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Pages (41,133,161,209) were omitted from the thesis as they were completely blank pages. / <p> In this thesis, we propose efficient approaches for design optimization of passive and active photonic devices. These approaches are based on utilizing gradient based optimization algorithms for efficient optimization of photonic devices. Some of the proposed approaches obtain the required gradient (sensitivity) information efficiently using adjoint variable method (AVM) applied directly to the exploited numerical techniques. Other approaches are based on formulating the design problem as an optimization problem using convex programming. These approaches utilize the gradient-based interior point method (IPM) for solving the design.</p> <p> The AVM aims at efficiently obtaining the sensitivity information using the numerical technique. This technique requires a solution of an additional simulation of the adjoint system. The information obtained from the original and the adjoint simulation is sufficient to obtain the response and the sensitivity of the response with respect to all the design parameters. The AVM technique differs for different numerical method. </p> <p> The obtained sensitivity using the AVM approach is not only useful for exploiting gradient based optimization for design optimization, but also for yield and tolerance analyses of the newly proposed designs. </p> <p> We proposed a second order accurate approach to obtain the sensitivity information using finite difference time domain (FDTD) technique. This approach utilizes the AVM to efficiently obtain the sensitivity information. This approach is exploited for efficiently obtaining the sensitivity of the power reflectivity and coupling coefficient of various devices. This approach has been also utilized for obtaining the sensitivity of the dispersion characteristics of different guided wave structures.</p> <p> We also introduce a novel approach for sensitivity analysis of photonic devices using the beam propagation method (BPM). This approach is simple and easy to implement. It exploits the existing factorization of the system matrices for efficient calculation of the sensitivity of the required objective function. This approach is also utilized for sensitivity analysis of the vectorial modal properties of different guided wave structures. This approach is also exploited for sensitivity analysis of various surface plasmon devices. </p> <p> This AVM approach is also exploited to propose a novel design of an optical switch with wide working wavelength band and compact size. The switch is based on the self imaging theory in multimode waveguide with a refractive index has approximate parabolic profile. The design problem is formulated as two stage optimization procedure. The optimization algorithm exploits the efficiently obtained sensitivity information from a BPM simulation. The final design has interesting characteristics.</p> <p> An efficient approach is also proposed to obtain the sensitivity of the energy levels and wavefunctions of different quantum structures obtained using time dependent and time independent Schrodinger equation. This approach is exploited for design optimization of different quantum well lasers.</p> <p> We also propose a convex formulation for the design problem of multilayer optical coatings. This formulation allows for efficient design of structures with large number of layers in fractions of a second without an initial design.</p> / Thesis / Doctor of Philosophy (PhD)

<p> A response conditioned to a specific stimulus will generalize to similar stimuli. Various reports have indicated that the slope of the gradient of generalization changes over a period of time. The experiments reported here investigated the generalization of an emotional response, originally conditioned to an 80 db. white noise to a 60 db. white noise. In different groups the tests for generalization were begun immediately after conditioning or after a 4 day waiting period. In further groups the animals' time during the delay period was variously taken up with bar pressing sessions; new conditioning trials with a light CS; unsignalled shock presentations, or they merely stayed in their home cages.</p> / Thesis / Master of Arts (MA)

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<p>There have been considerable requirements for improved products of sheet metal in automobile industry. A quick and economical route to new products is to design novel surface textures of varying scales for improved product enhancement in better optical appearance and formability. The critical deformation in the surface texturing is on the order of only a few microns, and can not be accurately predicted by the classical plasticity due to the size effect. The theory of strain gradient plasticity has been developed to capture the size effect based on the concept of geometrically necessary dislocations (GNDs). A selected strain gradient theory has been implemented into the finite element (FE) model to simulate the surface texturing process. A 3D FE model was developed to simulate the rolling process of sheet metal which has band-type feature on the original surface. The numerical results show that a textured roller can efficiently modify the band-type feature without changing the whole mechanical property of the sheet. Size effect has significant contribution to the magnitude of the rolling force. A FE model was developed to simulate the tensile test of the sheet with textured surface. A textured surface of the sheet is prepared through the indention on the sheet surface. The results show that the textured surface becomes harder due to the strain gradient effect, and finally improves the formability of the sheet.</p> / Master of Applied Science (MASc)

