This thesis fills in the gaps in the existing theory of wave phenomena in thick diffraction gratings at extreme angles of scattering, i.e. when the scattered wave propagates parallel or almost parallel to the grating boundaries. A consistent theory of a new type of Bragg scattering of bulk and guided optical modes in thick uniform and non-uniform, dissipative and non-dissipative, slanted periodic gratings has been developed. This type of scattering is called extremely asymmetrical scattering (EAS). One of the main distinctive features of EAS is the strong resonant increase of the scattered wave amplitude compared to the amplitude of the incident wave. Several unique combinations of strong resonances shaping a complex multi-resonant pattern of EAS in different types of gratings have been predicted and investigated theoretically and numerically. This includes the prediction of a new resonant wave effect in non-uniform gratings with varying phase – double-resonant EAS, the discovery of several sharp and strong resonances with respect to scattering angle in gratings with the scattered wave propagating almost parallel to the grating boundaries (grazing-angle scattering (GAS)) for the case of second-order scattering, and the prediction of a new type of eigenmode in gratings with second-order scattering (especially in gratings with large amplitude). In addition, several other important practical problems that may be crucial for the experimental observation and application of EAS and GAS have been solved. These are the determination of the tolerance of EAS to small grating imperfections, e.g., fluctuations of the grating amplitude, prediction of unusually high sensitivity of second-order EAS to small variations of mean structural parameters, determination of the effect of weak dissipation on EAS, etc. Physical reasons for the predicted resonances and effects are explained. In particular, the crucial role of the diffractional divergence for EAS and GAS has been revealed, especially for non-uniform gratings. Methods of analysis involve the approximate and rigorous approaches. The approximate method is based on understanding the role of the diffractional divergence in the geometry of EAS and the two-wave approximation (valid for any types of waves). The rigorous approach is based on the rigorous coupled-wave analysis (RCWA) and, in particular, the known enhanced T-matrix algorithm (by Moharam, et al.) that is numerically stable for narrow and wide gratings with arbitrary amplitude (valid only for bulk electromagnetic waves).

As tensões residuais influenciam o comportamento mecânico dos metais e ligas. O campo de tensões pode determinar o desempenho do material. Então, torna-se de grande importância o estudo e a determinação das tensões residuais. O método padrão da difração de raios X para medir tensões s residuais (Método sen2ψ ) apresenta limitações na determinação de tensões caracterizadas por alto gradiente. È por isso que o estudo do gradiente de tensão superficial é um dos mais importantes problemas teóricos e experimentais em mecânica, especialmente no caso da análise de tensões superficiais que surgem após vários tipos de tratamentos superficiais, como: processamento por laser e tecnologia de implantação iônica. A simulação computacional e os métodos numéricos nos dão a possibilidade de resolver os problemas da determinação dos parâmetros do gradiente de tensão. Neste trabalho foi desenvolvida e aplicada a modelação e simulação computacional para o estudo do comportamento de materiais na presença de distribuições de tensão caracterizadas por alto gradiente. Foi aplicada a modelagem para diferentes tipos de tensões com gradiente para metais puros e ligas metálicas. Foi determinada uma forma para usar a modelagem no caso de materiais compósitos e são apresentados resultados para o caso do silumínio, mostrando o comportamento similar deste material compósito aos materiais puros como aço e alumínio. Usando a análise de Fourier, foi determinada a função de distorção nos casos de perfis alargados pela existência de gradiente de tensão. Foi determinada também a relação entre as funções de atenuação e de tensão na função de distorção e são apresentados resultados para diferentes tipos de distribuições de tensão. Ademais, foi desenvolvida uma metodologia para a determinação dos parâmetros do gradiente de tensão usando a simulação computacional das linhas de difração desenvolvida neste trabalho. A metodologia desenvolvida é baseada na simulação dos perfis de difração distorcidos pelo gradiente de tensão superficial e na análise destas distorções. Das metodologias desenvolvidas para a determinação de distribuições de tensões para o caso de gradiente, a que usa transformada de Fourier é matematicamente correta, porem apresenta dificuldades na determinação das funções de gradiente para casos de distribuições muito complexas e na determinação dos relacionamentos das escalas das funções envolvidas no processo de deconvolução. A alta complexidade deste método e os problemas numéricos que acarreta nos levam a propor a metodologia desenvolvida usando as larguras integrais dos perfis de difração para a determinação aproximada da função de distribuição de tensões. Esta metodologia é de simples aplicação