Cette thèse comprend trois sujets différents, tous en rapport à des problèmes de structures électroniques. Ces trois sujets sont présentés dans trois parties indépendantes.Cette thèse commence par une introduction générale présentant les problématiques et les principaux résultats.La première partie traite de la théorie de la fonctionnelle de la densité lorsqu'elle est appliquée aux modèles d'électrons avec spins polarisés. Cette partie est divisée en deux chapitres. Dans le premier de ces chapitres, nous introduisons la notion de N-représentabilité, et nous caractérisons les ensembles de matrices de densité de spin représentables. Dans le second chapitre, nous montrons comment traiter mathématiquement le terme de Zeeman qui apparaît dans les modèles comprenant une polarisation de spin. Le résultat d'existence qui est démontré dans (Anantharaman, Cancès 2009) pour des systèmes de Kohn-Sham sans polarisation de spin est étendu au cas des systèmes avec polarisation de spin.Dans la seconde partie, nous étudions l'approximation GW. Dans un premier temps, nous donnons une définition mathématique de la fonction de Green à un corps, et nous expliquons comment les énergies d'excitation des molécules peuvent être obtenues à partir de cette fonction de Green. La fonction de Green peut être numériquement approchée par la résolution des équations GW. Nous discutons du caractère bien posé de ces équations, et nous démontrons que les équations GW0 sont bien posées dans un régime perturbatif. Ce travail a été effectué en collaboration avec Eric Cancès et Gabriel Stoltz.Dans le troisième et dernière partie, nous analysons des méthodes numériques pour calculer les diagrammes de bandes de structures cristallines. Cette partie est divisée en deux chapitres. Dans le premier, nous nous intéressons à l'approximation de Hartree-Fock réduite (voir (Cances, Deleurence, Lewin 2008)). Nous prouvons que si le cristal est un insolant ou un semi-conducteur, alors les calculs réalisés dans des supercellules convergent exponentiellement vite vers la solution exacte lorsque la taille de la supercellule tend vers l'infini. Ce travail a été réalisé en collaboration avec Salma Lahbabi. Dans le dernier chapitre, nous présentons une nouvelle méthode numérique pour le calcul des diagrammes de bandes de cristaux (qui peuvent être aussi bien isolants que conducteurs). Cette méthode utilise la technique des bases réduites, et accélère les méthodes traditionnelles. Ce travail a été fait en collaboration avec Eric Cancès, Virginie Ehrlacher et Damiano Lombardi / This thesis contains three different topics, all related to electronic structure problems. These three topics are presented in three independent parts.This thesis begins with a general introduction presenting the problematics and main results.The first part is concerned with Density Functional Theory (DFT), for spin-polarized models. This part is divided in two chapters. In the first of these chapters, the notion of N-representability is introduced and the characterizations of the N-representable sets of spin-density 2X2 matrices are given. In the second chapter, we show how to mathematically treat the Zeeman term in spin-polarized DFT models. The existence of minimizers that was proved in (Anantharaman, Cancès 2009) for spin-unpolarized Kohn-Sham models within the local density approximation is extended to spin-polarized models.The second part of this thesis focuses on the GW approximation. We first give a mathematical definition of the one-body Green's function, and explain why methods based on Green's functions can be used to calculate electronic-excited energies of molecules. One way to compute an approximation of the Green's function is through the self-consistent GW equations. The well-posedness of these equations is discussed, and proved in the GW0 case in a perturbative regime. This is joint work with Eric Cancès and Gabriel Stoltz.In the third and final part, numerical methods to compute band-diagrams of crystalline structure are analyzed. This part is divided in two chapters.In the first one, we consider a perfect crystal in the reduced Hartree-Fock approximation (see (Cances, Deleurence, Lewin 2008)). We prove that, if the crystal is an insulator or a semi-conductor, then supercell calculations converge to the exact solution with an exponential rate of convergence with respect to the size of the supercell. This is joint work with Salma Lahbabi. In the last chapter, we provide a new numerical method to calculate the band diagram of a crystal (which can be either an insulator or a conductor). This method, based on reduced basis techniques, speeds up traditional calculations. This is joint work with Eric Cancès, Virginie Ehrlacher, and Damiano Lombardi

