In many applications, it is necessary to simulate wave scattering from surfaces that have small radii of curvature relative to the incident wavelength. Surface features smaller than an electromagnetic wavelength are known to create diffracted fields over a wide range of scattering angles. In this thesis, the significance of such effects at low grazing angles with the presence of an extended planar surface is considered. The magnetic field integral equation (MFIE) describing the currents on such surfaces is used to solve for the bistatic scattered fields. The integral equations are discretized using the moment method and solved using the Method of Ordered Multiple Interactions (MOMI) iterative procedure. This thesis will concentrate on normal incidence and low grazing angle (LGA) incidence, specifically an incident angle of 80 degrees. The surface used in the analysis is a one-dimensional, perfectly-conducting wedge-on-a-plane with a varying radius of curvature at the wedge tip and Gaussian tails that smoothly extend the wedge to the plane surface. This surface displays continuous first and second derivatives over the entire surface. The radius of curvature at the wedge tip is varied between 0.0125 wavelengths and 8 wavelengths. The form of the bistatic scattered fields will be investigated for three different wedge height to wedge width geometries. The surface scattering mechanisms and their respective location and form in the scattered field will be discussed. The dependence of the scattered field pattern on the radius of curvature at the wedge tip and the beam width of the incident field will be considered. The difficulties associated with using a numerical technique on extended surfaces where a significant source of diffracted energy is present will also be examined. This includes the issue of sampling a surface that contains areas of small radii of curvature and the issue of surface truncation when significant currents due to tip diffraction are produced well outside the illuminated area. Both TE (VV) and TM (HH) polarization will be considered. This thesis also analyzes the scattered fields for a perfect electric conducting (PEC) ridge and well in the presence of an extended planar surface for an incident angle of 70 degrees. The dual-surface magnetic field integral equation (DMFIE) formulation for a one-dimensional extended surface will be used to solve for the unknown currents on the surface of the scatterer. The DMFIE formulation leads to a second kind integral equation that can be solved via the MOMI series with the proper choice of the parameters appearing in the DMFIE formulation. The bistatic scattered fields for several ridge and well geometries are examined for both TE and TM polarization. / Master of Science

A Tomografia por Emissão de Pósitrons (PET) está se definindo como um dos métodos preferidos para diagnóstico e seguimento de inúmeras doenças em Oncologia, Neurologia e Cardiologia. Esta modalidade é realizada com sistemas dedicados e sistemas baseados em câmaras de cintilação, que podem ser também usados em tomografia por emissão de fótons únicos (SPECT). Neste trabalho, efetuamos uma avaliação dos fatores que favorecem a quantificação em imagens PET com câmaras de cintilação em coincidência, caracterizadas por urna menor sensibilidade em relação a sistemas dedicados. Avaliamos as condições de quantificação de imagens sob os modos 2D e 3D de aquisição, obtidas por métodos de reconstrução 2D e 3D diversos e correções associadas. Dados de aquisição foram simulados por método de Monte Carlo empregando parâmetros realistas. Objetos de interesse diversos foram modelados. Imagens foram reconstruídas pelos métodos FBP, ART, MLEM e OSEM e consideramos correções de sensibilidade, normalização de detector, espalhamento e atenuação de radiação. Estabelecemos uma metodologia de avaliação de detectabilidade e recuperação de contrastes em imagens que contemplam, a partir de dois parâmetros mensuráveis, os aspectos mais relevantes em quantificação. Análises visuais também foram consideradas. Verificamos que o modo 3D é mais adequado que 2D na recuperação de baixos contrastes no objeto com a aplicação das correções selecionadas. A detectabilidade de pequenas estruturas está limitada pelos efeitos de volume parcial e pela resolução espacial finita dos sistemas de detecção. Os métodos ART, MLEM e, em particular, OSEM com 8 subconjuntos, apresentam-se adequados para estudos quantitativos no modo 3D. Os parâmetros definidos para avaliação podem ser empregados como indicadores de condições propícias a estudos quantitativos. / Volumetric reconstruction in gamma camera based PET imaging Positron Emission Tomography (PET) is considered as a very useful tool for diagnosing and following several diseases in Oncology, Neurology and Cardiology. Two types of systems are available for this imaging modality: the dedicated systems and those based on gamma camera technology. In this work, we assessed a number of factors affecting the quantitation of gamma camera based PET imaging, characterized by a lower sensitivity compared to those of dedicated systems. We also evaluated image quantitation conditions under 2D and 3D acquisition/reconstruction modes, for different reconstruction methods and associated corrections. Acquisition data were simulated by Monte Carla method, using realistic parameters. Several objects of interest were modelled. We reconstructed slices and volumes using FBP, ART, MLEM and OSEM and also included four corrections: detector sensitivity, detector normalization, scatter and attenuation of annihilation photons. We proposed a method to assess detectability and object contrast recovery by using two measurable parameters. Visual analysis was also considered. We found that 3D mode is more effective than 2D for low contrast recovery when the selected (J corrections are applied. Detectability of small structures is limited by partial volume effects and device finite spatial resolution. ART, MLEM and specially 8-subsets OSEM are the most adequate methods for quantitative studies in 3D mode. The parameter that we have defined may also be used as indicators of suitable conditions for quantitation in images.

