In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach.

<p>The concept of the transfer Hamiltonian formalism has been reconsidered and generalized to include the non-orthogonality between the electron states in an interacting region, e.g. quantum dot (QD), and the states in the conduction bands in the attached contacts. The electron correlations in the QD are described by means of a diagram technique for Hubbard operator Green functions for non-equilibrium states. </p><p>It is shown that the non-orthogonality between the electrons states in the contacts and the QD is reflected in the anti-commutation relations for the field operators of the subsystems. The derived forumla for the current contains corrections from the overlap of the same order as the widely used conventional tunneling coefficients. </p><p>It is also shown that kinematic interactions between the QD states and the electrons in the contacts, renormalizes the QD energies in a spin-dependent fashion. The structure of the renormalization provides an opportunity to include a spin splitting of the QD levels by polarizing the conduction bands in the contacts and/or imposing different hybridizations between the states in the contacts and the QD for the two spin channels. This leads to a substantial amplification of the spin polarization in the current, suggesting applications in magnetic sensors and spin-filters.</p>

The concept of the transfer Hamiltonian formalism has been reconsidered and generalized to include the non-orthogonality between the electron states in an interacting region, e.g. quantum dot (QD), and the states in the conduction bands in the attached contacts. The electron correlations in the QD are described by means of a diagram technique for Hubbard operator Green functions for non-equilibrium states. It is shown that the non-orthogonality between the electrons states in the contacts and the QD is reflected in the anti-commutation relations for the field operators of the subsystems. The derived forumla for the current contains corrections from the overlap of the same order as the widely used conventional tunneling coefficients. It is also shown that kinematic interactions between the QD states and the electrons in the contacts, renormalizes the QD energies in a spin-dependent fashion. The structure of the renormalization provides an opportunity to include a spin splitting of the QD levels by polarizing the conduction bands in the contacts and/or imposing different hybridizations between the states in the contacts and the QD for the two spin channels. This leads to a substantial amplification of the spin polarization in the current, suggesting applications in magnetic sensors and spin-filters.

