treatment of the atom-surface interaction, we developed a digital method for a non-perturbative treatment of the Casimir-Polder interaction and modelled the short-range atom-surface interaction by a Lennard-Jones potential. Each effect and uncertainties on the atomic states were evaluated so that we know if they could be observable or a limiting factor compared to the experiment precision. Finally we were focused on an out of thermal equilibrium situation between the miroir and environment temperature which may be induced by the lasers. We computed the correction to the Casimir-Polder potential due to this disequilibrium and evaluated the effect on the atomic states.

The master thesis presents an overview of face detection task in color, static images. Face detection term is posed in the context of various branches. Main concepts of face detection and also their relationships are described. Individual approaches are divided into groups and then define in turn. In the thesis is in detail described algorithm AdaBoost, which is selected on the basis of its properties. Especially speed of computation and good detection results are key features. In the scope of this work Viola-Jones detector was implemented. This detector was trained with face pictures from public accessible database. Combination of Viola-Jones detector with simple color detector is described. In the thesis is also presented experiment approach to facial features detection.

Denna studie undersöker indexinkluderingar och indexexkluderingars påverkan på europeiska företags aktiekurser genom att studera bolag som inkluderats i eller exkluderats ur hållbarhetsindexet Dow Jones Sustainability Index Europe under perioden 2017–2019. Vidare undersöks även specifikt svenska bolag som inkluderats, exkluderats eller bibehållit sin plats i indexet under samma tidsperiod. Detta till följd av det ökade intresset och utbudet av ESG- relaterade investeringar i världen, inte minst i Europa. En standardmässig eventstudiemetod baserad på marknadsmodellen används för att på kort sikt undersöka detta eventuella samband. Vi kan i resultatet inte finna några starka bevis på att en annonsering i sig har någon tydlig påverkan på företagens aktieavkastning för vare sig europeiska eller svenska bolag. Däremot finner vi att svenska bolag som behållit sin plats eller inkluderats i indexet visar en positiv genomsnittlig kumulativ avvikelseavkastning (CAR) mellan två och tio dagar efter annonseringsdagen. Det kan trots det inte bevisa indexets relevans för marknaden vilket stödjer tidigare studiers resultat. / This paper examines the impact of index inclusions and index exclusions on the share prices of European companies by studying companies that are included or excluded from the Dow Jones Sustainability Index Europe during the period 2017-2019. Furthermore, Swedish companies that have been included, excluded or retained their place in the index during the same time period are also specifically examined. This due to the increased interest and supply of ESG- related investments in the world, especially in Europe. A standard event study method based on the market model is used to investigate this possible connection in the short term. We cannot find strong evidence that an announcement has any evident impact on companies' return on investment for either European or Swedish companies. On the other hand, we find that Swedish companies that have retained their place or are included in the index show a positive average cumulative abnormal return (CAR) between two and ten days after the announcement date. Despite this, the results cannot prove the index's relevance to the market which supports previous studies.