Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira. / In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.

A presente tese tem por objetivo contribuir para o conhecimento do comportamento dependente do tempo das rochas de anidrita e gipso. O maior interesse é fornecer argumentos convincentes sobre os mecanismos físicos responsáveis pelas deformações lentas observadas em algumas escavações subterrâneas realizadas em maciços dessas rochas na Europa, aspecto este que hoje está bastante confuso e escassamente estudado. A hipótese central desta pesquisa é que o comportamento dependente do tempo das rochas de anidrita e gipso deve-se parcial e/ou totalmente às propriedades reológicas (fluência) e não exclusivamente a expansão decorrente da transformação anidrita – gipso como a maioria dos autores sustenta. Este problema será analisado a partir de uma perspectiva experimental através de ensaios específicos. Os ensaios de expansão axial livre em rochas de anidrita permitiram concluir que quando submersas em água destilada, experimentam diminuição de volume por dissolução. Já as amostras de anidrita em contato com solução saturada em 'CA'SO IND.4' mostram uma relação não linear entre deformação axial e o tempo indicando uma taxa de expansão que decresce com o tempo. As taxas de expansão axial variam entre 0,3 e 2,4%/ano. A novidade é que esta expansão se deve à deposição de uma camada contínua formada por neocristais de gipso e não a expansão por hidratação da anidrita como acontece com os argilominerais. O mecanismo de transformação consiste na dissolução da anidrita e posterior precipitação do gipso em condições de sobre-saturação da solução. A transformação mineralógica acontece, na natureza, em condições propícias de temperatura e saturação da solução com íons 'CA POT.2+' e 'SO IND.4'POT.2-'. Propõe-se uma teoria alternativa sobre deformações lentas de maciços sulfáticos baseada na força de cristalização decorrente da deposição de cristais de gipso nas juntas do maciço rochoso. Propõe-se utilizar as formulações termodinâmicas propostas para expansão de concretos por crescimento de etringita e gipso. Os ensaios de fluência uniaxial sob compressão axial constante mostram que ambos os tipos de rochas sulfáticas apresentam comportamentos elasto-visco-plásticos e taxas de deformação axial e lateral da ordem de '10 POT.-12' a '10 POT.-10' 'S POT.-1'. A deflagração da fluência secundária acontece sob tensões de 4 – 6 MPa para gipsitas e de 25 – 40 MPa para anidritas. As análises sobre os possíveis mecanismos de deformação por fluência foram inconsistentes e nenhuma conclusão definitiva foi atingida. Aparentemente a baixas tensões atuariam mecanismos de difusão e dissolução por pressão. A tensões intermediárias dominariam mecanismos de deslocamentos intra e intercristalinos e a altas tensões as rochas deformariam por propagação de microfissuramento. Ensaios de fluência acoplados a sensores de emissão acústica mostram a manifestação de eventos microssísmicos que usualmente se atribuem à propagação de microfraturas mas que podem dever-se a outros mecanismos. Tanto as taxas de expansão axial como de fluência são compatíveis com as taxas de convergência medidas em algumas obras subterrâneas escavadas em maciços sulfáticos, verificando a hipótese central da pesquisa / The purpose of this thesis is to contribute for the knowledge of time-dependent behavior of sulfatic rocks of anhydrite and gypsum. Emphasis is given to provide straightforward arguments about physical mechanisms responsible for creep observed in some underground excavations in those rocks in Europe. Explanation for this phenomena is not clear yet and studies about them are still scarce. The backbone idea behind this research is that the time-dependent behavior of anhydrite and gypsum is totally or at least partially due to rheological properties, and not exclusively due to swelling resulting from the anhydritegypsum transformation. This problem was investigated experimentally with specific tests. Free swelling tests on anhydrite led to the conclusion that when immersed into distilled water, volume decrease due to dissolution is observed. Anhydrite samples in contact with a saturated solution of 'CA'SO IND.4' present a nonlinear relationship between axial strain and time, indicating swelling rate decreasing with time. Axial swelling rates vary between 0,3% and 2,4%/year. The new concept is that this swelling is due to the deposition of a continuous layer of gypsum composed by gypsum neo-crystals, and not due to hydration swelling of anhydrite, a usual with clay minerals. The transformation mechanism consists of anhydrite dissolution and later precipitation of gypsum under over-saturation condition of the solution. The mineralogical transformation takes place in nature under favorable conditions of temperature and solution saturation with 'CA POT.2+' and 'SO IND.4'POT.2-' ions. An alternative theory is proposed about creep of sulfatic rock masses based on crystallization forces resulting from the deposition of gypsum crystals in the rock masses joints. The use of thermodynamic formulations is proposed for concrete swelling due to the growth of ettringite and gypsum. Uniaxial compression creep tests show that both types of sulfatic rocks present elasto-visco-plastic behavior and axial and lateral strain rates of the order of '10 POT.-12' to '10 POT.-10' 'S POT.-1'. Triggering of secondary creep takes places under stresses of the order of 4 – 6 MPa for gypsum and 25 – 40 MPa for anhydrite. The analyses about the possible creep mechanisms were not consistent and no definite conclusion has been reached get. Apparently under low stresses diffusion and pressure dissolution mechanism dominate. Under intermediate stresses, intra- and inter crystalline displacement mechanisms seem to dominate, and under high stresses rock deform due to microcrack propagation. Creep tests monitored with acoustic emission devices show the occurrence of microseismic events attributed to microcrack propagation. Both axial swelling and creep rock are compatible with convergence rocks measured in some underground works excavated in sulfatic rock masses, following the central idea of this thesis