e a sua precisão dependerá da quantidade de dados determinados na simulação direta para a obtenção dos gráficos de calibração. / The residual stress influences the mechanical behavior of metals and alloys. The stress field can determine the material performance. Then, become of great importance the study and determination of residual stress field. The standard X-ray diffraction method for residual stress measurement ent ( sen2ψ Method) presents limitations in the strong stress gradient determination. For that reason, the superficial stress gradient determination is one of the most important theoretical and experimental problem in engineering, especially in the analysis of the stress gradients due to surfaces treatments as laser or ionic implantation. The computational simulation and numerical methods give us the possibility of solve this problems. In this work is developed and applied two methods of modeling and simulation for the study of the material behavior with strong stress gradient. Is applied this modeling technique for different stress distribution in pure metals and metallic alloys. Is established a methodology for the composite material cases and is presents the results for the case of siluminium, showing that the behavior is similar to the other metals testing as steel and aluminum. Also, using Fourier analysis is determined the distortion function for the broadened profiles in the presence of stress gradient. In this work is shown the relation between the attenuation and stress distribution functions in the distortion. Is shown, results for several stress distribution functions. Moreover, is developed a methodology for the determination of stress gradient parameters using the computational simulation of the diffraction lines also developed in this work. The methodology is based in the simulation of the profiles broadened by stress gradient and the analysis of these distortions. Of the developed methodologies for the determination of stress distribution functions for the gradient case, the one that uses Fourier analysis is mathematically correct, but presents difficulties in the determination of the gradient functions for cases of complex stress distributions and in the scales determination of the functions involved in the deconvolution process. The high complexity of this method and the numeric problems that it carries leaves as, to propose the use of the developed methodology using the integral breath of the diffraction profiles for the approximate determination of the stress distribution function. The methodology application is simple and its accuracy will depend on the amount of data determined in the direct simulation to obtain the calibration graphics.

As tensões residuais influenciam o comportamento mecânico dos metais e ligas. O campo de tensões pode determinar o desempenho do material. Então, torna-se de grande importância o estudo e a determinação das tensões residuais. O método padrão da difração de raios X para medir tensões s residuais (Método sen2ψ ) apresenta limitações na determinação de tensões caracterizadas por alto gradiente. È por isso que o estudo do gradiente de tensão superficial é um dos mais importantes problemas teóricos e experimentais em mecânica, especialmente no caso da análise de tensões superficiais que surgem após vários tipos de tratamentos superficiais, como: processamento por laser e tecnologia de implantação iônica. A simulação computacional e os métodos numéricos nos dão a possibilidade de resolver os problemas da determinação dos parâmetros do gradiente de tensão. Neste trabalho foi desenvolvida e aplicada a modelação e simulação computacional para o estudo do comportamento de materiais na presença de distribuições de tensão caracterizadas por alto gradiente. Foi aplicada a modelagem para diferentes tipos de tensões com gradiente para metais puros e ligas metálicas. Foi determinada uma forma para usar a modelagem no caso de materiais compósitos e são apresentados resultados para o caso do silumínio, mostrando o comportamento similar deste material compósito aos materiais puros como aço e alumínio. Usando a análise de Fourier, foi determinada a função de distorção nos casos de perfis alargados pela existência de gradiente de tensão. Foi determinada também a relação entre as funções de atenuação e de tensão na função de distorção e são apresentados resultados para diferentes tipos de distribuições de tensão. Ademais, foi desenvolvida uma metodologia para a determinação dos parâmetros do gradiente de tensão usando a simulação computacional das linhas de difração desenvolvida neste trabalho. A metodologia desenvolvida é baseada na simulação dos perfis de difração distorcidos pelo gradiente de tensão superficial e na análise destas distorções. Das metodologias desenvolvidas para a determinação de distribuições de tensões para o caso de gradiente, a que usa transformada de Fourier é matematicamente correta, porem apresenta dificuldades na determinação das funções de gradiente para casos de distribuições muito complexas e na determinação dos relacionamentos das escalas das funções envolvidas no processo de deconvolução. A alta complexidade deste método e os problemas numéricos que acarreta nos levam a propor a metodologia