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.

We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to 0. We provide an alternate proof of the Combinatorial Riemann Mapping Theorem using circle packings (although this has been done before). We provide a new definition of conformal for subdivision rules of unbounded valence, show that the subdivision rules for the Borromean rings complement are conformal and show that barycentric subdivision is almost conformal. Finally, we show that subdivision rules can be degenerate on a dense set, while still having convergent circle packings.

La Craie, dépôt caractéristique de l'Europe du Nord durant le Crétacé supérieur, est un sédiment original dans l'histoire de la Terre, qui reste relativement mal compris. Cette étude vise à mieux établir la sédimentologie et la stratigraphie de la Craie du Bassin de Paris. Nous proposons un modèle de faciès de la Craie, depuis des environnements très proximaux, de shoreface, jusqu'à des dépôts distaux situés sous la limite d'action des vagues de tempêtes. Ce modèle et les données de subsurface sont utilisés pour réaliser des corrélations à haute-résolution à l'échelle du Bassin de Paris, en appliquant les méthodes de la stratigraphie séquentielle. Ces corrélations permettent de contraindre la géométrie 3D et la paléogéographie du Bassin de Paris au Crétacé supérieur. Ceci permet d'appréhender les différents paramètres (tectonique, eustatisme) qui contrôlent la sédimentation de la Craie. En particulier, nous montrons une réorganisation importante des contraintes intraplaques au Turonien supérieur depuis des contraintes orientées Est-Ouest vers un régime compressif globalement orienté Nord-Sud. Ce régime en compression, bien connu en Europe centrale et interprété comme la marque du début du cycle alpin, n'était jusqu'à présent pas reconnu à l'ouest du Massif Londres-Brabant. De même, cette étude apporte des éléments de contrainte pour la compréhension des variations eustatiques durant le Crétacé supérieur. Enfin, nous mettons en évidence, l'existence d'une circulation océanique, active à partir du Coniacien, associée à un contexte d'upwelling en Europe du Nord. À partir d'une confrontation entre la répartition mondiale de la craie et les données de prédiction des upwellings, nous avançons l'hypothèse que la présence de ce sédiment particulier sur des mers épicontinentales est directement lié à des dynamiques d'upwelling et à la paléocéanographie du Crétacé supérieur.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.

The linear elastodynamic two-dimensional anti-plane stress problem, where deformations occur in only one direction is considered for one sided non-planar faults. Fault dynamics are modeled using purely velocity dependent friction laws, and applied on boundaries with complex geometry. Summation-by-parts operators and energy estimates are used to couple a high-order finite difference method with an unstructured finite volume method. The unstructured finite volume method is used near the fault and the high-order finite difference method further away from the fault where no complex geometry is present. Boundary conditions are imposed weakly on characteristic form using the simultaneous approximation term technique, allowing explicit time integration to be used. Numerical computations are performed to verify the accuracy and time stability, of the method.

Various models featuring horizontal wells with multiple induced fractures have been proposed to characterize flow behavior over time in tight gas and shale gas systems. Currently, there is little consensus regarding the effects of non-ideal fracture geometries and coupled primary-secondary fracture interactions on reservoir performance in these unconventional gas reservoirs. This thesis provides a grid construction tool to generate high-resolution unstructured meshes using Voronoi grids, which provides the flexibility required to accurately represent complex geologic domains and fractures in three dimensions. Using these Voronoi grids, the interaction between propped hydraulic fractures and secondary "stress-release" fractures were evaluated. Additionally, various primary fracture configurations were examined, where the fractures may be non-planar or non-orthogonal. For this study, a numerical model was developed to assess the potential performance of tight gas and shale gas reservoirs. These simulations utilized up to a half-million grid-blocks and consider a period of up to 3,000 years in some cases. The aim is to provide very high-definition reference numerical solutions that will exhibit virtually all flow regimes we can expect in these unconventional gas reservoirs. The simulation results are analyzed to identify production signatures and flow regimes using diagnostic plots, and these interpretations are confirmed using pressure maps where useful. The coupled primary-secondary fracture systems with the largest fracture surface areas are shown to give the highest production in the traditional "linear flow" regime (which occurs for very high conductivity vertical fracture cases). The non-ideal hydraulic fracture geometries are shown to yield progressively lower production as the angularity of these fractures increases. Hence, to design optimum fracture completions, we should endeavor to keep the fractures as orthogonal to the horizontal well as possible. This work expands the current understanding of flow behavior in fractured tight-gas and shale-gas systems and may be used to optimize fracture and completion design, to validate analytical models and to facilitate more accurate reserves estimation.

