Este trabalho visou a implementação, no Estado de Minas Gerais, de uma rede geodésica GPS. Após a construção dos marcos, os dados foram coletados, em diversas sessões, empregando receptores de dupla freqüência operados por equipes de profissionais do Departamento de Geodésia do IBGE. A seguir, estes dados foram processados utilizando o programa científico OMNI e ajustados em rede com o programa ADJUST. Descreve-se a organização e a escolha dos dados para processamento testando-se diversas alternativas: a consideração ou não das covariâncias entre diferentes vetores observados, a influência da transformação dos vetores do ITRF97 para o WGS84 e a eliminação de outliers nas coordenadas calculadas, além de avaliar a qualidade das coordenadas de estações já conhecidas e que serviram de controle. Foram calculadas as coordenadas finais de cada estação da Rede Geodésica por GPS do Estado de Minas Gerais, salientando que cabe ao IBGE a escolha do método que considere mais adequado e a publicação oficial dessas coordenadas. Espera-se ter contribuído para isso. / This work aims the implementation, in the State of Minas Gerais, of a GPS network. After the construction of the benchmarks, professionals of the Department of Geodesy of IBGE, in different sections to collect data, occupy them. Then, these data were processed by the scientific program OMNI and adjusted by the program ADJUST. The organization and the selection of data to process, testing different strategies, were described: the consideration or not of the co-variances between different observed vectors, the influence of the transformation of the vectors from ITRF97 to the WGS84 and the elimination of outliers, in the calculated coordinates; besides of the evaluation of the quality of the coordinates of know stations that were used as control. The final coordinates of each station of the Geodesic Network of the State of Minas Gerais were calculated, emphasizing that is a responsibility of the IBGE the choice of the method that it consider most adequate and the publication of the official values of these coordinates. We hope to have been contributed to this.

O objetivo do presente estudo é a procura de evidências da presença de modos GAM nas descargas do tokamak TCABR, em distintos regimes de operação. As descargas selecionadas foram classicadas segundo a maneira de obter a melhora no connamento do plasma. Nós zemos essa procura nas descargas ôhmicas com incremento espontâneo da densidade do plasma, em descargas onde o plasma foi perturbado externamente pela injeção de ondas de Alfvén e pela alteração do campo elétrico radial via eletrodo de bias. Por causa da natureza eletrostática da oscilação GAM, nas descargas selecionadas foi relevante a presença das sondas eletrostáticas (conhecidas também como sondas de Langmuir). As bobinas de Mirnov foram importantes para identicar as oscilaçes MHD. Diversos métodos de análise espectral e estatístico foram usados na análise dos sinais experimentais como ajuda para identicar os modos GAM. Os métodos usados foram: correlação, espectro de auto-potência, espectro de potência cruzado, coerência e densidade espectral em número de onda e frequência. Para as bobinas de Mirnov, só o espectro de autopot ência foi usado. Os resultados da análise realizada nas descargas com crescimento espontâneo da densidade e nas descargas aquecidas com ondas de Alfvén, não mostram nenhuma presença de GAMs. Nessas descargas somente ocorreu um pequeno incremento na correlação que foi causado pela atividade MHD. Para as descargas com bias, a análise mostra a presença de um modo de f 40KHz, modo que não se observa nas bobinas de Mirnov e que tem simetria poloidal e toroidal. / The goal of the present study is to search for evidences of the presence of GAM modes in plasmas discharges of the TCABR tokamak at dierent operational regimes. The selected discharges were classied according to the way used to obtain plasma improvement of connement. We perform this search in pure ohmic discharges with a spontaneous increment of the plasma density and in discharges where the plasma was externally perturbed by the injection of Alfvén waves and by electrostatic edge biasing. Given the electrostatic nature of the GAM oscillation, in the selected discharges were relevant the presence of electrostatic probes (also known as Langmuir probes). The signals from Mirnov coils was important too, for identify the MHD oscillations. Several statistical and spectral methods were used to analyze the experimental signals in order to helps the identication of the GAM modes, correlation, auto-power spectra, cross-power spectra, coherence and spectral density in wave number and frequency (S(k; f)). For the Mirnov coil just auto-power spectra was used. The results of the analysis performed on the discharges with spontaneous increase of density and for those with Alfvén heating did not show any presence of GAMs. There was just an few increment of the correlation but it was due to the MHD activity. For the discharges with edge biasing, the analysis shows the presence of a f 40kHz mode that was not present in the Mirnov coil and that has toroidal and poloidal symmetry.

