Esta dissertação traz ideias para a inserção de novos conteúdos na matemática escolar. Ela trata da exploração de geometrias não-euclidianas, através de dois ambientes de geometria dinâmica, o "Spherical Easel” e o "Disco de Poincaré". O primeiro é um software livre e o segundo foi desenvolvido utilizando-se o recurso de macro-construção do GeoGebra. Na concepção das atividades tratamos as idéias que correspondem ao mundo não-euclidiano fazendo comparações com aquelas que fazem parte da geometria euclidiana e para cada atividade há um comentário que explica a sua intenção de aprendizagem. É a partir de considerações teóricas sobre a natureza da geometria e sua evolução histórica, bem como sobre o processo de aprendizagem da geometria, que é feita a apresentação da proposta. / This dissertation brings ideas to the inclusion of new contents in school mathematics. They are related to the exploitation of non-Euclidean geometries through two dynamic geometry environments, the "Spherical Easel" and the "Poincaré Disk". The first one is a free software and the second one was developed using the GeoGebra macro-construction. In the design of the activities the approach of ideas that correspond to non-euclidian worlds was made through comparison with the euclidian world and for each activity there is a comment that explain its learning objective. The proposal is supported by theoretical considerations about the nature of geometry and its historical evolution, as well as about the geometry learning process.

Esta dissertação traz ideias para a inserção de novos conteúdos na matemática escolar. Ela trata da exploração de geometrias não-euclidianas, através de dois ambientes de geometria dinâmica, o "Spherical Easel” e o "Disco de Poincaré". O primeiro é um software livre e o segundo foi desenvolvido utilizando-se o recurso de macro-construção do GeoGebra. Na concepção das atividades tratamos as idéias que correspondem ao mundo não-euclidiano fazendo comparações com aquelas que fazem parte da geometria euclidiana e para cada atividade há um comentário que explica a sua intenção de aprendizagem. É a partir de considerações teóricas sobre a natureza da geometria e sua evolução histórica, bem como sobre o processo de aprendizagem da geometria, que é feita a apresentação da proposta. / This dissertation brings ideas to the inclusion of new contents in school mathematics. They are related to the exploitation of non-Euclidean geometries through two dynamic geometry environments, the "Spherical Easel" and the "Poincaré Disk". The first one is a free software and the second one was developed using the GeoGebra macro-construction. In the design of the activities the approach of ideas that correspond to non-euclidian worlds was made through comparison with the euclidian world and for each activity there is a comment that explain its learning objective. The proposal is supported by theoretical considerations about the nature of geometry and its historical evolution, as well as about the geometry learning process.

Esta dissertação traz ideias para a inserção de novos conteúdos na matemática escolar. Ela trata da exploração de geometrias não-euclidianas, através de dois ambientes de geometria dinâmica, o "Spherical Easel” e o "Disco de Poincaré". O primeiro é um software livre e o segundo foi desenvolvido utilizando-se o recurso de macro-construção do GeoGebra. Na concepção das atividades tratamos as idéias que correspondem ao mundo não-euclidiano fazendo comparações com aquelas que fazem parte da geometria euclidiana e para cada atividade há um comentário que explica a sua intenção de aprendizagem. É a partir de considerações teóricas sobre a natureza da geometria e sua evolução histórica, bem como sobre o processo de aprendizagem da geometria, que é feita a apresentação da proposta. / This dissertation brings ideas to the inclusion of new contents in school mathematics. They are related to the exploitation of non-Euclidean geometries through two dynamic geometry environments, the "Spherical Easel" and the "Poincaré Disk". The first one is a free software and the second one was developed using the GeoGebra macro-construction. In the design of the activities the approach of ideas that correspond to non-euclidian worlds was made through comparison with the euclidian world and for each activity there is a comment that explain its learning objective. The proposal is supported by theoretical considerations about the nature of geometry and its historical evolution, as well as about the geometry learning process.