Cette thèse est consacrée à la simulation du comportement à la rupture de bois sous des chargements à long terme et sous des conditions d'Humidité Relatives (HR) de l'air variables. Il est connu que le bois est un matériau fortement hygroscopique, ses propriétés mécaniques et de rupture sont en effet très dépendantes de sa teneur en eau. En outre, la stabilité d'une fissure existante dans un élément structural peut être fortement influencée parles variations, en particulier brusques, d'humidité relative qui peut conduire à la rupture inattendue de l'élément.L'approche thermodynamique proposée intègre l'effet de mécanosorption dans l'expression analytique de la déformation, en découplant les déformations mécaniques et celles dues au comportement mécanosorptif du matériau. En outre, la rupture quasi-fragile du matériau boisest traduite par un modèle de zone cohésive dont les paramètres de cohésion sont fonctions de la teneur en eau afin de simuler l’effet de l'humidité sur les propriétés de rupture. Sur cette base, une formulation incrémentale permet l'intégration de l'effet des variations soudaines d’humidité relative (autrement dit, le choc hydrique) sur la zone d’élaboration(zone cohésive) en introduisant un champ de contraintes supplémentaires le long de cette zone. Fonction de la variation de HR, ce champ de contraintes supplémentaires dépend de l'état de contrainte et de l'ouverture de la fissure le long de la zone cohésive, mais également de l'humidité en pointe de fissure (matériau non endommagé). Dans l'analyse par éléments finis, un opérateur tangent algorithmique est utilisé pour résoudre le problème non linéaire en combinant le modèle de mécanosorption et le modèle de zone cohésive et en intégrant l'effet du choc hydrique.La simulation du comportement d'une éprouvette entaillée soumise à un chargement constant et à des variations cycliques de HR montre un fort couplage entre le comportement mécanosorptif et l'effet du choc hydrique HR sur la zone d’élaboration. Ce couplage entraîne une augmentation de la propagation des fissures et conduit à une fissuration plus précoce par rapport à celle obtenue à partir du modèle de mécanosorption seul ou à partir du modèle de zone cohésive en intégrant l'effet des variations soudaines de HR. En outre, le couplage entre le modèle mécanosorptif et le modèle de zone cohésive en intégrant l'effet du chochydrique montre l'intérêt d'une telle approche numérique pour décrire le comportement complexe des éléments de charpente en bois soumis à des conditions climatiques variables,comportement qui ne peut être prédit par une simple superposition des deux modélisations. / This thesis is dedicated to the simulation of the fracture behavior of wood under long-termloading and variable relative humidity conditions. Indeed, wood is well-known to be a highlyhygroscopic material in so far as its mechanical and fracture properties are very dependenton moisture. Moreover, the stability of an existent crack in a structural element can bestrongly affected by the sudden variations of relative humidity (RH) and can lead tounexpected failure of the element.The thermodynamic approach proposed in this thesis includes the mechano-sorptive effect inthe analytical expression of the deformation, by operating a decoupling of the strain in amechanical part and a mechano-sorptive part in material. Moreover, the quasi-brittle fractureof wood is here simulated from a cohesive zone model whose cohesive parameters arefunctions of the moisture in order to mimic the moisture-dependent character of the fractureproperties. On this basis, an increment formulation allows the integration of the effect ofsudden RH variations on the fracture process zone (cohesive zone) by introducing anadditional stress field along this zone. As a function of the RH variation, this additional stressfield depends on not only the stress state and the crack opening along the cohesive zone butalso the material moisture ahead of the zone (undamaged material). In the finite elementanalysis, an algorithmic tangent operator is used to solve the non-linear problem combiningmechano-sorptive model and cohesive zone model including the effect of sudden RHvariations.The simulation of a notched structural element submitted to a constant load and cyclic RHvariations exhibits a strong coupling between the mechano-sorptive behavior and the effectof the RH variations on the fracture process zone (FPZ). This coupling results in an increaseof the crack propagation kinetic and leads to a precocious failure compared to those obtainedfrom the mechano-sorptive model or from the effect of sudden RH variations on the FPZ.Moreover, the coupling between the mechano-sorptive model and the effect of sudden RHvariations on the FPZ which cannot be predicted by a simple superposition of both effects,showing the interest of such a numerical approach in order to describe the complex behaviorof wood structural elements submitted to variable climatic conditions.