Ce travail est concentré sur l'étude de la cosmologie primordiale et en particulier sur l'étude de l'inflation. Après une introduction sur la théorie standard du Big Bang, nous discutons de la physique du CMB et nous expliquons comment ses observations peuvent être utilisées pour définir des contraintes sur les modèles cosmologiques. Nous introduisons l'inflation et nous expliquons sa réalisation la plus simple. Nous présentons les observables et les contraintes expérimentales qui peuvent être utilisées pour mettre des contraintes sur les modèles d'inflation. La possibilité d'observer des ondes gravitationnelles primordiales (GW) produites au cours de l'inflation est examinée. Nous présentons les raisons pour définir une classification des modèles d'inflation et pour introduire le formalisme de la fonction 13 pour décrire l'inflation. En particulier nous expliquons pourquoi, dans ce cadre, nous pouvons naturellement définir un ensemble de classes d'universalité pour les modèles d'inflation. Les motivations théoriques pour soutenir la formulation de l'inflation en termes de ce formalisme sont présentées. Certains modèles généralisés d'inflation sont introduits et l'extension du formalisme de la fonction (3-formalisme à ces modèles est discutée. Enfin, nous nous concentrons sur l'étude des modèles où l’inflation (qui es assumé être pseudo-scalaire) est couplé non-minimalement à des champs de jauge abéliens qui peuvent être présents lors de l'inflation. L'analyse du problème est effectuée en utilisant une caractérisation de modèles d'inflation sur la base de leur comportement asymptotique. Un large éventail d'aspects théoriques et des conséquences d'observation est discuté. / This work is focused on the study of early time cosmology and in particular on the study of inflation. After an introduction on the standard Big Bang theory, we discuss the physics of CMB and we explain how its observations can be used to set constraints on cosmological models. We introduce inflation and we carry out its simplest realization by presenting the observables and the experimental constraints that can be set on inflationary models. The possibility of observing primordial gravitational wave (GW) produced during inflation is discussed. We present the reasons to deftne a classification of inflationary models and introduce the [3-function formalism for inflation by explaining why in this framework we can naturally define a set of universality classes for inflationary models. Theoretical motivations to support the formulation of inflation in terms of this formalism are presented. Some generalized models of inflation are introduced and the extension of the (3-function formalism for inflation to these models is discussed. Finally we focus on the study of models where the (pseudo-scalar) inflaton is non-minimally coupled to some Abelian gauge fields that can be present during inflation. The analysis of the problem is carried out by using a characterization of inflationary models in terms of their asymptotic behavior. A wide set of theoretical aspects and of observational consequences is discussed.

Neste ano a Anatel começou a adotar um novo modelo para as tarifas de interconexão das diversas áreas de telecomunicações do Brasil. Nesse modelo o WACC e o CAPM têm um papel central no cálculo da remuneração do capital empregado em cada setor. No caso do CAPM, entretanto, há muitas controvérsias sobre a sua aplicabilidade a países emergentes. ESTRADA (2002, 2003), por exemplo, encontrou resultados mais plausíves para esses países utilizando o modelo D-CAPM, uma variação do CAPM baseada no risco Downside. Sabe-se, por outro lado, que o CAPM é uma composição média entre os riscos Downside e Upside. Neste sentido, o objetivo deste trabalho é propor uma generalização do CAPM (Gw-CAPM), baseada em uma ponderação dos riscos Downside e Upside, e analisar a existência de modelos intermediários que estimem melhor o retorno do mercado local de telefonia fixa do Brasil, com vistas à nova orientação a custos adotada. Outro objetivo é elaborar uma metodologia específica para a telefonia fixa e aplicar o Gw-CAPM no cálculo do custo de capital próprio, analisando se há ou não diferenças significativas no resultado final do custo de capital do setor. Na avaliação do poder de estimação dos modelos utilizou-se o índice de Jensen e o REQM. Mostra-se, assim, que realmente há uma determinada combinação entre os riscos Downside e Upside que estima melhor o retorno das operadoras do setor e do mercado de telefonia fixa como um todo. Além disso, conclui-se que há diferenças significativas no cálculo do custo de capital quando o modelo utilizado é o Gw-CAPM. / This year Anatel began to adopt a new model to the interconnection tariffs to the several telecommunication areas of Brazil. According to this model, the WACC and the CAPM have a central role on determining the remuneration of the investment on each sector. However, there are much controversy about the applicability of CAPM to the emergent countries. For example, Estrada (2002, 2003) found more reasonable results to these countries using the D-CAPM, a variation of CAPM based on the Downside risk. It is also known that the CAPM is an average composition between the Donwside and Upside risks. The purpose of this work is to propose a generalization of the CAPM (Gw-CAPM), based on the weight of the Downside and Upside risks and analyse the existence of intermediate models that can evaluate more precisely the return of the brazilian local market of fixed telephony, aiming the new cost orientation adopted. Other objective is to build a specific methodology to the fixed telephony and apply the Gw-CAPM on the determination of the own capital cost, verifying whether there are significant differences on the final result of the sector capital cost. In the evaluation of the valuation power of the models, the Jensen index and the REQM were used. It is shown, therefore, that there is really a certain combination between the Downside and the Upside risks that evaluates more accurately the return of the sector operating companies and the fixed telephony market as a whole. In addition to this, we conclude that there are significant differences on determining the cost of capital when the model used is the Gw-CAPM.