Flattened Brazilian disc and modified ring test methods are attractive methods being simpler compared to the other mode I fracture toughness testing methods on rock cores. The aim of this study is to improve these simple methods to yield fracture toughness values that are close to the ones determined by the suggested methods. ABAQUS finite element program was used to determine stress intensity factors of models with various dimensions. Comparing fracture toughness to the results obtained by semicircular bending method tests (0.94 MPa&amp / #8730 / m for andesite and 0.56 MPa&amp / #8730 / m for marble) and the cracked chevron notched Brazilian disc method tests (1.45 MPa&amp / #8730 / m for andesite and 1.08 MPa&amp / #8730 / m for marble), proper geometrical parameters were investigated by changing diameter, central-hole diameter, and loading angle of Ankara andesite and Afyon marble specimens. Semicircular bending method results were lower than the cracked chevron notched Brazilian disc method results. With flattened Brazilian disc method, the closest results (1.45 MPa&amp / #8730 / m for andesite and 1.12 MPa&amp / #8730 / m for marble) to the suggested method was obtained by 54 mm diameter discs with loading angles between 32.5&deg / and 38.0&deg / and with thicknesses between 19 mm and 34 mm. With modified ring test on andesite, the closest results to the suggested method was obtained by 75 mm diameter discs with 8 mm central-hole diameter and 25&deg / loading angle (1.47 MPa&amp / #8730 / m for andesite and 1.07 MPa&amp / #8730 / m for marble), and with 14 mm central-hole diameter and 16&deg / loading angle (1.50 MPa&amp / #8730 / m for andesite and 1.05 MPa&amp / #8730 / m for marble).

The main objective of this research is to design, model and implement several antenna geometries using electromagnetic band gap (EBG) material and a defected ground plane. Several antenna applications are addressed with the aim of improving performance, particularly the mutual coupling between the elements. The EBG structures have the unique capability to prevent or assist the propagation of electromagnetic waves in a specific band of frequencies, and have been incorporated here in antenna structures to improve patterns and reduce mutual coupling in multielement arrays. A neutralization technique and defected ground plane structures have also been investigated as alternative approaches, and may be more practical in real applications. A new Uni-planar Compact EBG (UC-EBG) formed from a compact unit cell was presented, giving a stop band in the 2.4 GHz WLAN range. Dual band forms of the neutralization and defected ground plane techniques have also been developed and measured. The recorded results for all antenna configurations show good improvement in terms of the mutual coupling effect. The MIMO antenna performance with EBG, neutralization and defected ground of several wireless communication applications were analysed and evaluated. The correlation coefficient, total active reflection coefficient (TARC), channel capacity and capacity loss of the array antenna were computed and the results compared to measurements with good agreement. In addition, a computational method combining Genetic Algorithm (GA) with surface meshing code for the analysis of a 2×2 antenna arrays on EBG was developed. Here the impedance matrix resulting from the meshing analysis is manipulated by the GA process in order to find the optimal antenna and EBG operated at 2.4 GHz with the goal of targeting a specific fitness function. Furthermore, an investigation of GA on 2×2 printed slot on DGS was also done.

The work developed in this thesis focusses on the electrical activity of the heart, from the modeling of the action potential originating from cardiac cells and propagating through the heart, as well as its electrical manifestation at the body surface. The study is divided in two main parts: modeling the action potential, and numerical simulations. For modeling the action potential a dimensional and asymptotic analysis is done. The key advance in this part of the work is that this analysis gives the steps to reliably control the action potential. It allows predicting the time/space scales and speed of any action potential that is to say the shape of the action potential and its propagation. This can be done as the explicit relations on all the physiological constants are defined precisely. This method facilitates the integrative modeling of a complete human heart with tissue-specific ionic models. It even proves that using a single model for the cardiac action potential is enough in many situations. For efficient numerical simulations, a numerical method for solving the heart-torso coupling problem is explored according to a level set description of the domains. This is done in the perspective of using directly medical images for building computational domains. A finite element method is then developed to manage meshes not adapted to internal interfaces. Finally, an anisotropic adaptive remeshing methods for unstructured finite element meshes is used to efficiently capture propagating action potentials within complex, realistic two dimensional geometries.