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In this thesis, the implementation of the incremental scheme for open-shell systems with unrestricted Hartree-Fock reference wave functions is described. The implemented scheme is tested within robustness and performance with respect to the accuracy in the energy and the computation times. New approaches are discussed to implement a fully automated incremental scheme in combination with the domain-specific basis set approximation. The alpha Domain Partitioning and Template Equalization are presented to handle unrestricted wave functions for the local correlation treatment. Both orbital schemes are analyzed with a test set of structures and reactions. As a further goal, the DSBSenv orbital basis sets and auxiliary basis sets are optimized to be used as environmental basis in the domain-specific basis set approach. The performance with respect to the accuracy and computation times is analyzed with a test set of structures and reactions. In another project, a scheme for the optimization of auxiliary basis sets for uranium is presented. This scheme was used to optimize the MP2Fit auxiliary basis sets for uranium. These auxiliary basis enable density fitting in quantum chemical methods and the application of the incremental scheme for systems containing uranium. Another project was the systematical analysis of the binding energies of four water dodecamers. The incremental scheme in combination with the CCSD(T) and CCSD(T)(F12*) method were used to calculate benchmark energies for these large clusters.

<p dir="ltr">Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, volume 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the pre-chamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within 10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (p_r^o) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above p_r^o= 2.2. Case with p_r^o= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.</p>

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Zur numerischen L\"osung von Algebro-Differentialgleichungen (ADGln) m\"ussen konsistente Anfangswerte berechnet werden. Diese Arbeit befasst sich mit einem Ansatz zur Behandlung dieses Problems f\"ur Index-2 DAEs unter Verwendung von Projektoren auf die zur DAE zugeh\"origen Unterr\"aume. Die Arbeit hat zwei Schwerpunkte.\\ Zum einen werden neue Struktureigenschaften aus schwachen Voraussetzungen hergeleitet. Anschlie{\ss}end wird eine Vorgehensweise zur Auswahl von geeigneten Gleichungen einer Index-2 ADGln vorgeschlagen, deren Differentiation zu einer Indexreduktion f\"uhrt. Diese Indexreduktion liefert neue Existenz- und Eindeutigkeitsergebnisse f\"ur L\"osungen von Index-2 ADGln. Die Ergebnisse umfassen eine allgemeinere Aufgabenklasse als die bisherigen Resultate. Beruhend auf dieser Vorgehensweise wird ein stufenweiser Ansatz zur Berechnung konsistenter Anfangswerte hergeleitet. Auf diese Weise werden neue Einsichten hinsichtlich der Ausnutzung von Struktureigenschaften von Index-2 ADGln gewonnen. Insbesondere stellt sich heraus, dass im Vergleich zu Index-1 ADGln der zus\"atzliche Schritt oft in der L\"osung eines linearen Systems besteht. Die sich hieraus ergebenden numerischen Folgen werden f\"ur zwei in der Schaltungssimulation h\"aufig verwendete Verfahren, das implizite Eulerverfahren und die Trapezregel, erl\"autert. \\ Zum anderen wird die Anwendung der erhaltenen Ergebnisse auf die Gleichungen, die bei der Schaltungssimulation mittels modifizierter Knotenanalyse entstehen, ausgearbeitet. Abschlie{\ss}end wird eine kurze \"Ubersicht der durchgef\"uhrten Umsetzung gegeben.\\ / For solving DAEs numerically, consistent initial values have to be calculated. This thesis deals with an approach for handling this problem for index-2 DAEs by considering projectors onto the spaces related to the DAE. There are two major aspects in this work.\\ On the one hand, new structural properties are deduced from weak assumptions. Subsequently, a method is proposed to choose suitable equations of an index-2 DAE, whose differentiation leads to an index reduction. This index reduction yields new theoretical results for the existence and uniqueness of solutions of index-2 DAEs which apply to a wider class of applications than previous results. Based on this method, a step-by-step approach to compute consistent initial values is developed. In this way, we gain new insights about how to deal with structural properties of index-2 DAEs. In particular, it turns out that, in comparison to index-1 DAEs, the additional step that has to be undertaken in practice often consists in solving a linear system. The numerical consequences of this fact are exemplified for two methods commonly used in circuit simulation, the implicit Euler method and the trapezoidal rule.\\ On the other hand, the application of the obtained results to the equations arising in circuit simulation by means of the modified nodal analysis (MNA) is worked out. Finally, a short overview of the specifics of their realization is given.