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This thesis describes the processing and testing of homogeneous nickel and fully yttria stabilized cubic zirconia interpenetrating phase composites. This work was part of a research program investigating step graded Functionally Gradient Materials. This work was focused on understanding the deformation behaviour of the interpenetrating composites near the percolation threshold of the ceramic phase. The composite grades selected for this study included the pure materials, nickel and zirconia, as well as composites with volume fractions of zirconia of 5%, 10%, 15%, 20% and 25%. These compositions were selected to provide data near the zirconia percolation threshold. Processing of the composites involved tape casting, lamination, organic removal, reduction, and hot pressing. All composites except the 5% volume fraction achieved densities greater than 98% of theoretical. Tensile testing was performed on composite grades up to and including the 20% zirconia material, and flexural testing was carried out on the 25% material and pure zirconia. The maximum tensile strength of 530 MPa was obtained in the 10% material resulting from load transfer to the zirconia phase. Ductility decreased as the volume fraction of zirconia increased, with no macroscopic plasticity above 15% volume fraction zirconia. Hardness tests and compression tests were carried out on all composite grades and the yield stress was determined.The compressive yield stress was found to be related to the hardness by the equation: H=6σy This relationship is a result of the constraint imposed on the nickel phase by the zirconia network. Measurements of damage in one pure nickel sample were also performed. The area fraction of voids as a function of local strain was found to follow an exponential relationship. The Young’s modulus of each material was determined ultrasonically and found to be uniform as expected. Modeling of the tensile specimens indicated that materials above the zirconia percolation threshold work harden more rapidly than those below it. This is not accounted for in the model by Ravichandran. / Thesis / Master of Engineering (ME)

Tensegrity is the name given to a system of interconnected bars and tendons that can form a flexible self-standing structure. Its flexibility is due to the ability of the bars to move near-independent to each other, movement that can be caused by controlled tension forces in the tendons or external forces such as gravity. However, a balance of sorts must be maintained - if a tendon were to go slack, the entire structure could become unstable and collapse on itself. This thesis looks at placing a tensegrity structure in orbit around the Earth. As a spacecraft's orbit is moved further away from the Earth, the strength of the Earth's gravity field lessens. Ideally, such a flexible structure would be placed far enough away from the Earth so that the gravity field would have too weak an impact on its individual elements to cause major distortions. However, the author recognizes that altitudes below 2,000 km, where the Earth's gravity field is still very prevalent, are the most common altitudes used by orbiting spacecraft today. The goal of this thesis is to analyze the distortions of the tensegrity structure at these lower altitudes, and also look at methods for controlling these distortions. / Ph. D. / Tensegrity is the name given to a system of interconnected bars and tendons that can form a flexible self-standing structure. Its flexibility is due to the ability of the bars to move nearindependent to each other, movement that can be caused by controlled tension forces in the tendons or external forces such as gravity. However, a balance of sorts must be maintained - if a tendon were to go slack, the entire structure could become unstable and collapse on itself. This thesis looks at placing a tensegrity structure in orbit around the Earth. As a spacecraft’s orbit is moved further away from the Earth, the strength of the Earth’s gravity field lessens. Ideally, such a flexible structure would be placed far enough away from the Earth so that the gravity field would have too weak an impact on its individual elements to cause major distortions. However, the author recognizes that altitudes below 2,000 km, where the Earth’s gravity field is still very prevalent, are the most common altitudes used by orbiting spacecraft today. The goal of this thesis is to analyze the distortions of the tensegrity structure at these lower altitudes, and also look at methods for controlling these distortions.

