Thèse : Mécanique : Université, Faculté des sciences de Paris : 1841. / Titre provenant de l'écran-titre.

Circles, parabolas, ellipses and hyperbolas are conic sections and have many unique properties. The properties of the tangents to conic sections prove quite interesting. Dandelin spheres are tangent to ellipses inside a cone and support the geometric definition of an ellipse. Tangent lines to parabolas, ellipses and hyperbolas in the form of families of folds are shown to create conic sections in unique ways. The equations of these tangent lines to conic sections and their equations can be found without using calculus. The equations of the tangent lines are also used to prove the bisection theorem for all conic sections and prove uniqueness for the bisection theorem in connection to conic sections. / text

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Neste trabalho, consideramos uma nova parametrização para o problema de empacotar a maior quantidade possível de círculos idênticos uma região elíptica dada. Apresentamos algoritmos com propriedades de convergência global e algumas estratégias heurísticas. Ilustramos com experimentos numéricos extensivos cada uma das estratégias utilizadas / In this work we consider a new parametrization for the problem of packing the maximum number of identical circles within a given elliptical region. We present algorithms with global convergence properties and some heuristic strategies. We illustrate each described strategy with extensive numerical experiments

Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:36:54Z No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:48:24Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) / Made available in DSpace on 2015-11-27T11:48:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) Previous issue date: 2014-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study some applications of the Poncelet's Theorem for teaching geometry. One of our main motivations for this work is that in some the high school leved math courses the study of geometry is slightly used and in certain circunstances the theorems are not demonstrated to the knowledge of the theories discussed. Finally, a list of exercises is proposed. / Neste trabalho estudaremos algumas aplicações do Teorema de Poncelet à geometria do Ensino Médio. Uma das nossas principais motivações é que nos cursos de Matemática a nível de Ensino Médio a Geometria é pouco utilizada e em algumas circunstâncias os teoremas não são demonstrados para o conhecimento das teorias abordadas. Finalmente, uma lista de exercícios é proposta.

Neste trabalho, consideramos uma nova parametrização para o problema de empacotar a maior quantidade possível de círculos idênticos uma região elíptica dada. Apresentamos algoritmos com propriedades de convergência global e algumas estratégias heurísticas. Ilustramos com experimentos numéricos extensivos cada uma das estratégias utilizadas / In this work we consider a new parametrization for the problem of packing the maximum number of identical circles within a given elliptical region. We present algorithms with global convergence properties and some heuristic strategies. We illustrate each described strategy with extensive numerical experiments

