After giving a description of the basic physical phenomena to be modelled, we begin by formulating a sharp-interface free-boundary model for the destruction of superconductivity by an applied magnetic field, under isothermal and anisothermal conditions, which takes the form of a vectorial Stefan model similar to the classical scalar Stefan model of solid/liquid phase transitions and identical in certain two-dimensional situations. This model is found sometimes to have instabilities similar to those of the classical Stefan model. We then describe the Ginzburg-Landau theory of superconductivity, in which the sharp interface is `smoothed out' by the introduction of an order parameter, representing the number density of superconducting electrons. By performing a formal asymptotic analysis of this model as various parameters in it tend to zero we find that the leading order solution does indeed satisfy the vectorial Stefan model. However, at the next order we find the emergence of terms analogous to those of `surface tension' and `kinetic undercooling' in the scalar Stefan model. Moreover, the `surface energy' of a normal/superconducting interface is found to take both positive and negative values, defining Type I and Type II superconductors respectively. We discuss the response of superconductors to external influences by considering the nucleation of superconductivity with decreasing magnetic field and with decreasing temperature respectively, and find there to be a pitchfork bifurcation to a superconducting state which is subcritical for Type I superconductors and supercritical for Type II superconductors. We also examine the effects of boundaries on the nucleation field, and describe in more detail the nature of the superconducting solution in Type II superconductors - the so-called `mixed state'. Finally, we present some open questions concerning both the modelling and analysis of superconductors.

Gas hydrates are a solid, ice-like mixture of water and low molecular weight hydrocarbons. They are found under the permafrost and to a far greater extent under the ocean, usually at water depths greater than 300m. Hydrates are a potential energy resource, a possible factor in climate change, and a geohazard. For these reasons, it is critical that gas hydrate deposits are quantitatively assessed so that their concentrations, locations and distributions may be established. Due to their ice-like nature, hydrates are electrically insulating. Consequently, a method which remotely detects changes in seafloor electrical conductivity, such as marine controlled source electromagnetics (CSEM), is a useful geophysical tool for marine gas hydrate exploration. Hydrates are geometrically complex structures. Advanced electromagnetic modelling and imaging techniques are crucial for proper survey design and data interpretation. I develop a method to model thin resistive structures in conductive host media which may be useful in building approximate geological models of gas hydrate deposits using arrangements of multiple, bent sheets. I also investigate the possibility of interpreting diffusive electromagnetic data using seismic imaging techniques. To be processed in this way, such data must first be transformed into its non-diffusive, seismic-like counterpart. I examine such a transform from both an analytical and a numerical point of view, focusing on methods to overcome inherent numerical instabilities. This is the first step to applying seismic processing techniques to CSEM data to rapidly and efficiently image resistive gas hydrate structures. The University of Toronto marine electromagnetics group has deployed a permanent marine CSEM array offshore Vancouver Island, in the framework of the NEPTUNE Canada cabled observatory, for the purposes of monitoring gas hydrate deposits. In this thesis I also propose and examine a new CSEM survey technique for gas hydrate which would make use of the stationary seafloor transmitter already on the seafloor, along with a cabled receiver array, towed from a ship. I furthermore develop a modelling algorithm to examine the electromagnetic effects of conductive borehole casings which have been proposed to be placed in the vicinity of this permanent marine CSEM array, and make preliminary recommendations about their locations.

Gas hydrates are a solid, ice-like mixture of water and low molecular weight hydrocarbons. They are found under the permafrost and to a far greater extent under the ocean, usually at water depths greater than 300m. Hydrates are a potential energy resource, a possible factor in climate change, and a geohazard. For these reasons, it is critical that gas hydrate deposits are quantitatively assessed so that their concentrations, locations and distributions may be established. Due to their ice-like nature, hydrates are electrically insulating. Consequently, a method which remotely detects changes in seafloor electrical conductivity, such as marine controlled source electromagnetics (CSEM), is a useful geophysical tool for marine gas hydrate exploration. Hydrates are geometrically complex structures. Advanced electromagnetic modelling and imaging techniques are crucial for proper survey design and data interpretation. I develop a method to model thin resistive structures in conductive host media which may be useful in building approximate geological models of gas hydrate deposits using arrangements of multiple, bent sheets. I also investigate the possibility of interpreting diffusive electromagnetic data using seismic imaging techniques. To be processed in this way, such data must first be transformed into its non-diffusive, seismic-like counterpart. I examine such a transform from both an analytical and a numerical point of view, focusing on methods to overcome inherent numerical instabilities. This is the first step to applying seismic processing techniques to CSEM data to rapidly and efficiently image resistive gas hydrate structures. The University of Toronto marine electromagnetics group has deployed a permanent marine CSEM array offshore Vancouver Island, in the framework of the NEPTUNE Canada cabled observatory, for the purposes of monitoring gas hydrate deposits. In this thesis I also propose and examine a new CSEM survey technique for gas hydrate which would make use of the stationary seafloor transmitter already on the seafloor, along with a cabled receiver array, towed from a ship. I furthermore develop a modelling algorithm to examine the electromagnetic effects of conductive borehole casings which have been proposed to be placed in the vicinity of this permanent marine CSEM array, and make preliminary recommendations about their locations.

