Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Desenvolvemos nesta dissertação um método híbrido direto para o cálculo do fator de desvantagem e descrição da distribuição do fluxo de nêutrons em sistemas combustível-moderador. Na modelagem matemática, utilizamos a equação de transporte de Boltzmann independente do tempo, considerando espalhamento linearmente anisotrópico no modelo monoenergético e espalhamento isotrópico no modelo multigrupo, na formulação de ordenadas discretas (SN), em geometria unidimensional. Descrevemos uma análise espectral das equações de ordenadas discretas (SN)a um grupo e a dois grupos de energia, onde seguimos uma analogia com o método de Case. Utilizamos, neste método, quadraturas angulares diferentes no combustível (NC) e no moderador (NM), onde em geral assumimos que NC > NM . Condições de continuidade especiais que acoplam os fluxos angulares que emergem do combustível (moderador) e incidem no moderador (combustível), foram utilizadas com base na equivalência entre as equações SN e PN-1, o que caracteriza a propriedade híbrida do modelo proposto. Sendo um método híbrido direto, utilizamos as NC + NM equações lineares e algébricas constituídas pelas (NC + NM)/2 condições de contorno reflexivas e (NC + NM)/2 condições de continuidade para determinarmos as NC + NM constantes. Com essas constantes podemos calcular os valores dos fluxos angulares e dos fluxos escalares em qualquer ponto do domínio. Apresentamos resultados numéricos para ilustrar a eficiência e a precisão do método proposto. / In this masters dissertation we describe a hybrid direct method for calculating the disadvantage factor and the neutron flux distribution in fuel-moderator lattices. For the mathematical model, we used the discrete ordinates (SN) transport equation, considering linearly anisotropic scattering in the monoenergetic model and isotropic scattering in the energy multigroup model in slab geometry. We describe a spectral analysis of the monoenergetic and two-group SN equations, in a way which is very similar to the Case method. The basic idea is to use higher order angular quadrature set in the highly absorbing fuel region (SNF)and lower order angular quadrature set in the diffusive moderator region (SNM) i.e., NF > NM. Therefore, we apply special continuity conditions for the fuel existing fluxes that constitute the incoming fluxes for the moderator region, and conversely for the moderator existing fluxes that constitute the incoming fluxes for the fuel region, based on the equivalence of the SN and PN-1 equations, which characterize the hybrid model. As a direct hybrid method, we use NF + NM linear algebraic equations composed of (NF + NM)/2 reflexive boundary conditions and (NF + NM)/2 continuity conditions to solve for the NF + NM expansion coefficients. With these coefficients we can calculate the numerical values for the angular fluxes and for the scalar fluxes at any location of domain. We present numerical results to illustrate the efficiency and the accuracy of the offered method.

Im Rahmen von drei Teilstudien wurde mathematische Schülerleistung aus einer differentialpsychologischen Perspektive untersucht. Die hierfür verwendeten Daten stammten von 29.386 deutschen Neuntklässlern, die am Programme for International Student Assessment (PISA) im Jahr 2000 teilnahmen. In Studie 1 wurden ausgehend von Strukturtheorien kognitiver Fähigkeiten verschiedene Strukturmodelle mathematischer Schülerleistung konfirmatorisch geprüft. So wurde mathematische Schülerleistung in Form eines Nested-Faktormodell als additive Funktion einer mathematikspezifischen Fähigkeit (M´) und der allgemeinen kognitiven Fähigkeit (g) spezifiziert. Dieses Modell wies einen besseren Modellfit auf als das in der psychologischen Forschung dominierende Standardmodell. Für Letzteres wurde angenommen, dass Maße mathematischer Schülerleistung nur von einer generellen mathematischen Fähigkeit (M) beeinflusst werden. In Studie 2 wurden Schulformunterschiede mit konfirmatorischen Mehrgruppen-Faktormodellen untersucht. Schulformspezifische Mittelwertunterschiede in M waren im Standardmodell wesentlich stärker ausgeprägt als bei M´ im Nested-Faktormodell. Weiterhin wurde eine schulformspezifische Differenzierungshypothese für M´ untersucht. Entgegen der Erwartung konnte diese nur sehr eingeschränkt von den Daten gestützt werden. In Studie 3 wurde die Validität mathematischer Schülerleistung im Hinblick auf soziodemografische und motivationale Schülermerkmale sowie Schulnoten analysiert. Bei Verwendung des Nested-Faktormodells resultierte ein im Vergleich zum Standardmodell wesentlich differenzierteres Befundmuster. So waren Geschlechterunterschiede (zu Gunsten der Jungen) in M´ im Nested-Faktormodell deutlich stärker ausgeprägt als bei M im Standardmodell. Implikationen und Perspektiven der drei Teilstudien werden für die psychologische Forschung, die Lehr-Lernforschung, die Konzeption von Schülerleistungsstudien sowie für die pädagogische Praxis diskutiert. / Three studies investigated mathematics achievement from an individual differences perspective, using data from 29,386 German ninth graders who participated in the 2000 cycle of the OECD’s Programme for International Student Assessment (PISA). In study 1, different structural models of mathematics achievement were derived from structural theories of cognitive abilities, and tested empirically using confirmatory methods. In a nested-factor model, mathematics achievement was specified to be an additive function of specific mathematical ability (M´) and general cognitive ability (g). This model provided a better fit than the standard model that predominates in psychological research, which assumes that measures of mathematical achievement are only influenced by general mathematical ability (M). In study 2, differences between types of schools were analyzed using confirmatory multigroup factor analytic models. Mean differences in M in the standard model were much stronger than in M´ in the nested-factor model. A school-type-specific differentiation hypothesis for M´ was also investigated. Contrary to predictions, the data provided only limited support for this hypothesis. Study 3 analyzed the validity of mathematics achievement with respect to sociodemographic and motivational student characteristics and school grades. The nested-factor model yielded a much more differentiated pattern of results than the standard model. For example, gender differences (in favor of boys) were much more pronounced in M´ in the nested-factor model than in M in the standard model. The implications and future perspectives of studies 1 to 3 are discussed with respect to psychological and educational research, design of large-scale achievement studies, and educational practice.