Advances in computing capabilities have facilitated the application of quantum mechanical methods to increasingly larger and more complex chemical systems, including weakly interacting and biologically relevant species. One such ab initio-based composite methodology, the correlation consistent composite approach (ccCA), has been shown to be reliable for the prediction of enthalpies of formation and reaction energies of main group species in the gas phase to within 1 kcal mol-1, on average, of well-established experiment, without dependence on experimental parameterization or empirical corrections. In this collection of work, ccCA has been utilized to determine the proton affinities of deoxyribonucleosides within an ONIOM framework (ONIOM-ccCA) and to predict accurate enthalpies of formation for organophosphorus compounds. Despite the complexity of these systems, ccCA is shown to result in enthalpies of formation to within ~2 kcal mol-1 of experiment and predict reliable reaction energies for systems with little to no experimental data. New applications for the ccCA method have also been introduced, expanding the utility of ccCA to solvated systems and complexes with significant noncovalent interactions. By incorporating the SMD solvation model into the ccCA formulation, the Solv-ccCA method is able to predict the pKa values of nitrogen systems to within 0.7 pKa unit (less than 1.0 kcal mol-1), overall. A hydrogen bonding constant has also been developed for use with weakly interacting dimers and small cluster compounds, resulting in ccCA interaction energies for water clusters and dimers of the S66 set to within 1.0 kcal mol-1 of well-established theoretical values.

Given the lack of effective vaccine or medicine, changing an individual's risk behaviours has been crucial in preventing the spread of HIV. Consistent and correct condom use has been considered as the most effective form of HIV prevention among female sex workers. Despite coordinated national level interventions over the last decade, a consistent decline in condom use among female sex workers has been evidenced in the Ethiopian context, particularly with non-paying partners. Thus far, no study has been produced that has illustrated major determinants of consistent condom use among female sex workers which would help in developing effective intervention strategies for the prevention of HIV spread in the country. In other countries, the Information, Motivation and Behaviour (IMB) model has been used to identify individual level determents of condom use. However, the researcher postulated that behaviour emanating from the personality structure of individuals could be the fundamental individual level determents of adherence to condom use and chose to investigate this using the Enneagram theory of personality, which was acknowledged for its heuristic value in explaining and enhancing self-development of at-risk individuals. This cross-sectional study was conducted in Addis Ababa. With the Without Finite Population Correction of the Sample Size Estimation Formula, the sample size of 350 was set and participants were recruited using Respondent-Driven Sampling (RDS). Using trained female sex workers, the Essential Enneagram Test (EET) and an Information-Motivation-Behaviour (IMB) questionnaire were administered to collect data. General Linear Modeling (GLM) Multivariate analysis was carried out to assess the correlation between personality style and consistent condom use among participants in the last seven days before the interview. The finding of this study revealed that personality type, measured by the Essential Enneagram Test (EET), is able to predict adherence to condom use among female sex workers and provided a new dimension for policy makers and practitioners in behavioural intervention programmes, such as Information-Education-Communication, peer-to-peer approaches, as well as health and rehabilitation services by using the Enneagram principles and universal growth process. / Psychology / D. Litt. et Phil. (Psychology)

Given the lack of effective vaccine or medicine, changing an individual's risk behaviours has been crucial in preventing the spread of HIV. Consistent and correct condom use has been considered as the most effective form of HIV prevention among female sex workers. Despite coordinated national level interventions over the last decade, a consistent decline in condom use among female sex workers has been evidenced in the Ethiopian context, particularly with non-paying partners. Thus far, no study has been produced that has illustrated major determinants of consistent condom use among female sex workers which would help in developing effective intervention strategies for the prevention of HIV spread in the country. In other countries, the Information, Motivation and Behaviour (IMB) model has been used to identify individual level determents of condom use. However, the researcher postulated that behaviour emanating from the personality structure of individuals could be the fundamental individual level determents of adherence to condom use and chose to investigate this using the Enneagram theory of personality, which was acknowledged for its heuristic value in explaining and enhancing self-development of at-risk individuals. This cross-sectional study was conducted in Addis Ababa. With the Without Finite Population Correction of the Sample Size Estimation Formula, the sample size of 350 was set and participants were recruited using Respondent-Driven Sampling (RDS). Using trained female sex workers, the Essential Enneagram Test (EET) and an Information-Motivation-Behaviour (IMB) questionnaire were administered to collect data. General Linear Modeling (GLM) Multivariate analysis was carried out to assess the correlation between personality style and consistent condom use among participants in the last seven days before the interview. The finding of this study revealed that personality type, measured by the Essential Enneagram Test (EET), is able to predict adherence to condom use among female sex workers and provided a new dimension for policy makers and practitioners in behavioural intervention programmes, such as Information-Education-Communication, peer-to-peer approaches, as well as health and rehabilitation services by using the Enneagram principles and universal growth process. / Psychology / D. Litt. et Phil. (Psychology)