Το πρόβλημα που αντιμετωπίζει η διατριβή αφορά στη μοντελοποίηση μη-στασίμων τυχαίων ταλαντώσεων επί τη βάσει μετρήσεων του σήματος της ταλάντωσης, μέσω μοντέλων FS-TAR/TARMA. Οι στόχοι της διατριβής περιλαμβάνουν την αποτίμηση της εφαρμοσιμότητας των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση της ταλάντωσης χρονικά μεταβαλλόμενών κατασκευών, καθώς και τη σύγκρισή τους με εναλλακτικές παραμετρικές μεθόδους του πεδίου του χρόνου. Ιδιαίτερη βαρύτητα δίνεται και στην αντιμετώπιση θεμάτων που σχετίζονται με την εκτίμηση μοντέλων FS-ΤAR/TARMA, καθώς και στην θεωρητική ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών που χρησιμοποιούνται. Η διατριβή αρχικά παρουσιάζει μια συγκριτική ανασκόπηση της βιβλιογραφίας στο θέμα της μοντελοποίησης μη-στασίμων ταλαντώσεων μέσω παραμετρικών μεθόδων του πεδίου του χρόνου, η οποία και επιδεικνύει τα πλεονεκτήματα των μεθόδων FS-TAR/TARMA. Στη συνέχεια αντιμετωπίζεται μια σειρά προβλημάτων που εμφανίζονται κατά την εκτίμηση (των παραμέτρων) και την επιλογή της δομής του μοντέλου. Η αποτελεσματικότητα των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση μη-στάσίμων ταλαντώσεων επιδεικνύεται και πειραματικά μέσω εφαρμογής στην οποία πραγματοποιείται επιτυχής εξαγωγή των δυναμικών χαρακτηριστικών μιας εργαστηριακής χρονικά μεταβαλλόμενης κατασκευής. Στη συνέχεια, η διατριβή εστιάζει στην αναζήτηση ακριβέστερων εκτιμητριών, καθώς και στην ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών «γενικών» (όχι αναγκαστικά περιοδικά μεταβαλλόμενων) μοντέλων FS-TAR/TARMA. Συγκεκριμένα, εξετάζονται οι περιπτώσεις των εκτιμητριών σταθμισμένων ελαχίστων τετραγώνων [Weighted Least Squares (WLS)], μέγιστης πιθανοφάνειας [Maximum Likelihood (ML)], καθώς και μια εκτιμήτρια πολλαπλών σταδίων [Multi Stage (MS)], η οποία αναπτύσσεται στην παρούσα διατριβή και είναι ασυμπτωτικά ισοδύναμη με την εκτιμήτρια ML ενώ ταυτόχρονα χαρακτηρίζεται από μειωμένη υπολογιστική πολυπλοκότητα. Στη διατριβή αποδεικνύεται η συνέπεια (consistency) των εκτιμητριών αυτών και εξάγεται η ασυμπτωτική κατανομή (asymptotic distribution) τους. Παράλληλα, αναπτύσσεται μια συνεπής εκτιμήτρια του ασυμπτωτικού πίνακα συνδιασποράς και μια μέθοδος για τον έλεγχο εγκυρότητας των μοντέλων FS-TAR/TARMA. Η ορθότητα των αποτελεσμάτων της ασυμπτωτικής ανάλυσης επιβεβαιώνεται μέσω μελετών Monte Carlo. / The thesis studies the problem of non-stationary random vibration modeling and analysis based on available measurements of the vibration signal via Functional Series Time-dependent AutoRegressive / AutoRegressive Moving Average (FS-TAR/ TARMA) models. The aims of the thesis include the assessment of the applicability of FS-TAR/TARMA methods for the modeling and analysis of non-stationary random vibration, as well as their comparison with alternative time-domain parametric methods. In addition, significant attention has been paid to the FS-TAR/TARMA estimation problem and to the theoretical asymptotic analysis of the estimators. A critical overview and comparison of time-domain, parametric, non-stationary random vibration modeling and analysis methods is firstly presented, where the high potential of FS-TAR/TARMA methods is demonstrated. In the following, a number of issues concerning the FS-TAR/TARMA model (parameter) estimation and model structure selection are considered. The effectiveness of the FS-TARMA methods for non-stationary random vibration modeling and analysis is experimentally demonstrated, through their application for the recovery of the dynamical characteristics of a time-varying bridge-like laboratory structure. In the sequel, the thesis focuses on the asymptotic analysis of “general” (that is not necessarily periodically evolving) FS-TAR/TARMA estimators. In particular, the Weighted Least Squares (WLS) and Maximum Likelihood (ML) estimators are both investigated, while a Multi Stage (MS) estimator, that approximates the ML estimator at reduced complexity, is developed. The consistency of the considered estimators is established and their asymptotic distribution is extracted. Furthermore, a consistent estimator of the asymptotic covariance matrix is formulated and an FS-TAR/TARMA model validation method is proposed. The validity of the theoretical asymptotic analysis results is assessed through several Monte Carlo studies.

