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Thesis advisor: Joshua E. Greene / We study ribbon cobordisms between 3-manifolds, i.e. rational homology cobordisms that admit a handle decomposition without 3-handles. We first define and study the more general notion of quasi-ribbon cobordisms, and analyze how lattice-theoretic methods may be used to obstruct the existence of a quasi-ribbon cobordism between two given 3-manifolds. Building on this and on previous work of Lisca, we then determine when there exists such a cobordism between two connected sums of lens spaces. In particular, we show that if an oriented rational homology sphere Y admitsa quasi-ribbon cobordism to a lens space, then Y must be homeomorphic to L(n, 1), up to orientation-reversal. As an application, we classify ribbon χ-concordances between connected sums of 2-bridge links. Lastly, we show that the notion of ribbon rational homology cobordisms yields a partial order on the set consisting of aspherical 3-manifolds and lens spaces, thus providing evidence towards a conjecture formulated by Daemi, Lidman, Vela-Vick and Wong. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

<P> In this thesis, we mainly study geodesics on various two dimensional surfaces. All the background material needed throughout the thesis is provided, including an explanation of the theory of geodesics. We will calculate geodesics using two numerical methods: Euler's method and Runge-Kutta method of fourth order. Using Maple, we will test the accuracy of the numerical methods on a test case surface, the Poincare half plane. Later, we proceed to investigate several interesting surfaces by numerically calculating geodesics. From the investigated surfaces, we will draw similarities between the human cerebral cortex and certain surfaces. The human cerebral cortex is the most intensely studied part of the brain and it is believe that their exists a relation between the function and structure of the cortex. Geodesic analysis can possibly be an essential tool in better understanding the cortical surface as it is in many disciplines of science to understand the nature of physical based problems. </P> / Thesis / Master of Science (MSc)

<p> We look for time-dependent solutions to a general class of supergravity models in an arbitrary amount of dimensions. Previously, many static solutions of these models have been found and studied, of which a subclass of these solutions support membrane-like configurations. While many properties of these solutions are known, their dynamics - and therefore stability - are not. We follow this motivation, and investigate the possibility of time dependent solutions that will also support this membrane configuration. Under various conditions, it turns out this is the case, bringing a better understanding to the stability of these branes. In addition, the form of the time dependence found suggest possible applications of supergravity to cosmological models.</p> / Thesis / Master of Science (MSc)

<p> Software Evolution is unavoidable because software systems are subject to continuous change, continuing growth and increasing complexity. As software systems become mission-critical and large in size, the complexity in software development is now focused on software evolution rather than construction. In this work, we view a software system as an entity that is evolving throughout its lifetime, during development and maintenance. Based on a broad survey of software evolution approaches, we propose an architecture-based solution for software evolution, which is defined in terms of evolution specific operations on architectural elements, that is, adding, removing, replacing components and (or) connectors, transforming configurations according to the required changes. In our view of software architectures, connectors are more likely to change since they are the architectural elements which reflect business rules. This work is focused on the evolution of connectors in architectures describing detailed design. Coordination contracts are introduced by Fiadeiro et al. as a realization of connectors at this detailed architecture level, which enables a three-layer architecture to separate concerns of components, connectors and configuration during evolution. Furthermore, to constrain the evolution in a predictable direction, we have established a matching scheme for justifying behavioral relationships between coordination contracts by specification matching based on pre- and postconditions of contracts and methods. A number of specification matches, with various degrees of similarity between the evolved and evolving contracts, have been developed for system behaviors after evolution operations. Case studies are exhibited give a better understanding of these matches.</p> / Thesis / Master of Science (MSc)