A teoria do limite de similaridade é uma teoria central para o entendimento da estruturação das comunidades ecológicas, e prevê que a coexistência de duas espécies de forma estável somente é possível caso exista um limite de semelhança entre elas. Nesse sentido, é esperado que ocorra partilha de recursos entre espécies simpátricas aparentadas como Podocnemis unifilis e Podocnemis expansa, dois quelônios amplamente distribuídos e de grande importância econômica e cultural na região amazônica. Assim, o objetivo deste estudo foi determinar os padrões de consumo de duas espécies simpátricas de quelônios, P. unifilis e P. expansa, além de verificar possíveis interações tróficas que se estabeleçam entre elas, considerando suas possíveis variações sexuais, no rio Javaés, Estado do Tocantins, Brasil. Desta forma, foram feitas análises dos conteúdos estomacais e análises isotópicas das unhas de indivíduos dessas espécies visando a determinação de suas amplitudes e sobreposições de nicho alimentar e isotópico. As sobreposições de nicho alimentar foram comparadas às sobreposições de comunidade idealizadas sem competição, por meio de modelos nulos. As sobreposições de nicho isotópico foram calculadas através de elipses bayesianas. As espécies apresentaram baixos valores de amplitude de nicho independente da medida. Entretanto, apresentaram alta sobreposição de nicho alimentar e nenhuma sobreposição de nicho isotópico. Amplitudes foram sempre reduzidas e sobreposições sempre elevadas entre os sexos. As diferenças entre as sobreposições de nicho das espécies medidas a partir das duas metodologias se relacionaram a importância de outras dimensões além da alimentar para o nicho isotópico. Os padrões de uso de recursos observados indicam que competição por alimento não está sendo relevante para a coocorrência das espécies no sistema estudado, possivelmente devido à altas disponibilidades dos recursos alimentares utilizados por P. unifilis e P. expansa. / The limiting similarity theory is a central theory for the comprehension of the structure of ecological communities, and predicts that the stable coexistence of two species is possible only if there is a limit of similarity between them. Therefore, it is expected to occur resource partitioning among sympatric related species as Podocnemis unifilis and Podocnemis expansa, two freshwater turtles widely distributed and of great economic and cultural importance in the Amazon region. The objective of this study was to determine the consumption patterns of two sympatric species of freshwater turtles, P. unifilis and P. expansa, and to identify possible trophic interactions to be established between them, considering its possible sexual variations, in the Javaés River, State of Tocantins, Brazil. Thus, were made analyzes of stomach content and isotopic analyzes of claws from individuals of these species in order to determine their amplitudes and dietary overlaps of food niche and isotopic niche. The food niche overlaps were compared with overlaps of idealized communities without competition, through null models. The isotopic niche overlaps were calculated using bayesian ellipses. The species had low niche amplitude values independent of the measure. However, the species showed high overlap of food niche and no isotopic niche overlap. Amplitudes were always reduced and overlap always high between the sexes. Differences between the niche overlaps of the species measures due the two methodologies were related to the importance of other dimensions beyond that represented by feeding to the isotopic niche. The observed patterns of resources usage indicate that competition for food is not being relevant to the co-occurrence of these species in the system studied, possibly due to the high availability of food resources used by P. unifilis and P. expansa.

A teoria do limite de similaridade é uma teoria central para o entendimento da estruturação das comunidades ecológicas, e prevê que a coexistência de duas espécies de forma estável somente é possível caso exista um limite de semelhança entre elas. Nesse sentido, é esperado que ocorra partilha de recursos entre espécies simpátricas aparentadas como Podocnemis unifilis e Podocnemis expansa, dois quelônios amplamente distribuídos e de grande importância econômica e cultural na região amazônica. Assim, o objetivo deste estudo foi determinar os padrões de consumo de duas espécies simpátricas de quelônios, P. unifilis e P. expansa, além de verificar possíveis interações tróficas que se estabeleçam entre elas, considerando suas possíveis variações sexuais, no rio Javaés, Estado do Tocantins, Brasil. Desta forma, foram feitas análises dos conteúdos estomacais e análises isotópicas das unhas de indivíduos dessas espécies visando a determinação de suas amplitudes e sobreposições de nicho alimentar e isotópico. As sobreposições de nicho alimentar foram comparadas às sobreposições de comunidade idealizadas sem competição, por meio de modelos nulos. As sobreposições de nicho isotópico foram calculadas através de elipses bayesianas. As espécies apresentaram baixos valores de amplitude de nicho independente da medida. Entretanto, apresentaram alta sobreposição de nicho alimentar e nenhuma sobreposição de nicho isotópico. Amplitudes foram sempre reduzidas e sobreposições sempre elevadas entre os sexos. As diferenças entre as sobreposições de nicho das espécies medidas a partir das duas metodologias se relacionaram a importância de outras dimensões além da alimentar para o nicho isotópico. Os padrões de uso de recursos observados indicam que competição por alimento não está sendo relevante para a coocorrência das espécies no sistema estudado, possivelmente devido à altas disponibilidades dos recursos alimentares utilizados por P. unifilis e P. expansa. / The limiting similarity theory is a central theory for the comprehension of the structure of ecological communities, and predicts that the stable coexistence of two species is possible only if there is a limit of similarity between them. Therefore, it is expected to occur resource partitioning among sympatric related species as Podocnemis unifilis and Podocnemis expansa, two freshwater turtles widely distributed and of great economic and cultural importance in the Amazon region. The objective of this study was to determine the consumption patterns of two sympatric species of freshwater turtles, P. unifilis and P. expansa, and to identify possible trophic interactions to be established between them, considering its possible sexual variations, in the Javaés River, State of Tocantins, Brazil. Thus, were made analyzes of stomach content and isotopic analyzes of claws from individuals of these species in order to determine their amplitudes and dietary overlaps of food niche and isotopic niche. The food niche overlaps were compared with overlaps of idealized communities without competition, through null models. The isotopic niche overlaps were calculated using bayesian ellipses. The species had low niche amplitude values independent of the measure. However, the species showed high overlap of food niche and no isotopic niche overlap. Amplitudes were always reduced and overlap always high between the sexes. Differences between the niche overlaps of the species measures due the two methodologies were related to the importance of other dimensions beyond that represented by feeding to the isotopic niche. The observed patterns of resources usage indicate that competition for food is not being relevant to the co-occurrence of these species in the system studied, possibly due to the high availability of food resources used by P. unifilis and P. expansa.