Dans cette thèse, nous étudions l’estimation de modèles autorégressif-moyenne mobile<p>vectoriels ou VARMA, `a coefficients dépendant du temps, et avec une matrice de covariance<p>des innovations dépendant du temps. Ces modèles sont appel´es tdVARMA. Les éléments<p>des matrices des coefficients et de la matrice de covariance sont des fonctions déterministes<p>du temps dépendant d’un petit nombre de paramètres. Une première partie de la thèse<p>est consacrée à l’étude des propriétés asymptotiques de l’estimateur du quasi-maximum<p>de vraisemblance gaussienne. La convergence presque sûre et la normalité asymptotique<p>de cet estimateur sont démontrées sous certaine hypothèses vérifiables, dans le cas o`u les<p>coefficients dépendent du temps t mais pas de la taille des séries n. Avant cela nous considérons les propriétés asymptotiques des estimateurs de modèles non-stationnaires assez<p>généraux, pour une fonction de pénalité générale. Nous passons ensuite à l’application de<p>ces théorèmes en considérant que la fonction de pénalité est la fonction de vraisemblance<p>gaussienne (Chapitre 2). L’étude du comportement asymptotique de l’estimateur lorsque<p>les coefficients du modèle dépendent du temps t et aussi de n fait l’objet du Chapitre 3.<p>Dans ce cas, nous utilisons une loi faible des grands nombres et un théorème central limite<p>pour des tableaux de différences de martingales. Ensuite, nous présentons des conditions<p>qui assurent la consistance faible et la normalité asymptotique. Les principaux<p>résultats asymptotiques sont illustrés par des expériences de simulation et des exemples<p>dans la littérature. La deuxième partie de cette thèse est consacrée à un algorithme qui nous<p>permet d’évaluer la fonction de vraisemblance exacte d’un processus tdVARMA d’ordre (p, q) gaussien. Notre algorithme est basé sur la factorisation de Cholesky d’une matrice<p>bande partitionnée. Le point de départ est une généralisation au cas multivarié de Mélard<p>(1982) pour évaluer la fonction de vraisemblance exacte d’un modèle ARMA(p, q) univarié. Aussi, nous utilisons quelques résultats de Jonasson et Ferrando (2008) ainsi que les programmes Matlab de Jonasson (2008) dans le cadre d’une fonction de vraisemblance<p>gaussienne de modèles VARMA à coefficients constants. Par ailleurs, nous déduisons que<p>le nombre d’opérations requis pour l’évaluation de la fonction de vraisemblance en fonction de p, q et n est approximativement le double par rapport à un modèle VARMA à coefficients<p>constants. L’implémentation de cet algorithme a été testée en comparant ses résultats avec<p>d’autres programmes et logiciels très connus. L’utilisation des modèles VARMA à coefficients<p>dépendant du temps apparaît particulièrement adaptée pour la dynamique de quelques<p>séries financières en mettant en évidence l’existence de la dépendance des paramètres en<p>fonction du temps.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Halo nuclei are among the strangest nuclear structures.<p>They are viewed as a core containing most of the nucleons<p>surrounded by one or two loosely bound nucleons. <p>These have a high probability of presence at a large distance<p>from the core.<p>Therefore, they constitute a sort of halo surrounding the other nucleons.<p>The core, remaining almost unperturbed by the presence<p>of the halo is seen as a usual nucleus.<p><p><P><p><p>The Coulomb breakup reaction is one of the most useful<p>tools to study these nuclei. It corresponds to the<p>dissociation of the halo from the core during a collision<p>with a heavy (high <I>Z</I>) target.<p>In order to correctly extract information about the structure of<p>these nuclei from experimental cross sections, an accurate<p>theoretical description of this mechanism is necessary.<p><p><P><p><p>In this work, we present a theoretical method<p>for studying the Coulomb breakup of one-nucleon halo nuclei.<p>This method is based on a semiclassical approximation<p>in which the projectile is assumed to follow a classical trajectory.<p>In this approximation, the projectile is seen as evolving<p>in a time-varying potential simulating its interaction with the target.<p>This leads to the resolution of a time-dependent Schrödinger<p>equation for the projectile wave function.<p><p><P><p><p>In our method, the halo nucleus is described<p>with a two-body structure: a pointlike nucleon linked to a<p>pointlike core.