Cette thèse comprend trois sujets différents, tous en rapport à des problèmes de structures électroniques. Ces trois sujets sont présentés dans trois parties indépendantes.Cette thèse commence par une introduction générale présentant les problématiques et les principaux résultats.La première partie traite de la théorie de la fonctionnelle de la densité lorsqu'elle est appliquée aux modèles d'électrons avec spins polarisés. Cette partie est divisée en deux chapitres. Dans le premier de ces chapitres, nous introduisons la notion de N-représentabilité, et nous caractérisons les ensembles de matrices de densité de spin représentables. Dans le second chapitre, nous montrons comment traiter mathématiquement le terme de Zeeman qui apparaît dans les modèles comprenant une polarisation de spin. Le résultat d'existence qui est démontré dans (Anantharaman, Cancès 2009) pour des systèmes de Kohn-Sham sans polarisation de spin est étendu au cas des systèmes avec polarisation de spin.Dans la seconde partie, nous étudions l'approximation GW. Dans un premier temps, nous donnons une définition mathématique de la fonction de Green à un corps, et nous expliquons comment les énergies d'excitation des molécules peuvent être obtenues à partir de cette fonction de Green. La fonction de Green peut être numériquement approchée par la résolution des équations GW. Nous discutons du caractère bien posé de ces équations, et nous démontrons que les équations GW0 sont bien posées dans un régime perturbatif. Ce travail a été effectué en collaboration avec Eric Cancès et Gabriel Stoltz.Dans le troisième et dernière partie, nous analysons des méthodes numériques pour calculer les diagrammes de bandes de structures cristallines. Cette partie est divisée en deux chapitres. Dans le premier, nous nous intéressons à l'approximation de Hartree-Fock réduite (voir (Cances, Deleurence, Lewin 2008)). Nous prouvons que si le cristal est un insolant ou un semi-conducteur, alors les calculs réalisés dans des supercellules convergent exponentiellement vite vers la solution exacte lorsque la taille de la supercellule tend vers l'infini. Ce travail a été réalisé en collaboration avec Salma Lahbabi. Dans le dernier chapitre, nous présentons une nouvelle méthode numérique pour le calcul des diagrammes de bandes de cristaux (qui peuvent être aussi bien isolants que conducteurs). Cette méthode utilise la technique des bases réduites, et accélère les méthodes traditionnelles. Ce travail a été fait en collaboration avec Eric Cancès, Virginie Ehrlacher et Damiano Lombardi / This thesis contains three different topics, all related to electronic structure problems. These three topics are presented in three independent parts.This thesis begins with a general introduction presenting the problematics and main results.The first part is concerned with Density Functional Theory (DFT), for spin-polarized models. This part is divided in two chapters. In the first of these chapters, the notion of N-representability is introduced and the characterizations of the N-representable sets of spin-density 2X2 matrices are given. In the second chapter, we show how to mathematically treat the Zeeman term in spin-polarized DFT models. The existence of minimizers that was proved in (Anantharaman, Cancès 2009) for spin-unpolarized Kohn-Sham models within the local density approximation is extended to spin-polarized models.The second part of this thesis focuses on the GW approximation. We first give a mathematical definition of the one-body Green's function, and explain why methods based on Green's functions can be used to calculate electronic-excited energies of molecules. One way to compute an approximation of the Green's function is through the self-consistent GW equations. The well-posedness of these equations is discussed, and proved in the GW0 case in a perturbative regime. This is joint work with Eric Cancès and Gabriel Stoltz.In the third and final part, numerical methods to compute band-diagrams of crystalline structure are analyzed. This part is divided in two chapters.In the first one, we consider a perfect crystal in the reduced Hartree-Fock approximation (see (Cances, Deleurence, Lewin 2008)). We prove that, if the crystal is an insulator or a semi-conductor, then supercell calculations converge to the exact solution with an exponential rate of convergence with respect to the size of the supercell. This is joint work with Salma Lahbabi. In the last chapter, we provide a new numerical method to calculate the band diagram of a crystal (which can be either an insulator or a conductor). This method, based on reduced basis techniques, speeds up traditional calculations. This is joint work with Eric Cancès, Virginie Ehrlacher, and Damiano Lombardi

