In this dissertation, I report the results of my research on twisted moiré photonic crystals which can be formed through multi-beam holographic interference without a physical rotation and later fabricated by electron-beam lithography. Their optical properties, such as photonic bandgaps, multiple resonance modes, and quality factor are presented. Randomized moire photonic crystals in lattice are also studied. The applications of moire photonic crystals in improving light extraction efficiency are simulated and verified in light emitting devices. Furthermore, I simulated the light extraction efficiency in OLED when the Al layer is patterned with a triangular GPSC, square moiré PhC with defects in the uniform area, and random locations of the photonic lattice, and obtain light extraction efficiency of 78.9%, 79.9%, 81.7%, respectively. Also, the ratios of photoluminescence intensity of LED integrated with twisted moiré PhCs and random moiré PhCs over that without moiré PhCs are measured to be (1.3-1.9) and 1.74, respectively, in a good agreement with simulated ratios of 1.69 and 1.8.

Twisted particles carry Orbital Angular Momentum (OAM), an important property utilized to encode quantum information. The OAM of twisted photons can be trans- ferred onto condensed matter systems in the form of twisted excitons. Numerical solutions of the time-dependent Schr ̈odinger equation for a 3-arm molecular chain are used to demonstrate the manipulation of twisted excitons via an external magnetic field. We present the first design for an OAM transistor in a quasi-1D system that can be used to control the flow of OAM using the magnetic field. The underlying mechanism is the interaction between OAM and the magnetic field which leads to a orbit-resolved Bloch oscillation (ORBO). We present the semi-classical equations of motion for this phenomenon in a one-dimensional system. Unlike classical Bloch oscil- lation, an important effect in ultrafast electron dynamics, the magnet driven ORBO is not limited by electrical breakdown and can easily be observed in natural solids.

The growing demand for compact and compliant mobility assistive devices has driven interest in low-profile actuating technologies. With the increasing mobility needs of an aging population, such devices could meet this growing market if they can provide low power capabilities, high strength, and compatibility with standard industrial fabrication processes. As a result, researchers have been investigating smart materials, such as carbon nanotube (CNT) and their higher-order structures, as potential components for soft actuator systems. However, reported works using this material within actuators have remained limited due to the material's prohibitive cost and fabrication complexity. Furthermore, presented actuator designs are difficult to compare due to custom fabrication procedures and inconsistent characterizations. The recent availability of commercial higher-order CNT products and the superior material consistency they provide present an opportunity to comprehensively analyze these materials in actuators without the challenges faced in previous work. This thesis addressed this opportunity by evaluating a stiffness-variable actuator design leveraging a commercially available CNT fibre. The evaluation focused on the effects on the mechanical and electrical properties in addition to its electrothermal and electromechanical responses when changing selected actuator design and operational parameters. The findings highlight the importance of optimal coating and embedded pre-stretch to achieve optimal contractile stress and contractile strain performance, while increased fibre diameter diminishes these properties. Furthermore, the usage of commercial CNT yarn ensured consistent mechanical and electrical properties during the fabrication and testing of actuator prototypes. This in-depth understanding of this actuator design's strengths, weaknesses, and the influence of selected operational and design parameters on performance establishes a foundation for future CNT-based actuator research within a repeatable framework.

A set of equations describing the motion of a naturally curved and twisted slender elastic rod is determined in this thesis. In particular, a study of the vibration of a helical spring is made, and the natural frequencies from the theory presented are compared with those from a simpler theory. Comparison of the two theories shows that the simpler theory is valid for most springs. The simpler theory is then used to show how the natural frequencies for a helical spring can be obtained when the spring is subjected to any boundary conditions. Finally, an analytical and experimental study of the vibration of a helical spring clamped at both ends is made in order to investigate the validity of the theory presented. / Thesis / Master of Engineering (MEngr)

The bitwist construction, originally discovered by Cannon, Floyd, and Parry, gives us a new method for finding face pairing descriptions of 3-manifolds. In this paper, I will describe the construction in a way suitable for a more general audience than the original research papers. Along the way, I will describe Dehn Surgery and a set of moves which allows us to change the framings of a link without changing the topology of the manifold obtained by Dehn Surgery. Once the theory has been developed, I will apply it to find several bitwist representations of the Poincaré Sphere and 3-Torus. Finally, I discuss how one might attempt to find a set of moves that can take one bitwist representation of a manifold to any other bitwist representation of the same manifold. / Master of Science

No description available.