by He Xinggang. / "December 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 69-73). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Chan, Kwan Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 63-69). / Abstracts in English and Chinese. / Abstract --- p.v / Acknowledgements --- p.ix / List of Figures --- p.xiii / List of Tables --- p.xv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main contributions --- p.4 / Chapter 1.2 --- Overview --- p.4 / Chapter 2 --- Related Work --- p.7 / Chapter 2.1 --- Point cloud processing --- p.7 / Chapter 2.2 --- Model repairing --- p.9 / Chapter 2.3 --- Deformation and reconstruction --- p.10 / Chapter 3 --- Iterative Consolidation on Un-orientated Point Clouds --- p.11 / Chapter 3.1 --- Algorithm overview --- p.12 / Chapter 3.2 --- Down-sampling and outliers removal --- p.14 / Chapter 3.2.1 --- Normal estimation --- p.14 / Chapter 3.2.2 --- Down-sampling --- p.15 / Chapter 3.2.3 --- Particle noise removal --- p.17 / Chapter 3.3 --- APSS based repulsion --- p.19 / Chapter 3.4 --- Refinement --- p.22 / Chapter 3.4.1 --- Adaptive up-sampling --- p.22 / Chapter 3.4.2 --- Selection of up-sampled points --- p.23 / Chapter 3.4.3 --- Sample noise removal --- p.23 / Chapter 3.5 --- Set constraints to sample points --- p.24 / Chapter 4 --- Shape Modeling by Point Set --- p.27 / Chapter 4.1 --- Principle of deformation --- p.27 / Chapter 4.2 --- Selection --- p.29 / Chapter 4.3 --- Stretching and compressing --- p.30 / Chapter 4.4 --- Bending and twisting --- p.30 / Chapter 4.5 --- Inserting points --- p.30 / Chapter 5 --- Results and Discussion --- p.37 / Chapter 5.1 --- Program environment --- p.37 / Chapter 5.2 --- Results of iterative consolidation on un-orientated points --- p.37 / Chapter 5.3 --- Effect of our de-noising based on up-sampled points --- p.44 / Chapter 6 --- Conclusions --- p.49 / Chapter 6.1 --- Advantages --- p.49 / Chapter 6.2 --- Factors affecting our algorithm --- p.50 / Chapter 6.3 --- Possible future works --- p.51 / Chapter 6.3.1 --- Improve on the quality of results --- p.51 / Chapter 6.3.2 --- Reduce user input --- p.52 / Chapter 6.3.3 --- Multi-thread computation --- p.52 / Chapter A --- Finding Neighbors --- p.53 / Chapter A.1 --- k-d Tree --- p.53 / Chapter A.2 --- Octree --- p.54 / Chapter A.3 --- Minimum spanning tree --- p.55 / Chapter B --- Principle Component Analysis --- p.57 / Chapter B.1 --- Principle component analysis --- p.57 / Chapter C --- UI of the program --- p.59 / Chapter C.1 --- User Interface --- p.59 / Chapter D --- Publications --- p.61 / Bibliography --- p.63

Iterative solutions of the Boltzmann transport equation are computationally intensive. Spatial multigrid methods have led to efficient iterative algorithms for solving a variety of partial differential equations; thus, it is natural to explore their application to transport equations. Manteuffel et al. conducted such an exploration in one spatial dimension, using two-cell inversions as the relaxation or smoothing operation, and reported excellent results. In this dissertation we extensively test Manteuffel??s one-dimensional method and our modified versions thereof. We demonstrate that the performance of such spatial multigrid methods can degrade significantly given strong heterogeneities. We also extend Manteuffel??s basic approach to two-dimensional problems, employing four-cell inversions for the relaxation operation. We find that for uniform homogeneous problems the two-dimensional multigrid method is not as rapidly convergent as the one-dimensional method. For strongly heterogeneous problems the performance of the two-dimensional method is much like that of the one-dimensional method, which means it can be slow to converge. We conclude that this approach to spatial multigrid produces a method that converges rapidly for many problems but not for others. That is, this spatial multigrid method is not unconditionally rapidly convergent. However, our analysis of the distribution of eigenvalues of the iteration operators indicates that this spatial multigrid method may work very well as a preconditioner within a Krylov iteration algorithm, because its eigenvalues tend to be relatively well clustered. Further exploration of this promising result appears to be a fruitful area of further research.

Iterative solutions of the Boltzmann transport equation are computationally intensive. Spatial multigrid methods have led to efficient iterative algorithms for solving a variety of partial differential equations; thus, it is natural to explore their application to transport equations. Manteuffel et al. conducted such an exploration in one spatial dimension, using two-cell inversions as the relaxation or smoothing operation, and reported excellent results. In this dissertation we extensively test Manteuffel??s one-dimensional method and our modified versions thereof. We demonstrate that the performance of such spatial multigrid methods can degrade significantly given strong heterogeneities. We also extend Manteuffel??s basic approach to two-dimensional problems, employing four-cell inversions for the relaxation operation. We find that for uniform homogeneous problems the two-dimensional multigrid method is not as rapidly convergent as the one-dimensional method. For strongly heterogeneous problems the performance of the two-dimensional method is much like that of the one-dimensional method, which means it can be slow to converge. We conclude that this approach to spatial multigrid produces a method that converges rapidly for many problems but not for others. That is, this spatial multigrid method is not unconditionally rapidly convergent. However, our analysis of the distribution of eigenvalues of the iteration operators indicates that this spatial multigrid method may work very well as a preconditioner within a Krylov iteration algorithm, because its eigenvalues tend to be relatively well clustered. Further exploration of this promising result appears to be a fruitful area of further research.

Dissertation (Ph.D.)--Auburn University, 2008. / Abstract. Includes bibliographic references (p.73-80).

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: Newton; globalized; inexact Newton. Includes bibliographical references (p. 61).

We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods. / text

published_or_final_version / Mathematics / Master / Master of Philosophy