Les fonctionnelles de la densité couramment utilisées ont rencontrées un succès spectaculaire dans la modélisation des systèmes physiques, chimiques, et biologiques. Toutefois, elles se sont avérées inadaptées pour décrire certaines situations, comme par exemple les forces de dispersion de London ou les phénomènes de corrélation forte. Dans le cadre de cette thèse, nous nous sommes intéressés à des développements récents de la formulation de l’énergie de corrélation exprimée à partir du théorème de fluctuation-dissipation et connexion adiabatique, visant à pallier ces problèmes. En particulier, différentes implémentations des méthodes au-delà de l’approximation de la phase aléatoire, qui permettent la prise en compte de la contribution d’échange dans le calcul de l’énergie de corrélation, ont été comparées. Ensuite, afin de réduire drastiquement la complexité numérique, une procédure d’orthogonalisation des vecteurs utilisées pour représenter la matrice diélectrique a été développée. Ces méthodes ont ensuite été appliquées au calcul de l’énergie de liaison de petits complexes moléculaires. La formulation de l’énergie de corrélation de la théorie de perturbation de Møller-Plesset dans le contexte matrice diélectrique est aussi présentée et testée. En parallèle, des calculs utilisant les méthodes semi-empiriques numériquement efficaces ont été conduits sur trois ensembles de molécules afin d’en tester les performances concernant les énergies de liaisons en les comparant aux valeurs de références disponibles dans la littérature / Commonly used density functionals have encountered a spectacular success in the modelling of physical, chemical or biological systems. However, they have proven to be unsuitable to describe some situations, such as London’s dispersion forces or strong correlation behaviour. In this thesis, we have been interested in recent developments in the formulation of the correlation energy from the adiabatic connection fluctuation dissipation theorem, to overcome these problems. In particular, different implementations of methods beyond the random phase approximation, which allow to take into account the exchange contribution in the computation of the correlation energy, have been compared. Then, in order to drastically decrease the numerical complexity, an orthogonalization procedure of the vectors used to represent the dielectric matrix has been developed. Then these approaches were applied to the calculation of the binding energy of small molecular complexes. The formulation of the correlation energy of the Møller-Plesset perturbation theory within the dielectric matrix context is also presented and tested. In parallel, calculations using numerically efficient semi-empirical methods were conducted over three molecular sets in order to test their performances regarding the binding energies by comparing them to reference values available in the literature

Développées par la Cour de Justice, les invocabilités des directives européennes définissent les conditions permettant aux personnes juridiques de se prévaloir d'une directive dans leurs rapports juridiques. La Cour de Justice a réussi à introduire ces invocabilités dans les ordres juridiques nationaux, notamment en Italie et en France, en s'appuyant, d'une part, sur des éléments déjà existants dans les ordres juridiques des États membres, tels que la technique de l'interprétation conforme et le principe de la responsabilité de la puissance publique, en les faisant évoluer dans le sens européen. D'autre part, la Cour a aussi créé des outils nouveaux et, finalement, révolutionnaires, tels que les invocabilités de substitution et d'exclusion de la norme nationale incompatible avec une directive européenne. La mise en oeuvre de ces invocabilités a eu des répercussions importantes sur le rôle des juridictions nationales, qui ont vu l'ensemble de leurs missions s'étendre. La sphère juridique des particuliers a également été influencée, de façon imprévisible et, parfois, préjudiciable. / Developed by the European Court of Justice, the invocability of EU directives defines the conditions allowing legal subjects to exercise the rights conferred by a directive in their legal relationships. The ECJ has managed to introduce different types of invocability into the member States national legal orders, and notably in Italy and France, by, on the one hand using some pre-existing elements of the national legal orders, such as consistent interpretation and the principle of State liability, and making them evolve in a European way. And, on the other hand the ECJ has also created new and, finally, revolutionary tools, such as invocability of substitution and invocability of exclusion of the national law incompatible with a EU directive. The implementation of these different types of invocability has had a deep impact on the role of national courts, who have seen their mandate extended. The legal sphere of legal subjects had also been influenced, in unpredictable and sometimes detrimental ways.