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Superconductivity continues to be of great theoretical and practical interest and remains a challenging area of scientific inquiry. Most superconductors of practical utility are of type-II, i.e., they allow the penetration of magnetic fields in the form of tubes of flux that are referred to as "vortices." Motion of these vortices due to, e.g., applied currents, induce a loss of perfect conductivity. Knowing how vortices move and arrange themselves in lattice structures, how their movement is suppressed by pinning mechanisms, and how their movement is affected by thermal fluctuations is critical to understanding how to maintain resistanceless current flow. We study a variety of Ginzburg-Landau type models for superconductivity that can account for inhomogeneous and isotropy materials, grain boundaries, and thermal fluctuations. We develop robust, accurate, and efficient numerical codes and apply them to numerous studies of how vortex motions are affected by the various mechanisms mentioned above. We also examine some analytical aspects of type-II superconductors under the influence of thermal fluctuations. / Ph. D.

The effect of that the tire has on the overall aerodynamic drag in a car-tire assembly has been studied and deemed considerable from past studies. It has been shown that to know how tire parameters affect the drag on the car-tire assembly, it is important to understand how the vehicle body and the tires influence the flow structures. Previous studies have focused on the tire attributes that have some impact on the aerodynamic performance of the vehicle. These tire attributes, however, haven't been studied to the extent where one can get a better understanding of the impact of each of these attributes. This paper studies the impact that specific tire attributes have on the overall aerodynamic drag on the vehicle based on a thorough and systematic sensitivity study. The effect of tire attributes in a vehicle assembly as well as the sensitivity study of a rim protector on a standalone tire is conducted. This helps in better understanding the flow structures around the car body and around the tire for the improvement in the aerodynamic performance of the vehicle. This is a two-part study. One component of this study is a parametric sensitivity analysis of a tire in a tire – vehicle assembly. The other component is a parametric sensitivity analysis of the rim protector design on a standalone tire. / Master of Science / The drag performance is one of the most important factors that contributes to the overall efficiency of a vehicle. There has always been a huge demand in the automotive industry for such studies. Over the years, experimental studies conducted have shown to be invaluable to the industry. But a big downside to experimental studies is that they are extremely expensive. Experimental studies on Vehicle bodies require a wind tunnel and expensive measurement equipment. This has led to a high demand for more computational studies in this field. Various authors over the past few years have studied and challenged various solution procedures used in computational studies. The trade-off for these studies is always cost vs. accuracy. This thesis attempts to simulate both for a vehicle assembly as well as a standalone tire model to come up with a robust solution method for the computational analysis of flow over a vehicle body. The goal of this thesis is to conduct a parametric sensitivity study for the cross-section profile of the tire in vehicle assembly as well as a parametric sensitivity study for the rim protector profile of the tire in a standalone tire. At the end of the study, we will get a better understanding of the impact that each of the parameters have on the drag performance of the vehicle and the standalone tire.

<p>This thesis focuses on the numerical and theoretical studies of gas quenching in industrial furnaces. Gas quenching is the rapid cooling of metal pieces, aiming at forcing a phase transformation of the metal structure to improve its mechanical properties. The numerical methodology has been evaluated with respect to the desired accuracy and different aspects of the flow with importance for achieving an optimized process have been investigated. Initially, attention was paid to the flow and heat transfer fields both in an empty furnace and in a furnace loaded with different charges with the objective to study the influence of the charge configuration on the flow and heat transfer uniformity. This study led to the identification of several possible improvements, which are currently being implemented by the industrial partners of this project. As earlier studies had shown the importance of flow uniformity on the quality of the heat treatment, the subsequent work focused substantially on the flow uniformity upstream of the quenching zone resulting in design recommendations for the particular type of furnace under consideration. The dependence of the performance of the coolant medium on its composition was investigated theoretically and an analysis of most important parameters was carried out. Improved knowledge of the effect of gas mixture composition on heat transfer was added to the body of knowledge already available.</p>

Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling technique would permit a plethora of complex optical effects—including dispersion, birefringence, dichroism, and thin film interference, and the physical optical elements associated with these effects—to become naturally supported, fully integrated features in physically based rendering software.

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.

This thesis focuses on the numerical and theoretical studies of gas quenching in industrial furnaces. Gas quenching is the rapid cooling of metal pieces, aiming at forcing a phase transformation of the metal structure to improve its mechanical properties. The numerical methodology has been evaluated with respect to the desired accuracy and different aspects of the flow with importance for achieving an optimized process have been investigated. Initially, attention was paid to the flow and heat transfer fields both in an empty furnace and in a furnace loaded with different charges with the objective to study the influence of the charge configuration on the flow and heat transfer uniformity. This study led to the identification of several possible improvements, which are currently being implemented by the industrial partners of this project. As earlier studies had shown the importance of flow uniformity on the quality of the heat treatment, the subsequent work focused substantially on the flow uniformity upstream of the quenching zone resulting in design recommendations for the particular type of furnace under consideration. The dependence of the performance of the coolant medium on its composition was investigated theoretically and an analysis of most important parameters was carried out. Improved knowledge of the effect of gas mixture composition on heat transfer was added to the body of knowledge already available. / QC 20101019

This thesis is concerned with numerical techniques for resolving and continuing closed, compact invariant manifolds in parameter-dependent dynamical systems with specific emphasis on invariant tori under flows. In the first part, we review several numerical methods of continuing invariant tori and concentrate on one choice called the ``orthogonality condition'. We show that the orthogonality condition is equivalent to another condition on the smooth level and show that they both descend from the same geometrical relationship. Then we show that for hyperbolic, periodic orbits in the plane, the linearization of the orthogonality condition yields a scalar system whose characteristic multiplier is the same as the non-unity multiplier of the orbit. In the second part, we demonstrate that one class of discretizations of the orthogonality condition for periodic orbits represents a natural extension of collocation. Using this viewpoint, we give sufficient conditions for convergence of a periodic orbit. The stability argument does not extend to higher-dimensional tori, however, and we prove that the method is unconditionally unstable for some common types of two-tori embedded in R^3 with even numbers of points in both angular directions. In the third part, we develop several numerical examples and demonstrate that the convergence properties of the method and discretization can be quite complicated. In the fourth and final part, we extend the method to the general case of p-tori in R^n in a different way from previous implementations and solve the continuation problem for a three-torus embedded in R^8.