There are several reasons for using non-Cartesian k-space sampling methods in Magnetic Resonance Imaging (MRI). Such a method is radial sampling, which includes the advantage of continuous coverage of the k-space center which results in higher robustness to motion. On the other hand, radial imaging does have some limitations that must be considered. The method is more sensitive to gradient imperfections, such as eddy currents and gradient delays, resulting in inconsistencies between the nominal and actual gradient waveforms. This leads to distortions in the sampling trajectory, also called trajectory errors, yielding reconstructed images with artifacts caused by the gradient imperfections. The aim of this project was therefore to implement a method that takes these errors into account and perform a correction of the trajectory errors to yield images with reduced artifacts. Various methods have been proposed for correction of the gradient errors, some more effective than others. The method implemented in this project was based on the gradient impulse response function (GIRF) which characterizes the gradient system responses. When GIRF was acquired, the actual gradient waveforms played-out during the imaging measurement could be predicted by first modeling the nominal gradient waveforms and then performing a convolution with the corresponding GIRF for each gradient axis. The imaging experiments involved measurements on two different resolution phantoms and in-vivo measurements to note possible differences in correction performance. The used pulse sequences for imaging were FLASH and bSSFP. The results showed that the applied method using GIRF did reduce the artifacts caused by gradient imperfections in the reconstructed images taken with the FLASH sequence. On the other hand, the results for the bSSFP sequence were not as successful due to incomplete modeling of the gradient waveforms. The conclusion to be drawn is that the GIRF-correction does adequately compensate for the trajectory errors when using a radial sampling trajectory for the FLASH sequence and hence yield images with almost eliminated artifacts. A suggestion for future work would be to further investigate the bSSFP sequence modeling to obtain better bSSFP-images. / Det finns flera anledningar till att använda icke-Kartesiska k-space samplingsmetoder i magnetisk resonanstomografi. En sådan metod är radiell sampling, som har fördelen att kontinuerligt samla in mätdata från mittpunkten av k-space, vilket resulterar i lägre rörelsekänslighet under bildtagningstillfället. Radiell sampling har dock begränsningar som måste tas i beaktande, som gradient imperfektioner och gradientfördröjningar. Dessa leder till förvrängningar i samplingspositioneringen i k-space, även känt som trajektoriefel, vilket ger upphov till artefakter vid bildrekonstruktion. Syftet med projektet är att korrigera för dessa trajektoriefel så att den rekonstruerade bilden innehåller färre artefakter. Olika metoder har föreslagits för korrektion av gradientfel. Metoden som användes i detta projekt baseras på gradient impulsresponsfunktionen (GIRF), som karaktäriserar gradient systemet. För att estimera de verkliga samplingspositionerna i k-space beräknades de förvrängda gradientvågformerna efter varje mätning. Detta gjordes genom att först modellera de nominella gradientvågformerna och därefter utföra en faltning med GIRF. De utförda experimenten under projektets gång bestod av bildtagning av två fantomer och ett antal in-vivo mätningar för att identifiera eventuella skillnader i de rekonstruerade bilderna. Pulssekvenserna som användes under projektet var FLASH och bSSFP. Resultaten visade att GIRF-korrektionen reducerade artefakter orsakade av gradient imperfektioner i de rekonstruerade bilderna tagna med FLASH-sekvensen. Erhållna resultat med bSSFP-sekvensen var å andra sidan inte lika lyckade på grund av inkomplett modellering av gradientvågformerna. Slutsatsen som kan dras är att GIRF-korrektionen kompenserar för trajektoriefel i radiell sampling för FLASH-sekvensen och ger rekonstruerade bilder där artefakterna nästan eliminerats. Ett förslag för framtida arbeten är att vidare undersöka modelleringen av bSSFP-sekvensen för att erhålla bättre bilder.

In this thesis we study Sobolev gradient flows for Perona-Malik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. We show that these flows are well-posed in the forward and reverse directions which yields an effective linear sharpening algorithm. We furthermore establish a number of maximum principles for the forward flow and show that edges are preserved for a finite period of time. We then go on to study isotropic Sobolev gradient flows with respect to higher order Sobolev metrics. As the Sobolev order is increased, we observe an increasing reluctance to destroy fine details and texture. We then consider Sobolev gradient flows for non-linear anisotropic diffusion functionals of arbitrary order. We establish existence, uniqueness and continuous dependence on initial data for a broad class of such equations. The well-posedness of these new anisotropic gradient flows opens the door to a wide variety of sharpening and diffusion techniques which were previously impossible under L2 gradient descent. We show how one can easily use this framework to design an anisotropic sharpening algorithm which can sharpen image features while suppressing noise. We compare our sharpening algorithm to the well-known shock filter and show that Sobolev sharpening produces natural looking images without the "staircasing" artifacts that plague the shock filter. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-08-25 10:44:12.23