Stuttgart, Univ., Fakultät Mathematik, Diplomarb., 1997.

Jamming is a physical process which is both easy to describe and incredibly difficult to understand. One such difficulty is that mechanical treatments of jamming focus on pressure, force, stress, and strain, which are identically zero below jamming, making it hard to differentiate systems whcih which are near or far from the transition. Instead, I introduce a geometric framework based on the Voronoi tesselation which treats all of phase space on an equal footing. This work will show that the jamming transition can be seen entirely through the geometry of the local environment of particles encoded in the Voronoi tesselation, and it will build the framework for an as yet undefined field theory for jamming.

Fractured reservoirs are commonly simulated using the Dual Porosity model, but for many major fields, the model does not match field results. For these cases, it is necessary to perform a more complex simulation including either individual fractures or pseudofracture groups modeled in their own grid blocks. Discrete Fracture Modeling (DFN) is still a relatively new field, and most research on it up to this point has been done with Delaunay tessellations. This research investigates an alternative approach using Voronoi diagrams, yet applying the same DFN principles outlined in previous works. Through the careful positioning of node points, a grid of Voronoi polygons can be produced so that block boundaries fall along the fractures, allowing us to use the DFN simulation methods as proposed in the literature. Using Voronoi diagrams allows us to use far fewer polygons than the Delaunay approach, and also allows us to perfectly align flow so as to eliminate grid alignment errors that plagued previous static systems. The nature of the Voronoi polygon further allows us to simplify permeability calculations due to orthogonality and, by extension, is more accurate than the commonly used cornerpoint formulation for non-square grid blocks.

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 24, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Thesis advisor: Dr. Kannapan Palaniappan. Includes bibliographical references.

Thesis (M.S.)--Oregon State University, 2007. / Printout. Includes bibliographical references (leaves 70-74). Also available on the World Wide Web.

Dissertação (Mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. / Made available in DSpace on 2012-10-17T20:22:17Z (GMT). No. of bitstreams: 0Bitstream added on 2013-07-16T18:02:31Z : No. of bitstreams: 1 161179.pdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Esta dissertação apresenta um algoritmo incremental para geração do Diagrama de Voronoi interno a um contorno arbitrário convexo.

The objects studied in geoscience are often not man-made objects, but rather the spatial distribution of three-dimensional continuous geographical phenomena such as the salinity of a body of water, the humidity of the air or the percentage of gold in the rock (phenomena that tend to change over time). These are referred to as fields, and their modelling with geographical information systems is problematic because the structures of these systems are usually two dimensional and static. Raster structures (voxels or octrees) are the most popular solutions, but, as I argue in this thesis, they have several shortcomings for geoscientific fields. As an alternative to using rasters for representing and modelling three-dimensional fields, I propose using a new spatial model based the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT). I argue that constructing the VD/DT of the samples that were collected to study the field can be beneficial for extracting meaningful information from it. Firstly, the tessellation of space obtained with the VD gives a clear and consistent definition of neighbourhood for unconnected points in three dimensions, which is useful since geoscientific datasets often have highly anisotropic distributions. Secondly, the efficient and robust reconstruction of the field can be obtained with natural neighbour interpolation, which is entirely based on the properties of the VD. Thirdly, the tessellations of the VD and the DT make possible, and even optimise, several spatial analysis and visualisation operations. A further important consideration is that the VD/DT is locally modifiable (insertion, deletion and movement of points), which permits us to model the temporal dimension, and also to interactively explore a dataset, thus gaining insight by observing on the fly the consequences of manipulations and spatial analysis operations. In this thesis, the development of this new spatial model is from an algorithmic point of view, i.e. I describe in details algorithms to construct, manipulate, analyse and visualise fields represented with the VD/DT. A strong emphasis is put on the implementation of the spatial model, and, for this reason, the many degeneracies that arise in three-dimensional geometric computing are described and handled. A new data structure, the augmented quad-edge, is also presented. It permits us to store simultaneously both the VD and the DT, and helps in the analysis of fields. Finally, the usefulness of this Voronoi-based spatial model is demonstrated with a series of potential applications in geoscience.

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnologico / Made available in DSpace on 2016-01-08T20:51:00Z (GMT). No. of bitstreams: 1 103706.pdf: 3259262 bytes, checksum: 10c155fd5eec5abd7b49106708bbc4de (MD5) Previous issue date: 1996 / Neste trabalho é resolvido numericamente o modelo elíptico do problema da convecção natural em canais abertos, usando o método dos volumes finitos em coordenadas coincidentes com a fronteira. Para o tratamento das condições de contorno na entrada do canal, uma importante questão numérica quando o problema é formulado elipticamente, e proposta uma metodologia de cálculo, onde tanto a pressão como a velocidade são corrigidas durante o processo evolutivo de cálculo. Para a validação da metodologia de aplicação das condições de contorno mencionadas acima, são usados os diversos resultados experimentais e numéricos existentes na literatura para os canais formados por duas placas planas verticais. Finalmente, o problema de convecção natural em canais em forma de "L" é resolvido variando-se o número de Rayleigh e as dimensões geométricas.