Propõe-se neste trabalho a determinação dos padrões de corte em estruturas de membrana por meio de linhas geodésicas, sendo as membranas obrigatoriamente discretizadas em facetas triangulares (elementos finitos de membrana triangulares). Com base em procedimentos geometricamente simples, formulou-se o caminhamento das linhas geodésicas sobre malhas de facetas triangulares, indicando-se um vértice inicial, uma direção inicial de busca e um vértice final (vértice que se quer alcançar). Contudo, na grande maioria dos casos, o vértice de busca não é alcançado em uma primeira tentativa, tendo-se que introduzir correções para a direção inicial. Depois de alcançado o vértice de busca, tem-se uma malha composta por novas facetas triangulares e outras quadrangulares que devem ser reformuladas, a fim de se ter uma malha formada apenas por triângulos. Por conseqüência das linhas geodésicas traçadas na malha, deve-se proceder da planificação das faixas encontradas; desta forma, necessita-se transferir/transformar as tensões das facetas originais para as facetas resultantes do corte por linhas geodésicas. Em seguida, faz-se a planificação das faixas determinadas, onde se podem comparar faixas cortadas a partir das arestas das facetas com aquelas resultantes do traçado das linhas geodésicas. / This work proposes the determination of the cutting patterns in membrane structures with geodesic lines, being the membranes obligatorily divided in triangular facets (triangular finite elements of membrane). For this, basing on procedures geometrically simple, the progress of the geodesic lines was formulated in meshes of triangular facets, being indicated an initial vertex, an initial direction of search and a final vertex (vertex that one want to reach). However, in the great majority of the cases the search vertex is not reached in a first attempt, so we need to introduce corrections for the initial direction. After having reached the search vertex, a mesh is had composed by new triangular facets and other square ones that should be reformulated, with the purpose to have a mesh just formed by triangle. For consequence of the geodesic lines drawn in the mesh, it should be come from the planning of the found strips, for this it is needed to transfer (to transform) the stresses of the original facets for the resulting facets of the cut for geodesic lines. Soon afterwards is done to the planning of the certain strips, to compare cut strips on the edges of the facets with resulting strips of the geodesic lines

Estudamos exemplos de métricas Finsler simétricas e não-simétricas em S^n, CP^n e HP^n com uma quantidade finita de geodésicas fechadas ou com uma quantidade pequena de geodésicas fechadas \"curtas\". São os chamados exemplos de Katok. Usamos como referência o artigo \"Geometry of the Katok examples\" de Wolfgang Ziller. Verificamos que existem métricas Finsler cujo número de geodésicas fechadas é 2n (no caso de S^ e S^), n(n+1) (no caso de CP^n) e 2n(n+1) (no caso de CP^n). Tais exemplos são construídos numa vizinhança qualquer da métrica Riemanniana canônica dessas variedades. / We study examples of symmetric and non-symmetric Finsler metrics on S^n, CP^n and HP^n with a finite number of closed geodesics or with a small number of \"short\" closed geodesics. These are the well known Katok\'s examples. We use Ziller\'s article Geometry of the Katok examples. We exhibit Finsler metrics whose number of closed geodesics is 2n (in the case of S^ and S^), n(n+1) (in the case of CP^n) and 2n(n+1) (in the case of HP^n). Such examples are found in any neighborhood of the canonical Riemannian metric on these manifolds.