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

In this thesis, we have studied the electronic and optical properties of solar energy m-terials. The studies are performed in the framework of density functional theory (DFT), GW, Bethe-Salpeter equation (BSE) approaches and Kinetic Monte Carlo (KMC). We present four sets of results. In the first part, we report our results on the band gap engineering issues for BiNbO4and NaTaO3, both of which are good photocatalysts. The band gap tuning is required for these materials in order to achieve the maximum solar to hydrogen conversion efficiency. The most common method for the band gap reduction is an introduction of foreign elements. The mono-doping in the system generates electrons or holes states near band edges, which reduce the efficiency of photocatalytic process. Co-doping with anion and cation or anion and anion can provide a clean band gap. We have shown that further band gap reduction can be achieved by double-hole mediated coupling between two anionic dopants. In the second part, the structure and optical properties of (CdSxSe1x)42nanoclusters have been studied. Within this study, the structures of the (CdS)42, (CdSe)42, Cd42Se32S10, Cd42Se22S20, and Cd42Se10S32 clusters have been determined using the simulated annealing method. Factors influencing the band gap value have been analyzed. We show that the gap is most significantly reduced when strongly under coordinated atoms are present on the surface of the nanoclusters. In addition, the band gap depends on the S concentration as well as on the distribution of the S and Se atoms in the clusters. We present the optical absorption spectra calculated with BSE and random phase approximation (RPA) methods based on the GW corrected quasiparticle energies. In the third part, we have employed the state-of-art computational methods to investigate the electronic structure and optical properties of TiO2high pressure polymorphs. GW and BSE methods have been used in these calculations. Our calculations suggest that the band gap of fluorite and pyrite phases have optimal values for the photocatalytic process of decomposing water in the visible light range. In the fourth part we have built a kinetic model of the first water monolayer growth on TiO2(110) using the kinetic Monte Carlo (KMC) method based on parameters describing water diffusion and dissociation obtained from first principle calculations. Our simulations reproduce the experimental trends and rationalize these observations in terms of a competition between different elementary processes. At high temperatures our simulation shows that the structure is well equilibrated, while at lower temperatures adsorbed water molecules are trapped in hydrogen-bonded chains around pairs of hydroxyl groups, causing the observed higher number of molecularly adsorbed species at lower temperature. / <p>QC 20140603</p>

No description available.