In this work Voronoi diagrams which are drawn by the cellular automaton are discussed. The square and hexagon cellular automata were created and used for drawing Voronoi diagrams. As a result of using the created programs Voronoi diagrams, which are obtained in case of two and more dots, are observed. The following results of the research were achieved: § Voronoi diagram can be obtained by the cellular automaton. § Voronoi diagrams, which were obtained, are not precise due to different speed of movement in different directions. § In square - cell case the obtained diagrams depend on the chosen situation of the neighbors. § In hexagon - cell case the obtained Voronoi diagrams are more but not completely precise. The mathematic calculations are not being made while creating Voronoi diagrams by the cellular automaton.. The diagrams are obtained in short period of time. It is possible to watch the process of the diagram creation. A lot of computer's operation time is lost not during the calculation but for re-drawing the obtained image. This is the reason why it is necessary to optimize the image creating algorithm.

Orientador: Sérgio Augusto Cunha / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Educação Física / Made available in DSpace on 2018-08-17T12:23:18Z (GMT). No. of bitstreams: 1 Santana_JulianaExel_M.pdf: 6461488 bytes, checksum: 731aaed1e02fe448da4b39f4f7b8fb28 (MD5) Previous issue date: 2011 / Resumo: O desempenho de jogadores de futebol de elite durante uma partida é diretamente influenciado por fatores físicos, psicológicos, técnicos, táticos e entre outros. Um suporte científico capaz de buscar e aplicar metodologias que quantifiquem esses fatores é uma fonte importante de informações para que técnicos e treinadores tenham melhores condições de efetuar uma boa preparação da sua equipe. Dentro dos estudos cinemáticos no esporte, a videogrametria tem se mostrado uma ferramenta acurada para a obtenção da posição dos jogadores em função do tempo. Dentro dos aspectos táticos de um jogo de futebol, a forma como uma equipe divide o campo em áreas de responsabilidade e como essa distribuição se dá ao longo do jogo pode ser descrita através de técnicas matemáticas. Nesse sentido, o objetivo deste estudo será apresentar uma forma de representação da área de responsabilidade de jogadores de futebol durante partidas oficiais, através do Diagrama de Voronoi. Para tal, foram coletadas as imagens de 4 jogos de futebol. Os processos de segmentação das imagens e de rastreamento dos jogadores para a obtenção dos dados 2D em função do tempo foram realizados através do software DVideo®. Para as análises, foi aplicado a metodologia do Diagrama de Voronoi nas coordenadas 2D de 33 jogadores de uma mesma equipe, a cada instante de tempo, em cada jogo. Dado um conjunto de pontos no plano (que nesse caso, representam as posições dos jogadores em função do tempo), o Diagrama de Voronoi divide o plano em regiões de acordo com as distâncias entre os pontos desse conjunto, chamados Polígonos de Voronoi. As áreas dos polígonos foram calculadas. Essa ferramenta permite, através de uma representação por mapas de superfície, obter um resumo dos locais do campo contidos nos Polígonos de Voronoi associados a cada jogador, durante todo o jogo. As áreas de responsabilidade foram maiores para goleiros, laterais e atacantes, quando comparados aos zagueiros e volantes e meias.Para caracterizar a região de responsabilidade dos jogadores, foi utilizado o contorno topográfico correspondente às áreas do campo contidas nos Polígonos dos jogadores por no mínimo 60% do jogo. Os resultados obtidos para os jogos estudados mostram que o contorno que caracteriza a área de responsabilidade para os jogadores é uma boa ferramenta qualitativa e quantitativa, que representa a forma como os jogadores dividem a área do campo entre si. A utilização do Diagrama de Voronoi se mostrou uma técnica eficiente na determinação das áreas de responsabilidade dos jogadores. Técnicos e treinadores podem dessa maneira obter informações adicionais importantes para a criação de melhores estratégias de posicionamento da sua equipe para uma melhor cobertura do espaço do campo de futebol / Abstract: The performance of football elite players is directly influenced by physical, psychological, technical and tactical aspects. A scientific support capable of seek and apply methodologies to quantifying these factors is an important source of information to coaches improve their conditions to well prepare their teams. About football tactical aspects, the manner a team share the pitch in responsibility areas and how this distribution behaviours during the match can be described through mathematical techniques. Thus, the aim of this study is to show players' responsibility area during official matches using Voronoi Diagram (VD). To do so, we collected images of 4 football matches. To extract 2D players' coordinates during the entire match, images segmentation, tracking and 2D reconstruction were performed in DVideo® software. In the analysis, VD method was applied to players' 2D coordinates to all 33 players of a same team, at each instant of time and in the 4 matches. Given a set of points on plan (representing players positions as function of time), VD share the plan in regions according to distances between all points of the set, called Voronoi polygons (VP). Voronoi areas were calculated a determined as players' responsibility areas. This tool permits obtaining a summary of pitchlocations inside Voronoi polygons of each player, during the entire match, using hitmaps. To characterize responsibility areas, the contours of hitmaps corresponding to pitch areas inside VP by, at least, 60% of the match were performed. The results showed contours as an effective tool to qualitatively and quantitatively represent responsibility areas in a match. Besides, mathematical properties related to known geometric structures, as convex polygons, facilitate calculating areas. They showed be higher to goalkeepers, external defenders and forwards when compared to central defenders, defensive and offensive midfielders / Mestrado / Biodinamica do Movimento Humano / Mestre em Educação Física