[Truncated abstract. Formulae and special characters can only be approximated. See PDF version for accurate reproduction.] Theories of self-dual supersymmetric nonlinear electrodynamics are generalized to a curved superspace of 4D N = 1 supergravity, for both the old-minimal and the newminimal versions of N = 1 supergravity. We derive the self-duality equation, which has to be satisfied by the action functional of any U(1) duality invariant model of a massless vector multiplet, and show that such models are invariant under a superfield Legendre transformation. We construct a family of self-dual nonlinear models, which includes a minimal curved superspace extension of the N = 1 supersymmetric Born- Infeld action. The supercurrent and supertrace of such models are explicitly derived and proved to be duality invariant. The requirement of nonlinear self-duality turns out to yield nontrivial couplings of the vector multiplet to Kähler sigma models. We explicitly construct such couplings in the case when the matter chiral multiplets are inert under the duality rotations, and more specifically to the dilaton-axion chiral multiplet when the group of duality rotations is enhanced to SL(2,R). The component structure of the nonlinear dynamical systems introduced proves to be more complicated, especially in the presence of supergravity, as compared with well-studied effective supersymmetric theories containing at most two derivatives (including nonlinear Kähler sigma-models). As a result, when deriving their canonically normalized component actions, the traditional approach becomes impractical and cumbersome. We find it more efficient to follow the Kugo-Uehara scheme which consists of (i) extending the superfield theory to a super-Weyl invariant system; and then (ii) applying a plain component reduction along with imposing a suitable super-Weyl gauge condition. This scheme is implemented in order to derive the bosonic action of the SL(2,R) duality invariant coupling to the dilaton-axion chiral multiplet and a Kähler sigma-model.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Visualizações imersivas são muito valiosas para melhorar a compreensão de uma variedade de fenômenos físicos, que podem ser eventualmente modelados na forma discreta e simulados por computador. Dentre possíveis aplicações podemos utilizar a visualização imersiva como ferramenta pedagógica para percepção aumentada de tópicos complexos, ou como uma poderosa ferramenta de apoio analítico para ajudar os engenheiros a interpretarem os resultados de projetos. Este projeto de pesquisa aborda o uso da visualização imersiva de campos eletromagnéticos, especificamente os campos gerados por redes sem fio, largamente utilizadas no cotidiano como é o caso das redes IEEE 802.11 (Wi-Fi). Para tanto este trabalho propõe métodos novos para visualizar, em tres dimensões, campos eletromagnéticos variantes no tempo e distribuições de parâmetros interessantes relacionados a redes sem fio. Para atingir este objetivo, uma versão aprimorada do método de diferenças finitas no domínio do tempo (FDTD) é desenvolvido: o método FDTD de alta ordem e malha grosseira (Coarse Grid Higher Order FDTD, CGHO-FDTD). Portanto, soluções numéricas muito precisas, mais rápidas, e computacionalmente mais eficientes das equações de Maxwell podem ser obtidas. Os cálculos numéricos podem ser ainda mais rápidos pelo uso de computação paralela em um aglomerado de computadores. As características de domínio de tempo facilitam a criação de instantâneos de campos eletromagnéticos que estão se propagando, e desta maneira é possível criar figuras e animações tridimensionais que podem ser usadas para explicar alguns dos seguintes fenômenos físicos comuns em redes sem fio: difração, reflexão, e atenuação. Para que aumente a percepção física ainda mais, visualizações imersivas são feitas em um ambiente de realidade virtual. Por fim, a ferramenta desenvolvida também pode ser usada para criar distribuições muito detalhadas de parâmetros importantes que afetam o desempenho em uma rede sem fio. É mostrado que simulações de um ambiente fechado para prever a distribuição de potência de uma rede sem fio do tipo IEEE 802.11 (Wi-Fi), estão de acordo com as medidas. / Immersive visualizations are very valuable in order to improve the understanding of a variety of physical phenomena that can be modeled numerically and simulated by computers. Amongst the possible applications, we could utilize immersive visualizations as a pedagogical tool for enhanced perception of complex topics, or as a powerful tool that helps engineers interpret the outcome of simulations. This research project approaches the use of immersive visualizations of electromagnetic fields, especially fields generated by wireless networks widely utilized in the everyday life, as is the case for networks of the type IEEE 802.11 (Wi-Fi). For such a purpose this work proposes new methods to three-dimensionally visualize time-varying electromagnetic fields, and distributions of interesting parameters related to wireless networks. To achieve these objectives, a better version of the finite-difference time-domain (FDTD) method is developed: the Coarse Grid Higher Order FDTD (CGHO-FDTD) method. Thus highly accurate, faster and more computationally efficient numerical solutions of Maxwells equations can be obtained. The numerical calculations are made even faster by the use of parallel computing on a cluster of computers. The characteristics of the time domain facilitate the creation of snapshots of the propagating electromagnetic fields, and in this manner it is possible to create three-dimensional figures and animations that can be used to explain some of the following common physical effects found in wireless networks: diffraction, reflection, and attenuation. To further enhance the perception of the physics, immersive visualizations are carried out in a virtual reality environment. Finally, the developed tool can also be used to create highly detailed distributions of important parameters that affect the performance in wireless networks. It is shown that simulations to predict the power distribution in an indoor wireless network of the type IEEE 802.11 (Wi-Fi), agree very well with measurements.