Des milieux hétérogènes et désordonnés émergent dans plusieurs applications de la science et de l'ingénierie nucléaires, en particulier en ce qui concerne la propagation des neutrons et des photons. Les exemples sont très répandus et concernent par exemple la double hétérogénéité des éléments combustibles dans les réacteurs à lit de boulets ou l'évaluation de la probabilité de re-criticité suite aux arrangements aléatoires du combusitble résultant d'accidents graves. Dans cette thèse, nous étudierons le transport linéaire de particules dans des milieux aléatoires. Dans la première partie, nous nous concentrerons sur quelques modèles mathématiques qui peuvent être utilisés pour la description de matériaux aléatoires. Une attention particulière sera accordée aux tessellations stochastiques, où un domaine est partitionné en polyèdres convexes en échantillonnant des hyperplans aléatoires selon une probabilité donnée. Les inclusions stochastiques de sphères dans une matrice seront également brièvement introduites. Un code informatique sera développé afin de construire explicitement de telles géométries par des méthodes de Monte Carlo. Dans la deuxième partie, nous évaluerons ensuite les caractéristiques générales du transport de particules dans des milieux aléatoires. Pour ce faire, nous allons considérer quelques benchmarks assez simples pour permettre une compréhension approfondie des effets des géométries aléatoires sur les trajectoires de particules tout en conservant les propriétés clés du transport linéaire. Les calculs de transport seront réalisés en utilisant le code de transport de particules Monte Carlo Tripoli4, développé au SERMA. Les cas de modèles de désordre quenched et annealed seront considérés séparément. Dans le premier, un ensemble de géométries sera généré en utilisant notre code, et le problème de transport sera résolu pour chaque configuration: des moyennes d'ensemble seront alors prises pour les observables d'intérêt. Dans le second cas, un modèle de transport efficace capable de reproduire les effets du désordre dans une seule réalisation sera étudié. Les approximations des modèles annealed seront élucidées, et des améliorations significatives seront proposées. / Heterogeneous and disordered media emerges in several applications in nuclear science and engineering, especially in relation to neutron and photon propagation. Examples are widespread and concern for instance the double-heterogeneity of the fuel elements in pebble-bed reactors, or the assessment of re-criticality probability due to the random arrangement of fuel resulting from severe accidents. In this Thesis, we will investigate linear particle transport in random media. In the first part, we will focus on some mathematical models that can be used for the description of random media. Special emphasis will be given to stochastic tessellations, where a domain is partitioned into convex polyhedra by sampling random hyperplanes according to a given probability. Stochastic inclusions of spheres into a matrix will be also briefly introduced. A computer code will be developed in order to explicitly construct such geometries by Monte Carlo methods. In the second part, we will then assess the general features of particle transport within random media. For this purpose, we will consider some benchmark problems that are simple enough so as to allow for a thorough understanding of the effects of the random geometries on particle trajectories and yet retain the key properties of linear transport. Transport calculations will be realized by using the Monte Carlo particle transport code Tripoli4, developed at SERMA. The cases of quenched and annealed disorder models will be separately considered. In the former, an ensemble of geometries will be generated by using our computer code, and the transport problem will be solved for each configuration: ensemble averages will then be taken for the observables of interest. In the latter, effective transport model capable of reproducing the effects of disorder in a single realization will be investigated. The approximations of the annealed disorder models will be elucidated, and significant ameliorations will be proposed.

The permeability of rocks has a critical influence on their fluid transport response in critical geo-environmental applications, such as pollutant transport or underground storage of hazardous nuclear waste. In such processes, the materials microstructure may be altered as a result of various stimuli, thereby impacting the fluid transfer properties. Stress or strain state modifications are one of the main causes for such evolutions. To numerically address this concern, an integrated and automated numerical tool was developed and illustrated on subsets of microCT scans of a Vosges sandstone (i) to explore the links between the pore space properties and the corresponding macroscopic transfer properties, with (ii) an incorporation of the microstructural alterations associated with stress state variations by using a realistic image-based representation of the microstructural morphology. The ductile mechanical deformation behavior under high confining pressures at the scale of the microstructure, inducing pore closures by local plastifications, was modelled using finite elements simulations with a non-linear elastoplastic law, allowing to take into account the redistribution of local stresses. These simulations require robust discretization tools to capture the complex geometry of the porous network and the corresponding solid boundaries of the heterogeneous microstructural geometries. To achieve this, an integrated approach for the conformal discretization of complex implicit geometries based on signed distance fields was developed, producing high quality meshes from both imaging techniques and computational RVE generation methodologies. This conforming discretization approach was compared with an incompatible mode-based framework using a non conforming approach. This comparison highlighted the complementarity of both methods, the former capturing the effect of more detailed geometrical features, while the latter is more flexible as it allows using the same (non conforming) mesh for potentially variable geometries.The evolution of permeability was evaluated at different confining pressure levels using the Lattice-Bolzmann method. This uncoupled solid-fluid interaction made it possible to study the combined influence on the permeability, porosity and the pores size distribution of the pore space morphology and the solid skeleton constitutive law parameters during loading and unloading conditions. The results highlight the need to consider elastoplastic laws and heterogeneities in the rock model to simulate the ductile behavior of rocks at high confining pressures leading to significant permeability alterations under loading, and irreversible alterations under loading/unloading cycles induced by progressive pore closures.The proposed methodology is designed to be flexible thanks to the interfacing with 'classical' discretization approaches and can be easily readapted to other contexts given the block approach. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18800号 / 理博第4058号 / 新制||理||1584(附属図書館) / 31751 / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)教授 平原 和朗, 教授 澁谷 拓郎, 准教授 久家 慶子 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Die extensive Zunahme von lebendigem Wachstum am Beispiel der mathematischen Fibonacci-Folge ergibt räumliche Strukturen von eigentümlichen Stülpungen und Auffaltungen, die den universellen Gesetzmäßigkeiten des Kosmos gehorchen. Solche mathematisch-abstrakten Ideen wollte ich dreidimensional in Skulpturen umsetzen und versuchte erst vergeblich, mir die daraus enstehenden räumlichen Körper rein imaginär vorzustellen und zeichnerisch oder klassisch skulptural umzusetzen – doch erst als mir die Idee kam, entlang dieser Gesetzmäßigkeiten zu häkeln, gelang es.