The use of fiber-reinforced polymer composites formed via injection molding is of increasing interest due to their superior mechanical properties as compared to those of the polymer matrix alone. These mechanical properties, however, are strongly dependent on the fiber length and orientation distributions within a molded part. As such, there is a need to understand and model the orientation evolution of chopped fibers in flow in order to accurately simulate the final fiber orientation distribution within injection molded parts. As a result of this, accurate and reliable experimental measurement of fiber orientation is needed. Within this research, the application and validity of the Method of Ellipses for determining the orientation of long, semi-flexible glass fibers within injection molded composites has been investigated. A fiber suspension with an average length of approximately 3.9 mm was the focus of this study and assumed to be representative of commercial distributions. A novel method to quantify fiber curvature was developed and utilized to show that flexibility in center-gated disc and the end-gated plaque samples was minimal on average for the selected fiber length distribution. Thus, it was determined that the Method of Ellipses was applicable when utilized to obtain reliable orientation data for the selected long glass fiber suspension and within the chosen geometries that exhibit 1-, 2-, and 3-dimensional velocity fields. However, a modified image analysis width was found to be necessary in regions of highly aligned fibers, due to the increase in ellipse size and the need to reduce the number of partial objects and thus minimize error. This allowed for a direct comparison of the experimental orientation behavior of short and long glass fibers within the center-gated disc and the end-gated plaque, as well as the effect of the orientation distributions on the global modulus of the part. / Ph. D.

Injection molded short fiber reinforced composites have generated commercial interest in the manufacturing of lightweight parts used in semi-structural applications. Predicting these materials’ fiber orientation with quantitative accuracy is crucial for technological advancement, but the task is difficult because of the effect of inter-particle interactions at high concentrations of fiber found in parts of commercial interest. A complete sample preparation procedure was developed to obtain optical micrographs with optimal definition of elliptical and non-elliptical footprint borders. Two novel aspects in this procedure were the use of tridimensional markers to identify specific locations for analysis and the use of controlled-etching to produce small shadows where fibers recede into the matrix. These images were used to measure fiber orientation with a customized image analysis tool. This tool contains several modifications that we introduced in the method of ellipses which allow us to determine tridimensional fiber orientation and to obtain measurements in regions with fast changes in orientation. The tool uses the location of the shadow to eliminate the ambiguity problem in orientation and characterizes non-elliptical footprints to obtain the orientation in small sampling areas. Cavitywise measurements in two thin center-gated disks showed the existence of an asymmetric profile of orientation at the gate and an orientation profile that washed out gradually at the entry region until disappearing at about 32 gap widths. This data was used to assess the prediction of cavitywise orientation using a delay model for fiber orientation with model parameters obtained from rheometrical experiments. Model predictions combining slip correction and experimentally determined orientation at the gate are in agreement with experimental data for the core layers near the end-of-fill region. Radialwise measurements of orientation at the shell, transition and core layer, and microtextural description of the advancing front are included in this dissertation. The analysis and assessment of the radial evolution of fiber orientation and advancing front based on comparing the experimental data with simulation results are under ongoing investigation. / Ph. D.