Ce travail de thèse est consacré à la mise en œuvre d’une méthode de décomposition de domaine appliquée à l’équation du transport. L’objectif de ce travail est l’accès à des solutions déterministes haute-fidélité permettant de correctement traiter les hétérogénéités des réacteurs nucléaires, pour des problèmes dont la taille varie d’un motif d’assemblage en 3 dimensions jusqu’à celle d’un grand cœur complet en 3D. L’algorithme novateur développé au cours de la thèse vise à optimiser l’utilisation du parallélisme et celle de la mémoire. La démarche adoptée a aussi pour but la diminution de l’influence de l’implémentation parallèle sur les performances. Ces objectifs répondent aux besoins du projet APOLLO3, développé au CEA et soutenu par EDF et AREVA, qui se doit d’être un code portable (pas d’optimisation sur une architecture particulière) permettant de réaliser des modélisations haute-fidélité (best estimate) avec des ressources allant des machines de bureau aux calculateurs disponibles dans les laboratoires d’études. L’algorithme que nous proposons est un algorithme de Jacobi Parallèle par Bloc Multigroupe. Chaque sous domaine est un problème multigroupe à sources fixes ayant des sources volumiques (fission) et surfaciques (données par les flux d’interface entre les sous domaines). Le problème multigroupe est résolu dans chaque sous domaine et une seule communication des flux d’interface est requise par itération de puissance. Le rayon spectral de l’algorithme de résolution est rendu comparable à celui de l’algorithme de résolution classique grâce à une méthode d’accélération non linéaire par la diffusion bien connue nommée Coarse Mesh Finite Difference. De cette manière une scalabilité idéale est atteignable lors de la parallélisation. L’organisation de la mémoire, tirant parti du parallélisme à mémoire partagée, permet d’optimiser les ressources en évitant les copies de données redondantes entre les sous domaines. Les architectures de calcul à mémoire distribuée sont rendues accessibles par un parallélisme hybride qui combine le parallélisme à mémoire partagée et à mémoire distribuée. Pour des problèmes de grande taille, ces architectures permettent d’accéder à un plus grand nombre de processeurs et à la quantité de mémoire nécessaire aux modélisations haute-fidélité. Ainsi, nous avons réalisé plusieurs exercices de modélisation afin de démontrer le potentiel de la réalisation : calcul de cœur et de motifs d’assemblages en 2D et 3D prenant en compte les contraintes de discrétisation spatiales et énergétiques attendues. / This thesis is devoted to the implementation of a domain decomposition method applied to the neutron transport equation. The objective of this work is to access high-fidelity deterministic solutions to properly handle heterogeneities located in nuclear reactor cores, for problems’ size ranging from colorsets of assemblies to large reactor cores configurations in 2D and 3D. The innovative algorithm developed during the thesis intends to optimize the use of parallelism and memory. The approach also aims to minimize the influence of the parallel implementation on the performances. These goals match the needs of APOLLO3 project, developed at CEA and supported by EDF and AREVA, which must be a portable code (no optimization on a specific architecture) in order to achieve best estimate modeling with resources ranging from personal computer to compute cluster available for engineers analyses. The proposed algorithm is a Parallel Multigroup-Block Jacobi one. Each subdomain is considered as a multi-group fixed-source problem with volume-sources (fission) and surface-sources (interface flux between the subdomains). The multi-group problem is solved in each subdomain and a single communication of the interface flux is required at each power iteration. The spectral radius of the resolution algorithm is made similar to the one of a classical resolution algorithm with a nonlinear diffusion acceleration method: the well-known Coarse Mesh Finite Difference. In this way an ideal scalability is achievable when the calculation is parallelized. The memory organization, taking advantage of shared memory parallelism, optimizes the resources by avoiding redundant copies of the data shared between the subdomains. Distributed memory architectures are made available by a hybrid parallel method that combines both paradigms of shared memory parallelism and distributed memory parallelism. For large problems, these architectures provide a greater number of processors and the amount of memory required for high-fidelity modeling. Thus, we have completed several modeling exercises to demonstrate the potential of the method: 2D full core calculation of a large pressurized water reactor and 3D colorsets of assemblies taking into account the constraints of space and energy discretization expected for high-fidelity modeling.

The purpose of this current study was to determine the role of acculturation, ethnic identity, and religious fatalism regarding attitudes towards seeking psychological help among Coptic (Egyptian Christian) Americans. In addition, differences between groups of gender and generational status, first-generation adult immigrants versus U.S.-born second-generation Copts, were analyzed. The study had a total sample of 91 individuals that self-identified as Coptic by race and/or Coptic Orthodox by religion, who voluntarily completed an anonymous online questionnaire. Results indicate that ethnic identity and acculturation are strong predictors of religious fatalistic beliefs, and those who identified as having more Arab ethnic identity and less assimilation to dominate culture have stronger religious fatalistic beliefs than those who identified with more western culture and an American ethnic identity. However, religious fatalism and ethnic identity were not significant predictors of attitudes towards seeking psychological help, and other variables such as stigma, language barriers, and skepticism of western psychology may be better predictors of attitudes towards seeking psychological help. Between groups comparisons identified subtle differences between males and females, and between first and second-generation Coptic Americans on acculturation, ethnic identity, and religious fatalism, but the groups were not statistically significant from one another. Clinical implications and directions for future research will also be discussed.