<p>In the present state of our model, the interaction between<p>the two clusters is modelled by a local potential.<p><p><P><p><p>The main idea of our method is to expand the projectile wave function<p>on a three-dimensional spherical mesh.<p>With this mesh, the representation of the time-dependent potential<p>is fully diagonal.<p>Furthermore, it leads to a simple<p>representation of the Hamiltonian modelling the halo nucleus.<p>This expansion is used to derive an accurate evolution algorithm.<p><p><P><p><p>With this method, we study the Coulomb breakup<p>of three nuclei: ¹¹Be, ¹⁵C and ⁸B.<p>¹¹Be is the best known one-neutron halo nucleus.<p>Its Coulomb breakup has been extensively studied both experimentally<p>and theoretically.<p>Nevertheless, some uncertainty remains about its structure.<p>The good agreement between our calculations and recent<p>experimental data suggests that it can be seen as a<p><I>s1/2</I> neutron loosely bound to a ¹⁰Be core in its<p>0⁺ ground state.<p>However, the extraction of the corresponding spectroscopic factor<p>have to wait for the publication of these data.<p><p><P><p><p>¹⁵C is a candidate one-neutron halo nucleus<p>whose Coulomb breakup has just been studied experimentally.<p>The results of our model are in good agreement with<p>the preliminary experimental data. It seems therefore that<p>¹⁵C can be seen as a ¹⁴C core in its 0⁺<p>ground state surrounded by a <I>s1/2</I> neutron.<p>Our analysis suggests that the spectroscopic factor<p>corresponding to this configuration should be slightly lower<p>than unity.<p><p><P><p><p>We have also used our method to study the Coulomb breakup<p>of the candidate one-proton halo nucleus ⁸B.<p>Unfortunately, no quantitative agreement could be obtained<p>between our results and the experimental data.<p>This is mainly due to an inaccuracy in the treatment<p>of the results of our calculations.<p>Accordingly, no conclusion can be drawn about the pertinence<p>of the two-body model of ⁸B before an accurate reanalysis of these<p>results.<p><p><P><p><p>In the future, we plan to improve our method in two ways.<p>The first concerns the modelling of the halo nuclei.<p>It would be indeed of particular interest to test<p>other models of halo nuclei than the simple two-body structure<p>used up to now.<p>The second is the extension of this semiclassical model to<p>two-neutron halo nuclei.<p>However, this cannot be achieved<p>without improving significantly the time-evolution algorithm so as to<p>reach affordable computational times. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

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Neste trabalho utilizamos sistemas modelos no desenvolvimento, implementação e análise de funcionais orbitais da densidade, focando, em particular, nas correções de autointeração de Perdew-Zunger (PZSIC) e Lundin-Eriksson (LESIC). Aplicamos as correções de auto-interação ao funcional local (LDA) do modelo de Hubbard e de poços quânticos semicondutores, ambos unidimensionais, no caso estático e dependente do tempo, respectivamente. Para o modelo de Hubbard unidimensional, comparamos a LDA, LDA+PZSIC e LDA+LESIC, identificando o desempenho para energias e densidades do estado fundamental, com e sem impurezas locais, além do gap fundamental de energia. Em adição, averiguamos o desempenho diante de cargas fracionárias, estabelecendo conexões com o erro de delocalização da LDA. Mostramos a possibilidade da correta descrição das freqüências das oscilações de Friedel no modelo de Hubbard, além de investigar como a falha da LDA em reproduzir esse aspecto pode estar relacionada com os erros de auto-interação e delocalização. Investigamos ainda as diferentes possibilidades de implementação autoconsistente de qualquer funcional orbital da densidade, analisando a relação entre funcionais aproximados e suas implementações aproximadas. Nos poços quânticos, sob o enfoque dependente do tempo, analisamos a descontinuidade do potencial de troca e correlação ao variarmos o número de partículas, em dois processos distintos: a ionização eletrônica em um poço simples e dissociação de um poço duplo assimétrico. No último caso, avaliamos os efeitos da descontinuidade no número total de partículas em cada poço, revelando os mecanismos que resgatam a neutralidade elétrica durante processos de dissociação, com a correta carga final inteira. / In this work we use model systems to develop, implement and analyse orbital-dependent density