Neste ano a Anatel começou a adotar um novo modelo para as tarifas de interconexão das diversas áreas de telecomunicações do Brasil. Nesse modelo o WACC e o CAPM têm um papel central no cálculo da remuneração do capital empregado em cada setor. No caso do CAPM, entretanto, há muitas controvérsias sobre a sua aplicabilidade a países emergentes. ESTRADA (2002, 2003), por exemplo, encontrou resultados mais plausíves para esses países utilizando o modelo D-CAPM, uma variação do CAPM baseada no risco Downside. Sabe-se, por outro lado, que o CAPM é uma composição média entre os riscos Downside e Upside. Neste sentido, o objetivo deste trabalho é propor uma generalização do CAPM (Gw-CAPM), baseada em uma ponderação dos riscos Downside e Upside, e analisar a existência de modelos intermediários que estimem melhor o retorno do mercado local de telefonia fixa do Brasil, com vistas à nova orientação a custos adotada. Outro objetivo é elaborar uma metodologia específica para a telefonia fixa e aplicar o Gw-CAPM no cálculo do custo de capital próprio, analisando se há ou não diferenças significativas no resultado final do custo de capital do setor. Na avaliação do poder de estimação dos modelos utilizou-se o índice de Jensen e o REQM. Mostra-se, assim, que realmente há uma determinada combinação entre os riscos Downside e Upside que estima melhor o retorno das operadoras do setor e do mercado de telefonia fixa como um todo. Além disso, conclui-se que há diferenças significativas no cálculo do custo de capital quando o modelo utilizado é o Gw-CAPM. / This year Anatel began to adopt a new model to the interconnection tariffs to the several telecommunication areas of Brazil. According to this model, the WACC and the CAPM have a central role on determining the remuneration of the investment on each sector. However, there are much controversy about the applicability of CAPM to the emergent countries. For example, Estrada (2002, 2003) found more reasonable results to these countries using the D-CAPM, a variation of CAPM based on the Downside risk. It is also known that the CAPM is an average composition between the Donwside and Upside risks. The purpose of this work is to propose a generalization of the CAPM (Gw-CAPM), based on the weight of the Downside and Upside risks and analyse the existence of intermediate models that can evaluate more precisely the return of the brazilian local market of fixed telephony, aiming the new cost orientation adopted. Other objective is to build a specific methodology to the fixed telephony and apply the Gw-CAPM on the determination of the own capital cost, verifying whether there are significant differences on the final result of the sector capital cost. In the evaluation of the valuation power of the models, the Jensen index and the REQM were used. It is shown, therefore, that there is really a certain combination between the Downside and the Upside risks that evaluates more accurately the return of the sector operating companies and the fixed telephony market as a whole. In addition to this, we conclude that there are significant differences on determining the cost of capital when the model used is the Gw-CAPM.

La combinaison de la spintronique et de I' électronique organique est censée conduire à une nouvelle gamme d'applications en la domaine de spintronique organique. Ce travail se concentre sur la physique des molécules organiques adsorbées sur des surfaces métalliques, en mettant I' accent sur les changements de leurs structures électroniques en raison de I' effet important du substrat métallique. Nous avons étudié le complexe Ni2 adsorbé sur le Cu qui montre un effet Kondo à basses températures. Nous avons ensuite étudié des chaînes d'oligoacènes (anneaux de benzène fusionnè) qui présentent une propriété prédite: une oscillation de la bande interdite d' énergies en fonction de la longueur de la molécule. Cette propriété peut survivre même lorsque la molécule est adsorbée sur une surface, comme I' Au ou le Si02. Pour terminer, nous avons étudié des petites molécules, telles que l'éthane ou I'éthylène, adsorbées sur un subtrat de Cu et de Co. La différence d' énergie entre I' orbitale vide la plus basse (LUMO) et I' orbitale moléculaire occupée la plus élevée (HOMO) est étudiée dans les approximations de la théorie de la fonctionnelle de la densité (DFT) et la méthode GW. / The combination of spintronics and organic electronics, is believed to lead to a new generation of spin based devices, which would likely open a new broad range of applications in the field of organic spintronics. ln this context, this work focuses on organic molecules adsorbed on metallic surfaces and their electronic structure changes due to the important screening of the metallic environment. We have studied different systems, starting with a Ni2 complex adsorbed on Cu (001), where Kondo effect sets in. This study is followed by oligoacene chains (fused benzene rings) where an extraordinary property is seen: an oscillation of the energy band gap with respect to the molecular length. This property is proved to survive under the screening of surfaces such as Au(111) and Si02. We finally focused on small molecules, like ethane and ethylene, adsorbed on Cu and Co. The difference of energy between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) is studied using density functional theory (DFT)and GW methodologies.

The aim of this thesis is acquaintance with the EPS system of LTE and IMS subsystem. The thesis is aimed on analysis of the control procedures related to operations between the terminal and the packet core network of the fourth generation such as logging into the system, user authentication, change the viewing area, handover and disconnection from the network.