desenvolvida usando as larguras integrais dos perfis de difração para a determinação aproximada da função de distribuição de tensões. Esta metodologia é de simples aplicação e a sua precisão dependerá da quantidade de dados determinados na simulação direta para a obtenção dos gráficos de calibração. / The residual stress influences the mechanical behavior of metals and alloys. The stress field can determine the material performance. Then, become of great importance the study and determination of residual stress field. The standard X-ray diffraction method for residual stress measurement ent ( sen2ψ Method) presents limitations in the strong stress gradient determination. For that reason, the superficial stress gradient determination is one of the most important theoretical and experimental problem in engineering, especially in the analysis of the stress gradients due to surfaces treatments as laser or ionic implantation. The computational simulation and numerical methods give us the possibility of solve this problems. In this work is developed and applied two methods of modeling and simulation for the study of the material behavior with strong stress gradient. Is applied this modeling technique for different stress distribution in pure metals and metallic alloys. Is established a methodology for the composite material cases and is presents the results for the case of siluminium, showing that the behavior is similar to the other metals testing as steel and aluminum. Also, using Fourier analysis is determined the distortion function for the broadened profiles in the presence of stress gradient. In this work is shown the relation between the attenuation and stress distribution functions in the distortion. Is shown, results for several stress distribution functions. Moreover, is developed a methodology for the determination of stress gradient parameters using the computational simulation of the diffraction lines also developed in this work. The methodology is based in the simulation of the profiles broadened by stress gradient and the analysis of these distortions. Of the developed methodologies for the determination of stress distribution functions for the gradient case, the one that uses Fourier analysis is mathematically correct, but presents difficulties in the determination of the gradient functions for cases of complex stress distributions and in the scales determination of the functions involved in the deconvolution process. The high complexity of this method and the numeric problems that it carries leaves as, to propose the use of the developed methodology using the integral breath of the diffraction profiles for the approximate determination of the stress distribution function. The methodology application is simple and its accuracy will depend on the amount of data determined in the direct simulation to obtain the calibration graphics.

Cette thèse est essentiellement composée de deux parties traitant des problèmes de Cauchy ou des problèmes périodiques. Dans la première partie, on étudie la stabilité de solutions régulières au voisinage d'états d'équilibre non constants pour un système d'Euler-Maxwell isentropique compressible bipolaire. Par des estimations d'énergie classiques et un argument de récurrence sur l'ordre des dérivées des solutions, on montre l'existence globale et l'unicité des solutions régulières du système lorsque les données initiales sont proches des états d'équilibre. On obtient aussi le comportement asymptotique des solutions quand le temps tend vers l'infini. Dans la deuxième partie, on considère la stabilité en temps long des solutions régulières de systèmes d'Euler-Maxwell et de Navier-Stokes-Maxwell compressibles dans le cas non isentropique lorsque les états d'équilibre sont constants. Grâce à des choix convenables de symétriseurs des systèmes et à des estimations d'énergie, on montre l'existence globale et l'unicité des solutions régulières des systèmes avec données initiales petites. De plus, par le principe de Duhamel et l'outil d'analyse de Fourier, on obtient des taux de décroissance des solutions quand le temps tend vers l'infini. / This thesis is essentially composed of two parts dealing with Cauchy problems and periodic problems. In the first part, we study the stability of smooth solutions near non constant equilibrium states for a two-fluid isentropic compressible Euler-Maxwell system.By classical energy estimates together with an induction argument on the order of the derivatives of solutions, we prove the existence and uniqueness of global solutions to the system when the given initial data are near the equilibrium states. We also obtain the asymptotic behavior of solutions when the time goes to infinity. In the second part, we consider the long time stability of the global smooth solutions for compressible Euler-Maxwell and Navier-Stokes-Maxwell systems in non isentropic case when the equilibrium solutions are constants. With the help of suitable choices of symmetrizers and energy estimates, we prove the existence and uniqueness of global solutions to the systems with given small initial data. Furthermore, using the Duhamel principle and the Fourier analysis tool, we obtain the decay rates of smooth solutions as the time goes to infinity.