Contexte. Les études cas-témoins sont très fréquemment utilisées par les épidémiologistes pour évaluer l’impact de certaines expositions sur une maladie particulière. Ces expositions peuvent être représentées par plusieurs variables dépendant du temps, et de nouvelles méthodes sont nécessaires pour estimer de manière précise leurs effets. En effet, la régression logistique qui est la méthode conventionnelle pour analyser les données cas-témoins ne tient pas directement compte des changements de valeurs des covariables au cours du temps. Par opposition, les méthodes d’analyse des données de survie telles que le modèle de Cox à risques instantanés proportionnels peuvent directement incorporer des covariables dépendant du temps représentant les histoires individuelles d’exposition. Cependant, cela nécessite de manipuler les ensembles de sujets à risque avec précaution à cause du sur-échantillonnage des cas, en comparaison avec les témoins, dans les études cas-témoins. Comme montré dans une étude de simulation précédente, la définition optimale des ensembles de sujets à risque pour l’analyse des données cas-témoins reste encore à être élucidée, et à être étudiée dans le cas des variables dépendant du temps. Objectif: L’objectif général est de proposer et d’étudier de nouvelles versions du modèle de Cox pour estimer l’impact d’expositions variant dans le temps dans les études cas-témoins, et de les appliquer à des données réelles cas-témoins sur le cancer du poumon et le tabac. Méthodes. J’ai identifié de nouvelles définitions d’ensemble de sujets à risque, potentiellement optimales (le Weighted Cox model and le Simple weighted Cox model), dans lesquelles différentes pondérations ont été affectées aux cas et aux témoins, afin de refléter les proportions de cas et de non cas dans la population source. Les propriétés des estimateurs des effets d’exposition ont été étudiées par simulation. Différents aspects d’exposition ont été générés (intensité, durée, valeur cumulée d’exposition). Les données cas-témoins générées ont été ensuite analysées avec différentes versions du modèle de Cox, incluant les définitions anciennes et nouvelles des ensembles de sujets à risque, ainsi qu’avec la régression logistique conventionnelle, à des fins de comparaison. Les différents modèles de régression ont ensuite été appliqués sur des données réelles cas-témoins sur le cancer du poumon. Les estimations des effets de différentes variables de tabac, obtenues avec les différentes méthodes, ont été comparées entre elles, et comparées aux résultats des simulations. Résultats. Les résultats des simulations montrent que les estimations des nouveaux modèles de Cox pondérés proposés, surtout celles du Weighted Cox model, sont bien moins biaisées que les estimations des modèles de Cox existants qui incluent ou excluent simplement les futurs cas de chaque ensemble de sujets à risque. De plus, les estimations du Weighted Cox model étaient légèrement, mais systématiquement, moins biaisées que celles de la régression logistique. L’application aux données réelles montre de plus grandes différences entre les estimations de la régression logistique et des modèles de Cox pondérés, pour quelques variables de tabac dépendant du temps. Conclusions. Les résultats suggèrent que le nouveau modèle de Cox pondéré propose pourrait être une alternative intéressante au modèle de régression logistique, pour estimer les effets d’expositions dépendant du temps dans les études cas-témoins / Background: Case-control studies are very often used by epidemiologists to assess the impact of specific exposure(s) on a particular disease. These exposures may be represented by several time-dependent covariates and new methods are needed to accurately estimate their effects. Indeed, conventional logistic regression, which is the standard method to analyze case-control data, does not directly account for changes in covariate values over time. By contrast, survival analytic methods such as the Cox proportional hazards model can directly incorporate time-dependent covariates representing the individual entire exposure histories. However, it requires some careful manipulation of risk sets because of the over-sampling of cases, compared to controls, in case-control studies. As shown in a preliminary simulation study, the optimal definition of risk sets for the analysis of case-control data remains unclear and has to be investigated in the case of time-dependent variables. Objective: The overall objective is to propose and to investigate new versions of the Cox model for assessing the impact of time-dependent exposures in case-control studies, and to apply them to a real case-control dataset on lung cancer and smoking. Methods: I identified some potential new risk sets definitions (the weighted Cox model and the simple weighted Cox model), in which different weights were given to cases and controls, in order to reflect the proportions of cases and non cases in the source population. The properties of the estimates of the exposure effects that result from these new risk sets definitions were investigated through a simulation study. Various aspects of exposure were generated (intensity, duration, cumulative exposure value). The simulated case-control data were then analysed using different versions of Cox’s models corresponding to existing and new definitions of risk sets, as well as with standard logistic regression, for comparison purpose. The different regression models were then applied to real case-control data on lung cancer. The estimates of the effects of different smoking variables, obtained with the different methods, were compared to each other, as well as to simulation results. Results: The simulation results show that the estimates from the new proposed weighted Cox models, especially those from the weighted Cox model, are much less biased than the estimates from the existing Cox models that simply include or exclude future cases. In addition, the weighted Cox model was slightly, but systematically, less biased than logistic regression. The real life application shows some greater discrepancies between the estimates of the proposed Cox models and logistic regression, for some smoking time-dependent covariates. Conclusions: The results suggest that the new proposed weighted Cox models could be an interesting alternative to logistic regression for estimating the effects of time-dependent exposures in case-control studies.

In this work, experimental and theoretical approaches are applied to the study of chemical reaction dynamics. In Chapter 2, two applications of transition state theory are presented: (1) Application of microcanonical transition state theory to determine the rate constant of dissociation of C2F3I after π∗ ← π excitation. It was found that this reaction has a very fast rate constant and thus is a promising system for testing the statistical assumption of molecular reaction dynamics. (2) A general rate constant expression for the reaction of atoms and molecules at surfaces was derived within the statistical framework of flexible transition state theory. In Chapter 4, a computationally efficient TDDFT approach was found to produce useful potential energy surface landscapes for application to non-adiabatic predissociative dynamics of the molecule CS2 after excitation from the ground state to the singlet C-state. In Chapter 5, ultrafast experimental results of excitation of CS2 to the predissociative neutral singlet C-state is presented. The bandwidth of the excitation laser was carefully tuned to span a two-component scattering resonance with each component differently evolving electronically with respect to excited state character during the quasi-bound oscillation. Scalar time-resolved photoelectron spectra (TRPES) and vector time-resolved photoelectron angular distribution (TRPAD) observables were recorded during the predissociation. The TRPES yield of photoelectrons was found to oscillate with a quantum beat pattern for the photoelectrons corresponding to ionization to the vibrationless cation ground state; this beat pattern was obscured for photoelectron energies corresponding to ionization from the vibrationally excited CS2 cation. The TRPAD data was recorded for two general molecular ensemble cases: with and without a pre-excitation alignment laser pulse. It was found that in the case of ensemble alignment (Chapter 6), the “molecular frame” TRPAD (i.e. TRMFPAD) was able to image the purely valence electronic dynamics of the evolving CS2 C-state. The unaligned ensemble TRPAD observable suffers from excessive orientational averaging and was unable to observe the quantum beat. Engineering efforts were also undertaken to eliminate scattered light background signal (Chapter 7, Appendix A) and improve laser stability as a function of ambient pressure (Appendix B) for TRMFPAD experiments. / Thesis (Ph.D, Chemistry) -- Queen's University, 2012-09-11 22:18:20.89