Materiais compósitos são conhecidos pela alta resistência mecânica e baixo peso, desempenho superior, resistência à corrosão e baixa densidade. A produção de um material composto possui vários processos com particularidades diferentes. O enrolamento filamentar (Filament Winding) é um processo no qual fibras de reforço contínuas são posicionadas de maneira precisa e de acordo com um padrão predeterminado para compor a forma do componente desejado. As fibras, submetidas à tração, são enroladas continuamente ao redor de um mandril que tem a forma do produto final, em geral utilizando equipamentos automáticos. No final do processo, após a cura da resina, o mandril é geralmente removido. Desta forma, é de fundamental importância que o projetista disponha de recursos computacionais adequados para o cálculo das trajetórias e sequenciamento de posicionamento das fibras. Esse trabalho tem como objetivo o desenvolvimento de procedimentos matemáticos para cálculo de trajetórias geodésicas no processo de \"Filament Winding\" e implementá-los em um ambiente computacional em linguagem de alto nível Java, considerando-se os casos de revestimento circunferencial, helicoidal e polar. São desenvolvidos dois estudos de caso: tubos cônicos e vasos de pressão, e os resultados apresentados e discutidos, validando os procedimentos e ambiente implementado. / Composite materials are well known by the high strength and low weight, superior performance, resistance to the corrosion and low density. The production of a composite material part involves some processes with different requirements. The filament winding process is an automated process in which continuous reinforcement fibers are lay down in prescribed paths on the surface of a mandrel, which is generally removed after the cure of the resin. In such a way, it is fundamental that the designer uses computational resources for the calculation of the paths and sequence of the fibers. In this work is developed the mathematical procedures for calculation of geodesic trajectories in the Filament Winding process and implements them in a computational environment in high level language Java, considering the circumferential, helical and polar strategies. Two case studies are developed successfully: conical pipes and pressure vessels, and the results presented and discussed, validating the procedures and implemented environment.

Radiation therapy (RT) is commonly used to treat patients with lung cancer. One of the limitations of RT is that irradiation of the surrounding healthy lung tissues during RT may cause damage to the lungs. Radiation-induced pulmonary toxicity may be mitigated by minimizing doses to high-function lung tissues, which we refer to as functional avoidance RT. Lung function can be computed by image registration of treatment planning four-dimensional computed tomography (4DCT), which we refer to as CT ventilation imaging. However, the accuracy of functional avoidance RT is limited by lung function imaging accuracy and artifacts in 4DCT. The goal of this dissertation is to improve the accuracy of functional avoidance RT by overcoming those two limitations. A common method for estimating lung ventilation uses image registration to align the peak exhale and inhale 3DCT images. This approach called the 2-phase local expansion ratio is limited because it assumes no out-of-phase lung ventilation and may underestimate local lung ventilation. Out-of-phase ventilation occurs when regions of the lung reach their maximum (minimum) local volume in a phase other than the peak of inhalation (end of exhalation). This dissertation presents a new method called the N-phase local expansion ratio for detecting and characterizing locations of the lung that experience out-of-phase ventilation. The N-phase LER measure uses all 4DCT phases instead of two peak phases to estimate lung ventilation. Results show that out-of-phase breathing was common in the lungs and that the spatial distribution of out-of-phase ventilation varied from subject to subject. On average, 49% of the out-of-phase regions were mislabeled as low-function by the 2-phase LER. 4DCT and Xenon-enhanced CT (Xe-CT) of four sheep were used to evaluate the accuracy of 2-phase LER and N-phase LER. Results show that the N-phase LER measure was more correlated with the Xe-CT than the 2-phase LER measure. These results suggest that it may be better to use all 4DCT phases instead of the two peak phases to estimate lung function. The accuracy of functional avoidance RT may also be improved by reducing the impact of artifacts in 4DCT. In this dissertation, we propose a a geodesic density regression (GDR) algorithm to correct artifacts in one breathing phase by using artifact-free data in corresponding regions of the other breathing phases. Local tissue density change associated with CT intensity change during respiration is accommodated in the GDR algorithm. Binary artifact masks are used to exclude regions of artifacts from the regression, i.e., the GDR algorithm only uses artifact-free data. The GDR algorithm estimates an artifact-free CT template image and its time flow through a respiratory cycle. Evaluation of the GDR algorithm was performed using both 2D CT time-series images with simulated known motion artifacts and treatment planning 4DCT with real motion artifacts. The 2D results show that there is no significant difference (p-value = 0.95) between GDR regression of artifact data using artifact masks and regression of artifact-free data. In contrast, significant errors (p-value = 0.005) were present in the estimated Jacobian images when artifact masks were not used. We also demonstrated the effectiveness of the GDR algorithm for removing real duplication, misalignment, and interpolation artifacts in 4DCT. Overall this dissertation proposes methods that have the potential to improve functional avoidance RT by accommodating out-of-phase ventilation, and removing motion artifacts in 4DCT using geodesic image regression.