This thesis treats two essentially different subjects: V-cycle schemes are considered in Chapters 2-4, whereas the aggregation-based coarsening is analysed in Chapters 5-6. As a matter of paradox, these two multigrid ingredients, when combined together, can hardly lead to an optimal algorithm. Indeed, a V-cycle needs more accurate prolongations than the simple piecewise-constant one, associated to aggregation-based coarsening. On the other hand, aggregation-based approaches use almost exclusively piecewise constant prolongations, and therefore need more involved cycling strategies, K-cycle <a href=http://www3.interscience.wiley.com/journal/114286660/abstract?CRETRY=1&SRETRY=0>[Num.Lin.Alg.Appl. vol.15(2008), pp.473-487]</a> being an attractive alternative in this respect.<p><br><p><br><p>Chapter 2 considers more precisely the well-known V-cycle convergence theories: the approximation property based analyses by Hackbusch (see [Multi-Grid Methods and Applications, 1985, pp.164-167]) and by McCormick [SIAM J.Numer.Anal. vol.22(1985), pp.634-643] and the successive subspace correction theory, as presented in [SIAM Review, vol.34(1992), pp.581-613] by Xu and in [Acta Numerica, vol.2(1993), pp.285-326.] by Yserentant. Under the constraint that the resulting upper bound on the convergence rate must be expressed with respect to parameters involving two successive levels at a time, these theories are compared. Unlike [Acta Numerica, vol.2(1993), pp.285-326.], where the comparison is performed on the basis of underlying assumptions in a particular PDE context, we compare directly the upper bounds. We show that these analyses are equivalent from the qualitative point of view. From the quantitative point of view,<p>we show that the bound due to McCormick is always the best one.<p><br><p><br><p>When the upper bound on the V-cycle convergence factor involves only two successive levels at a time, it can further be compared with the two-level convergence factor. Such comparison is performed in Chapter 3, showing that a nice two-grid convergence (at every level) leads to an optimal McCormick's bound (the best bound from the previous chapter) if and only if a norm of a given projector is bounded on every level.<p><br><p><br><p>In Chapter 4 we consider the Fourier analysis setting for scalar PDEs and extend the comparison between two-grid and V-cycle multigrid methods to the smoothing factor. In particular, a two-sided bound involving the smoothing factor is obtained that defines an interval containing both the two-grid and V-cycle convergence rates. This interval is narrow when an additional parameter α is small enough, this latter being a simple function of Fourier components.<p><br><p><br><p>Chapter 5 provides a theoretical framework for coarsening by aggregation. An upper bound is presented that relates the two-grid convergence factor with local quantities, each being related to a particular aggregate. The bound is shown to be asymptotically sharp for a large class of elliptic boundary value problems, including problems with anisotropic and discontinuous coefficients.<p><br><p><br><p>In Chapter 6 we consider problems resulting from the discretization with edge finite elements of 3D curl-curl equation. The variables in such discretization are associated with edges. We investigate the performance of the Reitzinger and Schöberl algorithm [Num.Lin.Alg.Appl. vol.9(2002), pp.223-238], which uses aggregation techniques to construct the edge prolongation matrix. More precisely, we perform a Fourier analysis of the method in two-grid setting, showing its optimality. The analysis is supplemented with some numerical investigations. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Dans cette thèse, on étudie la structuration des phases de la transformée de Fourier d'images naturelles, ce qui, du point de vue applicatif, débouche sur plusieurs mesures de netteté ainsi que sur des algorithmes rapides pour la synthèse de texture par l'exemple. Le Chapitre 2 présente dans un cadre unifié plusieurs modèles de champs aléatoires, notamment les champs spot noise et champs gaussiens, en prêtant une attention particulière aux représentations fréquentielles de ces champs aléatoires. Le Chapitre 3 détaille l'utilisation des champs à phase aléatoire à la synthèse de textures peu structurées (microtextures). On montre qu'une microtexture peut être résumée en une image de petite taille s'intégrant à un algorithme de synthèse très rapide et flexible via le modèle spot noise. Aussi on propose un algorithme de désocclusion de zones texturales uniformes basé sur la simulation gaussienne conditionnelle. Le Chapitre 4 présente trois mesures de cohérence globale des phases de la transformée de Fourier. Après une étude théorique et pratique établissant leur lien avec la netteté d'image, on propose un algorithme de déflouage aveugle basé sur l'optimisation stochastique de ces indices. Enfin, dans le Chapitre 5, après une discussion sur l'analyse et la synthèse directe de l'information de phase, on propose deux modèles de textures à phases cohérentes qui permettent la synthèse de textures plus structurées tout en conservant quelques garanties mathématiques simples. / This thesis deals with the Fourier phase structure of natural images, and addresses no-reference sharpness assessment and fast texture synthesis by example. In Chapter 2, we present several models of random fields in a unified framework, like the spot noise model and the Gaussian model, with particular attention to the spectral representation of these random fields. In Chapter 3, random phase models are used to perform by-example synthesis of microtextures (textures with no salient features). We show that a microtexture can be summarized by a small image that can be used for fast and flexible synthesis based on the spot noise model. Besides, we address microtexture inpainting through the use of Gaussian conditional simulation. In Chapter 4, we present three measures of the global Fourier phase coherence. Their link with the image sharpness is established based on a theoretical and practical study. We then derive a stochastic optimization scheme for these indices, which leads to a blind deblurring algorithm. Finally, in Chapter 5, after discussing the possibility of direct phase analysis or synthesis, we propose two non random phase texture models which allow for synthesis of more structured textures and still have simple mathematical guarantees.