No / Pressure variation during the coextrusion of two low density polyethylene melts was investigated. Melt streams were delivered to a die from two separate extruders to converge in a 30 degrees degrees geometry to form a two layer extrudate. Melt flow in the confluent region and die land to the die exit was observed through side windows of a visualisation cell. Stream velocity ratio was varied by control of extruder screw speeds. Layer thickness ratios producing wave type interfacial instability were quantified for each melt coextruded on itself and for the combined melts. Stream pressures and screw speeds were monitored and analysed. Wave type interfacial instability was present during the processing of the melts at specific, repeatable, stream layer ratios. Increased melt elasticity appeared to promote this type of instability. Analysis of process data indicates little correlation between perturbations in extruder screw speeds and stream pressures. The analysis did however show covariance between the individual stream pressure perturbations. Interestingly there was significant correlation even when interfacial instability was not present. We conclude that naturally occurring variation in extruder screw speeds do not perturb stream pressures and, more importantly, natural perturbations in stream pressures do not promote interfacial instability.

No / An investigation of the surface current distribution in a normal-mode helical antenna (NMHA) is reported. This enables precise prediction of the performance of NMHAs, since traditional wire-antenna simulations ignore important details, such as non-uniform and transverse current distributions. A moment-method formulation is developed, using two-dimensional basis functions to represent the total non-uniform surface current distribution over the surface of the wire of the helix. Piecewise-sinusoidal basis functions are employed in two normal directions, with an exact kernel formulation and application of Galerkin's solution method. The numerical solution of the singular integrals associated with self-impedance terms was computed with a very low relative error. The surface current distribution was computed for different helix geometries. It was found that the axially-directed component of the current distribution around the surface of the wire was highly non-uniform and that there was also a significant circumferential current flow due to inter-turn capacitance, both effects that are overlooked by standard filamentary current representations.

O presente trabalho apresenta um método de interação fluido estrutura chamado de fronteira virtual para modelagem de escoamentos sobre geometrias complexas. A principal característica do método é que a condição de contorno interna da superfície do corpo imerso é obtida usando uma função que calcula a força de campo das equações de momentum. Este método de cálculo da força de campo é conhecido como método direto. A principal vantagem do método da fronteira virtual é que se trabalha com duas malhas, uma cartesiana (também conhecida como euleriana) para o fluido e outra curvilínea (também conhecida como malha lagrangiana) para o objeto imerso. Como estas malhas são independentes uma da outra, os algoritmos de geração das malhas são simples em comparação com outros métodos de geração de malha, nos quais a esta precisa se adaptar ao corpo que se quer analisar. Nos métodos de body fitted, algoritmos complexos com custo computacional muito elevado são necessários para se trabalhar com geometrias complexas. Neste trabalho, o método de fronteira virtual é desenvolvido para trabalhar escoamentos compressíveis não viscosos em duas dimensões sobre geometrias complexas, e testado sobre um cilindro de seção circular e sobre uma série de aerofólios NACA da série 4. O regime de principal interesse é o regime transônico, em particular para velocidades abaixo da velocidade do som (Mach entre 0,8 e 1). No entanto, resultados para outros regimes de escoamento (subsônico incompressível, subsônico compressível, transônico e supersônico) também são mostrados. / This work presents a fluid-structure interaction method, known as virtual boundary method, developed for flow modeling, over complex geometries. The main characteristic of the method is that, the internal boundary condition at the surface are created using a function, that compute the body force from the momentum equations. This method is known as direct method. The virtual boundary method main advantage is the easy and quick mesh generation. Due the use two different grids, a Cartesian grid for the fluid and a curvilinear grid for the body that interact with the fluid. As these two grids are independent one of other, the grid generation algorithms are easier compared with other methods on CFD as the body fitted. Where the grid has to be adapted to the body of interest. The body fitted methods are implemented with complex algorithms, and high computational cost, especially when complex geometries are analyzed. In this work, the virtual boundary method are developed in order to work with in viscid compressible flow in two dimensions over complex geometries, tested over a cylinder and several NACA series 4 and critical airfoils. The regime of interest is the transonic, below the speed of sound, nevertheless results for several flow regimens (incompressible subsonic, compressible subsonic, transonic and supersonic) are also presented.