This work investigates the correlation of structural and photovoltaic properties of dyes used in dye-sensitized solar cells. Experimental methods, including ultraviolet-visible spectroscopy, fluorescence spectroscopy, cyclic voltammetry and electrochemical impedance spectroscopy are employed to study optical and electrochemical properties of dye molecules. Computational methods, including density functional theory and time-dependent density functional theory, are used to validate and predict the optical and electronic properties of dye molecules, in their isolated state and once embedded into a working electrode device environment that comprises a dye...TiO2 interface. The results chapters begin with the presentation of a series of quinodimethene dyes that are experimentally validated for their photovoltaic application, and associated computational studies reveal that an inner structural factor - a phenyl ring rotation occurring during the optical excitation process - leads to the competitive photovoltaic device performance of these dyes. Carbazole-based dyes are then systematically studied by computation, especially considering charge transfer paths and binding modes of these dyes on a titania surface. The theoretical models for the basic building block of this chemical family of dyes, known as MK-44, successfully support and explain structural discoveries from X-ray diffraction and reflectometry that impact of their function. A benzothiadiazole-based dye, RK-1, is then systematically studied by both experimental and computational methods, and the results show that the π-bridge composed of thiophene, benzothiadiazole and benzene rings leads to excellent charge separation; and the rotation of these rings during the optical excitation process may well be consistent with the fluorescence spectrum. Finally, the well-known ruthenium-based dyes are theoretically studied to determine the properties of different ligands connected to the metal core of the complex. Conformations with different NCS ligands are calculated in terms of energy and explain well the corresponding results from X-ray diffraction. Acid-base properties of carboxyl groups connected to pyridine ligands in N3 and N749 are theoretically calculated based on thermodynamics and density functional theory. Implicit and explicit models are both adopted to predict these acid dissociative constant values, which are generally in a good agreement with the reported experimental data. The thesis concludes with conclusions and a future outlook.

Les travaux réalisés au cours de cette thèse portent sur la dynamique quantique de diffusion d'atomes d'hydrogène sur une surface de palladium (111). L'étude du système 3D a permis de détailler le spectre infrarouge de H/Pd(111) en mettant en évidence l'existence sur différents sites d'adsorption d'états localisés fortement couplés (résonance de Fermi). Ce phénomène gouverne la diffusion des atomes d'hydrogène sur une échelle de temps ultra-rapide (fs).L'étude du système 6D (H2/Pd(111)) a montré que les transitions observées sont, en fait, des bandes de transition entre plusieurs états d'adsorption quasi-dégénérés. L'accord entre les valeurs calculées et mesurées est, par contre, significativement moins bon qu'entre celles calculées pour le système 3D et les données mesurées. Est-ce que l'hydrogène adsorbé sur le palladium existe sous la forme d'une molécule diatomique faiblement lié? Cette thèse a fourni certains éléments de réponse à cette question, qui reste cependant encore ouverte. / The work carried out during this thesis focuses on the quantum dynamics of the diffusion of hydrogen atoms on a surface of palladium (111). The study of the 3D system allowed us to detail the infrared spectrum of H/Pd (111), showing the existence of different adsorption sites on which localized states exist that are strongly coupled (Fermi resonance). This phenomenon governs the diffusion of hydrogen atoms in an ultra-fast time scale (fs).The study of the (6D) H2/Pd(111) system has shown that the transitions observed are in fact transition bands between several quasi-degenerate adsorption states. The agreement between the calculated and measured values is significantly less good than that between the data calculated for the 3D system and the measured data. Does adsorbed hydrogen on palladium exist in the form of a weakly bound H2 molecule? This thesis has provided some answers to this question, which remains open, hovewer, to some extent.