functionals, focusing, specifically, on the self-interaction corrections (SICs) of Perdew and Zunger (PZSIC) and of Lundin and Eriksson (LESIC). These self-interaction corrections are applied to the local-density approximation (LDA) for the one-dimensional Hubbard model and for semiconductor quantum wells, in one-dimensional static and time-dependent situations. For the one-dimensional Hubbard model we compare LDA, LDA+PZSIC and LDA+LESIC, and investigate the performance of these approaches for ground-state energies, densities and energy gaps, with and without impurities in the system. We also consider the case of fractional charges, where a connection to the delocalization error of the LDA can be made. We show that in principle a correct description of the frequences of Friedel oscillations in the Hubbard model can be obtained from DFT, and investigate how the failure of the LDA in reproducing this is related to the selfinteraction and delocalization errors. Moreover, we investigate different procedures for the selfconsistent implementation of any orbital-dependent functional, and analyse the question of the interplay between an approximate functional and its approximate implementation. For quantum wells sytems we analyse, in a time-dependent framework, the discontinuity of the exchange-correlation potential under variation of the particle number in two different processes: the ionization of a simple quantum well and the dissociation of an asymmetric double well. In the latter case, we also consider the effect of changes in the particle number in each subwell, thus revealing the mechanism that restores electric neutrality during dissociation, with correct final charge.

Cette thèse de doctorat est dédiée à l’étude, avec des méthodes de calcul ab initio, desplasmons de surface et des états de surface de surfaces d’or, plate ou comportant desmarches (surface vicinale), par la simulation numérique de spectres de perte d’énergieélectronique (EEL) au moyen de la théorie de la fonctionnelle de la densité (DFT) et de lathéorie de perturbation de la fonctionnelle de la densité dépendant du temps (TDDFPT).L’influence du couplage spin-orbite (CSO) et celle de la géométrie de la surface ont étéétudiées. Dans l’or cristallin, j’ai étudié l’effet des électrons de semicoeur sur les spectresEEL à q = 0. J’ai montré en particulier que pour produire un spectre EEL sur une largegamme de fréquences, de 0 à 60 eV, il est nécessaire de tenir compte des électrons desemicoeur dans le pseudopotentiel, et qu’ils peuvent néanmoins être gelés dans le coeurpour l’étude de la partie basse en énergie du spectre EEL, pour des énergies inférieures à20 eV. J’ai réalisé des développements méthodologiques pour la TDDFPT avec CSO cou-plée à l’emploi de pseudopotentiels ultradoux, qui ont permis l’implémentation pratiquede cette approche dans les algorithmes de Liouville-Lanczos et de Sternheimer. J’ai utiliséavec succès ces approches qui m’ont permis de traiter des systèmes à plusieurs centainesd’atomes. J’ai examiné à nouveau le spectre EEL de l’or cristallin à q = 0, montrant enparticulier les traces d’un plasmon écranté dans le spectre EEL calculé sans inclure leseffets de CSO. J’ai ensuite montré que l’inclusion du CSO a un effet petit mais détectablesur le spectre EEL et le pic de plasmon, donnant un meilleur accord avec l’expérienceà q = 0. J’ai trouvé que la dispersion du plasmon acoustique (PAS) de la surface Au(111) est légèrement modifiée par le CSO, provenant du fait que la structure de bandesest elle-même modifiée par le dédoublement de Rashba de certains niveaux électroniques,dédoublement induit par le CSO. Puis, pour étudier les effets de géométrie, j’ai étudié lessurfaces vicinales (322), (455) et (788) de l’or. J’ai en particulier mené l’étude théoriquedes états électroniques de surface, et analysé l’évolution de l’état de surface de Shockleyentre la surface plate Au(111) et les surfaces ayant des marches dont les terrasses avaientdifférentes largeurs. J’ai montré la transition d’un état de surface résonant pour Au(322)à un état localisé pour Au(455) et pour Au(788), ainsi que le passage d’un état 2D étenduà travers la marche pour Au(322) à un état quasi-1D confiné dans la terrasse de la marchepour Au(455) et pour Au(788). Ces résultats sont en accord avec l’expérience, et avecceux d’un modèle de Kronig-Penney de potentiel périodique. J’ai calculé le spectre EELSpour la surface d’or (455) que