Indiana University-Purdue University Indianapolis (IUPUI) / Object segmentation, quantification, and shape modeling are important areas inmedical image processing. By combining these techniques, researchers can find valuableways to extract and represent details on user-desired structures, which can functionas the base for subsequent analyses such as feature classification, regression, and prediction. This thesis presents a new framework for building a three-dimensional (3D) hippocampal atlas model with subfield information mapped onto its surface, with which hippocampal surface registration can be done, and the comparison and analysis can be facilitated and easily visualized. This framework combines three powerful tools for automatic subcortical segmentation and 3D surface modeling. Freesurfer and Functional magnetic resonance imaging of the brain's Integrated Registration and Segmentation Tool (FIRST) are employed for hippocampal segmentation and quantification, while SPherical HARMonics (SPHARM) is employed for parametric surface modeling. This pipeline is shown to be effective in creating a hippocampal surface atlas using the Alzheimer's Disease Neuroimaging Initiative Grand Opportunity and phase 2 (ADNI GO/2) dataset. Intra-class Correlation Coefficients (ICCs) are calculated for evaluating the reliability of the extracted hippocampal subfields. The complex folding anatomy of the hippocampus offers many analytical challenges, especially when informative hippocampal subfields are usually ignored in detailed morphometric studies. Thus, current research results are inadequate to accurately characterize hippocampal morphometry and effectively identify hippocampal structural changes related to different conditions. To address this challenge, one contribution of this study is to model the hippocampal surface using a parametric spherical harmonic model, which is a Fourier descriptor for general a 3D surface. The second contribution of this study is to extend hippocampal studies by incorporating valuable hippocampal subfield information. Based on the subfield distributions, a surface atlas is created for both left and right hippocampi. The third contribution is achieved by calculating Fourier coefficients in the parametric space. Based on the coefficient values and user-desired degrees, a pair of averaged hippocampal surface atlas models can be reconstructed. These contributions lay a solid foundation to facilitate a more accurate, subfield-guided morphometric analysis of the hippocampus and have the potential to reveal subtle hippocampal structural damage associated.

[pt] Nesta tese estudamos o potencial que terão a próxima geração de detectores de neutrinos (JUNO, Hyper-Kamiokande e DUNE) para a detecção dos efeitos da matéria da Terra através da identificação das modulações no espectro de energia dos neutrinos de supernovas de colapso de núcleo em nossa galáxia, assumindo a possibilidade do decaimiento invisível de v2 após os neutrinos terem deixado a estrela, caminho da Terra. Simulações recentes do colapso gravitacional (e subsequente explosão) de estrelas com massa maior do que ~ 8Mo mostram que durante a fase de esfriamento as energias médias (Eve) e (Evx) tornam-se muito semelhantes e os fluxos tendem a se igualar, tornando difícil observar os efeitos da matéria da Terra usando um único detector. Neste trabalho mostramos que a inclusão do decaimiento dos neutrinos também cria a possibilidade de observar os efeitos em consideração no canal de detecção de neutrinos se o ordenamento de massa for normal e no canal anti-neutrino se o ordenamento for invertido, o que não é esperado na ausência de decaimento. Em particular, se a taxa de decaimento for maior do que ~ 70%, descobrimos que o decaimento invisível de v2 pode aumentar as possibilidades de observação dos efeitos da matéria da Terra, mesmo para supernovas a uma distância de 10 kpc de nós. / [en] In this thesis we studied the potential that the next-generation neutrino detectors (JUNO, Hyper-Kamiokande and DUNE) will have to the detection of the Earth matter effects through the identification of the modulations in the energy spectrum of neutrinos from core-collapse supernovae in our galaxy, assuming the possibility of the invisible decay of v2 after the neutrinos have left the star, on their way to Earth. Recent simulations of gravitational collapse (and subsequent explosion) of stars more massive than ~ 8Mo show that during the cooling phase the average energies (EVe) and (Evx) become very similar and the fluxes tend to equalize, making it difficult to observe the Earth matter effects using a single detector. In this work we show that the inclusion of neutrino decay creates also the possibility of observing the effects under consideration in the neutrino detection channel if the mass ordering is normal and in the anti-neutrino channel if the ordering is inverted, which is not expected in the absence of neutrino decay. In particular, if the decay rate is more than ~ 70%, we find that the invisible neutrino decay of v2 can enhance the observation possibilities of Earth matter effects even for supernovae at a distance of 10 kpc from us.