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As three-dimensional (3D) imaging and fluorescence techniques become standard in optical microscopy, novel approaches to 3D fluorescence microscopy are emerging. One such approach is based on the incoherent holography technique called optical scanning holography (OSH). The main advantage of OSH-based microscopy is that only a single two-dimensional (2D) scan is required to record 3D information, whereas most current 3D microscopes rely on sectioning techniques. To acquire a 3D representation of an object, current microscopes must physically scan the specimen in a series of 2D sections along the z-axis. In order to record holograms by OSH, the fluorescent specimen is scanned with an optically heterodyned laser field consisting of a Fresnel zone pattern. A unique acousto-optic modulator configuration is employed to generate a suitable heterodyne frequency for excitation of the fluorescent object. The optical response of a solution containing a high concentration of 15 um fluorescent latex beads to this type of excitation field has been recorded. In addition, holograms of the same beads have been recorded and reconstructed. To demonstrate the 3D imaging capability of the technique, the hologram includes beads with longitudinal separation of about 2 mm. A detailed comparison of 3D fluorescence microscopy by OSH and the confocal approach was conducted. Areas for comparison were 3D image acquisition time, resolution limits and photobleaching. The analysis shows that an optimized OSH-based fluorescence microscope can offer improved image acquisition time with equal lateral resolution, but with degraded longitudinal resolution when compared to confocal scanning optical microscopy (CSOM). For the photobleaching investigation, the parameter of concern is the fluence received by the specimen during excitation, which takes into account both the irradiance level and the time of illumination. Both peak and average fluence levels are addressed in the comparison. The analysis shows that during a 3D image acquisition, the OSH system will deliver lower peak fluence but higher average fluence levels to the specimen when compared to CSOM. / Ph. D.

Ensuring inspection performance is not a trivial design problem, because inspection is a complex and difficult task that tends to be error-prone, whether performed by human or by automated machines. Due to economical or technological reasons, human inspectors are responsible for inspection functions in many cases. Humans, however, are rarely perfect. A system of manual inspection was found to be approximately 80-90% effective, thus allowing non-confirming parts to be processed (Harris & Chaney, 1969; Drury, 1975). As the attributes of interest or the variety of products increases, the complexity of an inspection task increases. The inspection system becomes less effective because of the sensory and cognitive limitations of human inspectors. Any means that can support or aid the human inspectors is necessary to compensate for inspection difficulty. Augmented reality offers a new approach in designing an inspection system as a means to augment the cognitive capability of inspectors. To realize the potential benefits of AR, however the design of AR-aided inspection requires a through understanding of the inspection process as well as AR technology. The cognitive demands of inspection and the capabilities of AR to aid inspectors need to be evaluated to decide when and how to use AR for a dimensional inspection. The objectives of this study are to improve the performance of a dimensional inspection task by using AR and to develop guidelines in designing an AR-aided inspection system. The performance of four inspection methods (i.e., manual, 2D-aided, 3D-aided, and AR-aided inspections) was compared in terms of inspection time and measurement accuracy. The results suggest that AR might be an effective tool that reduces inspection time. However, the measuring accuracy was basically the same across all inspection methods. The questionnaire results showed that the AR and 3D-aided inspection conditions are preferred over the manual and 2D-aided inspection. Based on the results, four design guidelines were formed in using AR technology for a dimensional inspection. / Ph. D.

MnZn ferrites are widely used in power electronics applications where the switching frequency is in the range of several tens of kilohertz to a megahertz. In this range of frequencies the combination of relatively high permeability and relatively low conductivity found in MnZn ferrite helps to minimize the size of magnetic devices while maintaining high efficiency. The continuing improvement in semiconductor switches and circuit topologies has led to use of high-frequency switching circuits at ever increasing power levels. The magnetic devices for these high-power, high-frequency circuits require magnetic CORES that are significantly larger than standard ferrite-core devices used at lower power levels. Often such large ferrite cores must be custom designed, and at present this custom design is based on available material information without regard for the physical size of the structure. This thesis examines the issues encountered in the use of larger MnZn ferrite cores for high-frequency, high-power applications. The two main issues of concern are the increased power dissipation due to induced currents in the structure and the change in inductance that results as the flux within the core is redistributed at higher frequencies. In order to model these problems using either numerical or analytical methods requires a reliable and complete set of material information. A significant portion of this work is devoted to methods for acquiring such material information since such information is not generally available from the manufacturers. Once the material constants required for the analysis are determined, they are used in both closed-form and numerical model to illustrate that large ferrite cores suffer significant increases in loss and significant decreases in inductance for frequencies as low as several hundred kilohertz. The separate impacts of the electrical and magnetic losses in the core are illustrated through the use of linear finite element analyses of several example core structures. The device impedances calculated using the FEA tools show fair agreement with measurement. An analysis of gapped structures and segmented cross-sections shows that these design options can reduce the severity of the dimensional problems for some designs. / Ph. D.