Performance analysis of Digital Subscriber Line (DSL) technologies, which are implemented on existing telephone subscriber loops, is of vital importance to DSL service providers. This type of analysis requires accurate prediction of the local loop structure and precise identification of the cable parameters. These cables are the main components of the loop and are typically comprised of multi-conductor twisted pair type currently being used on existing telephone subscriber loops. This system identification problem was investigated through the application of single port measurements, with preference being placed on measurements taken from the service provider's end of the loop under investigation. Once the cabling system has been identified, the performance analysis of the loop was obtained through simulation. Accurate modeling is an important aspect of any system identification solution; therefore, the modeling of the twisted pair cables was thoroughly investigated in this research. Early modeling attempts of twisted pair cabling systems for use with (DSL) technology has not been vigorously investigated due to the difficulty in obtaining wideband physical data necessary for the task as well as the limitations of simulators to accurately model the skin effects of the conductors. Models are developed in this research that produce a wideband representation of the twisted pair cables through the use of the data measured in high frequency spectra. The twisted-pair cable models were then applied to the system identification problem through a de-embedding type approach. The identification process accurately characterizes the sections of the subscriber loop closest to the measurements node, and these identified sections were then modeled and de-embedded from the system measurement in a layer removing, or "peeling", type process. After each identified section was de-embedded from the system measurement, the process was repeated until the entire system was identified. Upon completion of the system identification process, the resulting system model was simulated between the central office (CO) and resulting identified customer nodes for the evaluation of performance analysis. The performance analysis allows the providers to identify points where the DSL technology is feasible, and where so, the rates of the data transfer to the nodes that can be expected. / Ph. D.

Dans cette thèse, on donne une formule géométrique explicite pour les intégrales orbitales semisimples tordues du noyau de la chaleur sur un espace symétrique, en utilisant la méthode du laplacien hypoelliptique développée par Bismut. On montre que nos résultats sont compatibles avec les résultats classiques de la théorie de l'indice équivariant local sur les espaces localement symétriques compacts. On utilise notre formule explicite pour évaluer le terme dominant dans l'asymptotique quand d -> + ∞ de la torsion analytique équivariante de Ray-Singer associée à une famille de fibrés vectoriels plats Fd sur un espace localement symétrique compact. On montre que le terme dominant peut être calculé à l'aide de W-invariants au sens de Bismut-Ma-Zhang. / In this thesis, we give an explicit geometric formula for the twisted semisimple orbital integrals associated with the heat kernel on symmetric spaces. For that purpose, we use the method of the hypoelliptic Laplacian developed by Bismut. We show that our results are compatible with classical results in local equivariant index theory. We also use this formula to evaluate the leading term of the asymptotics as d -> + ∞ of the equivariant Ray-Singer analytic torsion associated with a sequence of flat vector bundles Fd on a compact locally symmetric space. We show that the leading term can be evaluated in terms of the W-invariants constructed by Bismut-Ma-Zhang.

In this paper we explore the slice-ribbon conjecture for some families of pretzel knots. Donaldson's diagonalization theorem provides a powerful obstruction to sliceness via the union of the double branched cover W of B⁴ over a slicing disk and a plumbing manifold P([capital gamma]). Donaldson's theorem classifies all slice 4-strand pretzel knots up to mutation. The correction term is another 3-manifold invariant defined by Ozsváth and Szabó. For a slice knot K the number of vanishing correction terms of Y[subscript K] is at least the square root of the order of H₁(Y[subscript K];Z). Donaldson's theorem and the correction term argument together give a strong condition for 5-strand pretzel knots to be slice. However, neither Donaldson's theorem nor the correction terms can distinguish 4-strand and 5-strand slice pretzel knots from their mutants. A version of the twisted Alexander polynomial proposed by Paul Kirk and Charles Livingston provides a feasible way to distinguish those 5-strand slice pretzel knots and their mutants; however the twisted Alexander polynomial fails on 4-strand slice pretzel knots. / text

Neste trabalho fazemos um estudo do conceito de soma torcida de F-espaços. Apresentamos algumas propriedades e simplificações na construção de somas torcidas de F-espaços localmente limitados. Em particular, estudamos uma condição suficiente para que uma soma torcida de espaços de Banach seja um espaço de Banach. Finalmente aplicamos esses conceitos para definir o espaço construído por N. J. Kalton, que é um exemplo de um espaço de Banach não isomorfo ao conjugado complexo. Este espaço X de Kalton corresponde a uma soma torcida de espaços de Hilbert, isto é, X possui um subespaço fechado E tal que E e X/E são isomorfos a espaços de Hilbert. / In this work we study the concept of twisted sum of F-spaces. We also study some properties and simplifications in the construction of twisted sums of locally bounded F-spaces. In particular, we study a sufficient condition for a twisted sum of Banach spaces to be a Banach space. Finally we apply these concepts to define the space constructed by N. J. Kalton, which is an example of a Banach space not isomorphic to its complex conjugate. The Kalton space X is a twisted sum of Hilbert spaces, i.e. X has a closed subspace E such that E and X/E are isomorphic to Hilbert spaces.