Nous étudions la sensibilité de Belle II avec 50 ab-1 de données sur l'angle βc du triangle d'unitarité, avec une mesure en fonction du temps de l'asymétrie de CP dans les désintégrations des mésons D0. Nous montrons que cette mesure est limitée statistiquement, avec une incertitude totale attendue de l'ordre de 3°. La mesure de βc nécessite la reconstruction de trajectoires de particules de très faible impulsion, impactée par le bruit de fond induit par SuperKEKB. Deux échelles PLUME vont être utilisées pour étudier ce bruit de fond. Ici, une étude des performances de PLUME est effectuée. Ainsi, la résolution spatiale avec des traces à 0° et 36° est mesurée, de 1,8 µm et 3,5µm respectivement. Par ailleurs nous proposons d'améliorer la mesure des faibles impulsions en utilisant la charge déposée par la particule dans le trajectomètre interne au silicium. L'estimateur permet d'améliorer par 2% la résolution sur l'impulsion pour les particules n'atteignant pas le trajectomètre interne. / We are studying the sensitivity of Belle II with 50 ab-1 data to the βc angle of the c-u unitarity triangle, with a time-dependent measurement of the CP asymmetry in the D0 decays. We show that such a measurement is still statistically limited, with a total expected incertitude of 3°.This measurement relies on the reconstruction of soft momenta, impacted by the SuperKEKB induced background.Two PLUME ladders will be used to study this background, therefore a study on the performances of PLUME was performed. The spatial resolution is of 1.8 µm and 3.5 µm for 0° and 36° tilted tracks respectivelly.We also propose to improve the estimation of soft momenta using the energy depositions of charged particles in the silicon layers of the inner tracker. Our estimator improves by approximately 2 % the resolution on momentum for particles which do not penetrate the central tracking system.

Les réactions de fusion-évaporation et de transfert de nucléons entre ions lourds à des énergies proches de la barrière de Coulomb jouent un rôle essentiel dans l’étude de la structure nucléaire et des mécanismes de réaction. Dans le cadre de cette thèse, deux expériences de fusion-évaporation et de transfert de nucléons ont été réalisées au Laboratoire National de Legnaro en Italie : 40Ca+58Ni et 40Ca+64Ni. Dans une première expérience, les sections efficaces de fusion de 40Ca+58,64Ni ont été mesurées à des énergies au-dessus et en dessous de la barrière de Coulomb et ont été interprétées à l’aide de calculs en voies couplées et Hartree-Fock dépendants du temps (TDHF). Les résultats montrent l’importance de l’excitation à un phonon octupolaire dans le noyau 40Ca et les excitations à un phonon quadripolaire dans les noyaux 58Ni et 64Ni, ainsi que l’importance des voies de transfert de nucléons dans le système riche en neutrons 40Ca+64Ni. Dans une expérience complémentaire, les probabilités de transfert de nucléons de 40Ca+58,64Ni ont été mesurées dans le même domaine d’énergie que l’expérience précédente et ont été interprétées en effectuant des calculs TDHF+BCS. Les résultats confirment l’importance des voies de transfert de nucléons dans 40Ca+64Ni. Une description conjointe des probabilités de transfert de nucléons et des sections efficaces de fusion a été réalisée pour les deux réactions étudiées en utilisant une approche en voies couplées. / Heavy-ion fusion-evaporation and nucleon transfer reactions at energies close to the Coulomb barrier play an essential role in the study of nuclear structure and reaction dynamics. In the framework of this PhD thesis, two fusion-evaporation and nucleon transfer experiments have been performed at the Laboratori Nazionali di Legnaro in Italy : 40Ca+58Ni and 40Ca+64Ni. In a first experiment, fusion cross sections for 40Ca+58,64Ni have been measured from above to below the Coulomb barrier and have been interpreted by means of coupled-channels and Time-Dependent Hartree-Fock (TDHF) calculations. The results show the importance of the one-phonon octupole excitation in the 40Ca nucleus and the one-phonon quadrupole excitations in the 58Ni and 64Ni nuclei, as well as the importance of the nucleon transfer channels in the neutron-rich system 40Ca+64Ni. In a complementary experiment, nucleon transfer probabilities for 40Ca+58,64Ni have been measured in the same energy region as the previous experiment and have been interpreted by performing TDHF+BCS calculations. The results confirm the importance of nucleon transfer channels in 40Ca+64Ni. A simultaneous description of the nucleon transfer probabilities and the fusion cross sections has been performed for both reactions, using a coupled-channels approach.