Nesta tese demonstramos, entre outras coisas, a existência de innitas geodésicas fechadas em good orbifolds Riemannianos M/, onde é um grupo de isometrias virtualmente Abeliano. No caso particular onde é um produto semi-direto de um grupo nito por um grupo Abeliano, concluimos a existência de uma família de geodésicas fechadas com comprimentos tendendo a innito. / In this PhD theses we prove, among other things, the existence of innity many (geometric distinct) closed geodesics on good Riemannian compact orbifolds M/, where is a virtual abelian group of isometries. In the particular case where is a semi-direct product of a nite group with an abelian group, we also assure that there isa family of closed geodesics for which the lengths tend to innity.

This thesis is concerned with the well-posedness, dynamical properties and numerical treatment of the generalised Euler equations on the Bott-Virasoro group with respect to the general H[superscript]k metric , k[is greater than or equal to]2. The term “generalised Euler equations” is used to describe geodesic equations on Lie groups, which unifies many differential equations and has found many applications in such as hydrodynamics, medical imaging in the computational anatomy, and many other fields. The generalised Euler equations on the Bott-Virasoro group for k = 0, 1 are well-known and intensively studied— the Korteweg-de Vries equation for k = 0 and the Camassa-Holm equation for k = 1. Unlike these, the equations for k[is greater than or equal to]2, which we call the modified Camassa-Holm (mCH) equation, is not known to be integrable. This distinction motivates the study of the mCH equation. In this thesis, we derive the mCH equation and establish the short time existence of solutions, the well-posedness of the mCH equation, long time existence, the existence of the weak solutions, both on the circle S and [blackboard bold] R, and three conservation laws, show some quite interesting properties, for example, they do not lead to the blowup in finite time, unlike the Camassa-Holm equation. We then consider two numerical methods for the modified Camassa-Holm equation: the particle method and the box scheme. We prove the convergence result of the particle method. The numerical simulations indicate another interesting phenomenon: although mCH does not admit blowup in finite time, it admits solutions that blow up (which means their maximum value becomes infinity) at infinite time, which we call weak blowup. We study this novel phenomenon using the method of matched asymptotic expansion. A whole family of self-consistent blowup profiles is obtained. We propose a mechanism by which the actual profile is selected that is consistent with the simulations, but the mechanism is only partly supported by the analysis. We study the four particle systems for the mCH equation finding numerical evidence both for the non-integrability of the mCH equations and for the existence of the fourth integral. We also study the higher dimensional case and obtain the short time existence and well-posedness for the generalised Euler equation in the two dimension case.

[No abstract supplied with this thesis - The first page (of three) of the Introduction follows] ¶ This thesis is largely concerned with the changing representations of 'boundary' or 'ideal' points of a pseudo-Riemannian manifold -- and our primary interest is in the space-times of general relativity. In particular, we are interested in the following question: What assumptions about the 'nature' of 'portions' of a certain 'ideal boundary' construction (essentially the 'abstract boundary' of Scott and Szekeres (1994)) allow us to define precisely the topological type of these 'portions', i.e., to show that different representations of this ideal boundary, corresponding to different embeddings of the manifold into others, have corresponding 'portions' that are homeomorphic? ¶ Certain topological properties of these 'portions' are preserved, even allowing for quite unpleasant properties of the metric (Fama and Scott 1995). These results are given in Appendix D, since they are not used elsewhere and, as well as representing the main portion of work undertaken under the supervision of Scott, which deserves recognition, may serve as an interesting example of the relative ease with which certain simple results about the abstract boundary can be obtained. ¶ An answer to a more precisely formulated version of this question appears very diffcult in general. However, we can give a rather complete answer in certain cases, where we dictate certain 'generalised regularity' requirements for our embeddings, but make no demands on the precise functional form of our metrics apart from these. For example, we get a complete answer to our question for abstract boundary sets which do not 'wiggle about' too much -- i.e., they satisfy a certain Lipschitz condition -- and through which the metric can be extended in a manner which is not required to be differentiable (C[superscript1]), but is continuous and non--degenerate. We allow similar freedoms on the interior of the manifold, thereby bringing gravitational wave space-times within our sphere of discussion. In fact, in the course of developing these results in progressively greater generality, we get, almost 'free', certain abilities to begin looking at geodesic structure on quite general pseudo-Riemannian manifolds. ¶ It is possible to delineate most of this work cleanly into two major parts. Firstly, there are results which use classical geometric constructs and can be given for the original abstract boundary construction, which requires differentiability of both manifolds and metrics, and which we summarise below. The second -- and significantly longer -- part involves extensions of those constructs and results to more general metrics.

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