j’ai modélisé par une tranche de 5 nm d’or séparée de sesvoisines (répétées périodiquement) par 5 nm de vide. J’ai identifié la signature du plas-mon acoustique de surface. J’ai montré que, pour un moment transféré perpendiculaireà la marche de la surface, la dispersion du PAS n’est pas modifiée par rapport à celle duPAS de la surface plate Au(111) pour q < 0.125 Å −1 . Cependant, pour des valeurs plusgrandes du moment transféré, le pic du PAS a une énergie plus basse que celle du PASde Au(111), montrant les signes du confinement du PAS et suggérant que deux types dePAS peuvent se produire: un plasmon intra(sous)bande, similaire à celui de la surfaceAu(111), et un plasmon inter(sub)band, caractéristique de cette surface vicinale. / The PhD thesis is devoted to the ab initio study of surface plasmons and surface states offlat and vicinal surfaces of Au through the simulation of electron energy loss (EEL) spectraby means of the density functional theory (DFT) and the time-dependent density func-tional perturbation theory (TDDFPT). The influence of the spin-orbit coupling (SOC)and of the surface geometry has been investigated. In bulk Au I have studied the effect ofthe inclusion of semi-core electrons on the EEL spectrum at q = 0 and the plasmon peakposition and intensity. In particular, I have shown that in order to reproduce the EELspectrum on a wide frequency range (0-60 eV) it is important to account for semi-coreelectrons in the pseudopotential although they can be frozen in the core in studies of thelow energy part of the spectrum (below 20 eV). I have made methodological developmentsfor TDDFPT with SOC in the ultrasoft pseudopotential scheme that led to the practicalimplementation of SOC in the Liouville-Lanczos and Sternheimer approaches. I have thensuccessfully applied these approaches that allowed me to model systems with hundreds ofatoms. I have revisited the plasmonic excitations in bulk Au, pointing out that, in partic-ular, one can observe traces of an unscreened s-like bulk plasmon in the EEL spectrum atq = 0 calculated without SOC. I have also demonstrated that SOC has a small but notice-able effect on the Au EEL spectrum and plasmon peak, mainly modifying the unscreeneds-like plasmon peak and thus bringing the calculated spectrum into a better agreementwith experimental results at q = 0. Moreover I have observed that the dispersion ofthe acoustic surface plasmon (ASP) on the Au(111) surface is slightly modified by SOC,because the ASP comes from the surface state that itself is modified by SOC through theRashba splitting. To investigate the effect of geometry I have studied the vicinal (322),(455) and (788) surfaces of Au. In particular I have performed the theoretical study of thesurface states, analyzing the evolution of the Shockley surface state from the flat Au(111)surface towards the surfaces with terraces of different width. I have shown the surfaceresonance-to-surface state transition from (322) to (455) and (788) surfaces. I have shownalso the transition from the average-surface-modulated to the terrace-modulated statefrom (322) to (455) and (788) surfaces, as well as the transition from the extended 2Dstate to the quasi-1D state confined within the terrace. These results are in agreementwith experiments and results obtained with the Kronig-Penney periodic potential model.I have performed the EEL spectrum calculations for the Au(455) surface which I havemodeled with a 5 nm sized slab separated from its periodic neighbors by 5 nm of vacuum.I have identified signatures of the ASP in these spectra, showing that indeed, for the caseof the transferred electron wavevector momentum perpendicular to the step, the ASPdispersion is not changed with respect to the ASP dispersion of the Au(111) surface forq < 0.125 Å −1 . For bigger values of q, however, the ASP peak has a lower energy com-pared to the ASP peak of the Au(111) surface, showing signs of the ASP confinement, andsuggesting that two types of the ASP could occur: an intra(sub)band plasmon, similarto the Au(111) surface plasmon, and an inter(sub)band plasmon, characteristic of thisvicinal surface.

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura. / [CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura. / [EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined. / Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798 / TESIS

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