[pt] Este trabalho apresenta uma nova técnica para aproximação de uma superfície refletora definida numericamente, i.e., por pontos fornecidos pelo processo de síntese da antena. As limitações inerentes às técnicas usuais são aqui eliminadas pela utilização de Pseudo-Splines Quínticas que interpolam uma distribuição arbitrária de pontos por uma superfície suave, com derivadas primeiras e segundas contínuas, assegurando uma representação única para o domínio de interesse. O procedimento é, então, aplicado ao subrefletor modelado de uma antena Cassegrain, com subseqüente cálculo do campo eletromagnético espalhado, permitindo uma análise detalhada de sua aplicabilidade. Uma teoria assintótica uniforme de difração é, também, aqui desenvolvida de modo a acomodar o espalhamento de feixes Gaussianos, descritivos, em freqüências altas, do diagrama de irradiação de alimentadores comumente empregados em sistemas refletores, por superfícies condutoras, através do rastreamento do campo eletromagnético ao longo de raios no espaço complexo. A análise do problema canônico (difração por semi-plano) estabelece as particularidades do método e a comparação com a solução rigorosa existente comprova sua acurácia, permitindo a extensão a problemas tridimensionais vetorais. A teoria Complexa da Difração, assim formulada, é, então aplicada ao cálculo do campo espalhado por diferentes geometrias de antenas refletoras, ilustrando a versatilidade do método bem como suas limitações. / [en] In order to evaluate the electromagnetic field scattered by shaped reflector antennas, one has to fit a surface to a set of points furnished by a synthesis technique. A new method, capable of interpolating arbitrarily located data points by a smooth surface is here presented. The interpolating function, called Quintic Pseudo-Spline, has continuous first and seconde order derivatives and yields a unique representation for the entire domain. The method is tested on the shaped subreflector of a Cassegrain antenna providing a thorough investigation of its applicability. Also, an uniform asymptotic theory of diffraction is derived in order to analyse the scattering of Gaussin beams, descriptive of the high-frequency radiation pattern of feed horns commonly employed in reflector systems, by conducting surfaces with edges. The constraints inherent to usual methods of analysis are hereby avoided by tracking these beam-type fields along straight rays in a complex coordinate space. Investigation of the canonical problem of scattering of a Gaussian beam by a conducting half-plane establishes the characteristics of the complex ray diffraction process. Comparison of the results thus obtained with the rigorous solution reveals the accuracy of the proposed theory and permits its extension to the three-dimensional vector problem. The resulting Complex Theory of Diffraction is then applied to the evaluation of the scattered field for several reflector antenna geometries, illustrating the versatility of the method as well as its limitation.

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No description available.

Finite element techniques have been applied to a wide variety of problems in electro magnetics, but have been handicapped by the appearance of spurious solutions. Both weighted residual methods and variational methods are the basic finite element techniques that are examined to establish a framework for the discussion of spurious solutions. A simple waveguide example is used to explore the fundamental problem with these spurious solutions. A method is developed that focuses on the functional form as the fundamental cause underlying the difficulties with spurious solutions. By using analytical rather than numerical means, it is shown that the solution form allows for the existence of an improper gradient behavior in a general field expansion. A new functional that satisfies Maxwell's equations and eliminates spurious solutions is introduced. This new functional is shown to be self-adjoint and positive definite, thus providing an error minimization. The analytical form as well as the finite element method is applied to demonstrate the robust nature of the functional. / Ph. D.