Nanophotonics is a booming field of research with the promise of chip-scale devices which harness the tremendous potency of light. In this regard, surface plasmons have shown great potential for confining and manipulating light at extreme sub-wavelength scales. Advances in fabrication technology have enabled the scientific community to realize metasurfaces with unconventional properties that push the limits of possible applications of light. This thesis is comprised of computational and experimental studies on plasmonic metasurfaces. The computational study presents efficient design principles for plasmonic half-wave plates using L-shaped nanoantennas. These principles can be used to design waveplates at an operating wavelength of choice and for specific application requirements. The impact of this study goes beyond the efficient design of waveplates: it provides useful insights into the Physics of L-shaped nanoantenna arrays which have been proposed as building blocks for plasmonic metasurfaces. The experimental work investigates the interaction of a plasmonic metasurface, composed of dipole antenna arrays, with an epsilon-near-zero (ENZ) material. This work thus forms a bridge between plasmonics and ENZ materials science, which is a rapidly advancing field in its own right. The first experimental study investigates the exciting unconventional response of plasmonic dipole antennas when placed on a thin indium tin oxide (ITO) film near its ENZ wavelength of 1417 nm. The antenna-on-ITO system has split resonances whose spectral positions are largely independent of the antenna dimensions. The resonance splitting occurs due to coupling between the antenna resonance and the ENZ mode of the ITO film. This coupling results in field intensity enhancements on the order of a 100 in the ITO film. The second experimental study demonstrates, using the z-scan method, that this large field enhancement in the antenna-on-ITO structure further enhances the already strong nonlinearity of ITO around its ENZ wavelength. In particular, the antenna-on-ITO structure exhibits an extremely large nonlinear absorption coefficient, which is two orders of magnitude larger than that of a bare ITO film, and three to five orders of magnitude larger than that of many other nonlinear materials. This thesis thus constitutes a beautiful blend of three thriving areas of research: plasmonics, ENZ materials science and nonlinear optics. The findings reported here have the potential to contribute to all of these fields, and thus have relevance to a broad spectrum of optical scientists.

This thesis deals with the modelling and circuit simulation problems of nonlinear electronic devices. Emphasis has been aimed at MOSFET devices. A Piecewise Linear (PWL) modelling scheme has been proposed for a general four-terminal nonlinear charge device. The charge functions are all nonlinear and are approximated by PWL functions. If analytical expressions for the nonlinear functions are not available, PWL function approximations can be built from a data table in which discrete data points are recorded. In the time domain, the critical-damping-adjustment (CDA ) scheme is used as the integration rule in the discretization of dynamic charge devices. Piecewise linear modelling combined with the CDA integration scheme gives a fast yet adequately accurate simulation algorithm. The algorithm is based on linear analysis because the entire circuit becomes linear with PWL modelling of nonlinear elements. In order to avoid an iterative solution, PWL region extrapolation is permitted when the circuit solution switches PWL regions. The extrapolation approximation will generate an overshoot error in the solution vector. However, with caution in the selection of the integration step size, the error can be limited to an acceptable range. Two types of MOSFETs have been modelled and simulated with the algorithm introduced in this thesis, and satisfactory results have been obtained as compared to Newton's iteration solutions. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

It is felt the position of the Scheffé polynomials as the primary, or sometimes sole recourse for practitioners of mixture experiments leads to a lack of enquiry regarding the type of blending behaviour that is used to describe the response and that this could be detrimental to achieving experimental objectives. Consequently, a new class of models and new experimental designs are proposed allowing a more thorough exploration of the experimental region with respect to different blending behaviours, especially those not associated with established models for mixtures, in particular the Scheffé polynomials. The proposed General Blending Models for Mixtures (GBMM) are a powerful tool allowing a broad range of blending behaviour to be described. These include those of the Scheffé polynomials (and its reparameterisations) and Becker's models. The potential benefits to be gained from their application include greater model parsimony and increased interpretability. Through this class of models it is possible for a practitioner to reject the assumptions inherent in choosing to model with the Scheffé polynomials and instead adopt a more open approach, flexible to many different types of behaviour. These models are presented alongside a fitting procedure, implementing a stepwise regression approach to the estimation of partially linear models with multiple nonlinear terms. The new class of models has been used to develop designs which allow the response surface to be explored fully with respect to the range of blending behaviours the GBMM may describe. These designs may additionally be targeted at exploring deviation from the behaviour described by the established models. As such, these designs may be thought to possess an enhanced optimality with respect to these models. They both possess good properties with respect to optimality criterion, but are also designed to be robust against model uncertainty.

M.Sc. (Mathematics) / Please refer to full text to view abstract

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In this thesis, we study problems with heterogeneities using the zeroth order optimized Schwarz preconditioning. There are three main parts in this thesis. In the first part, we propose an Optimized Restricted Additive Schwarz Preconditioned Exact Newton approach (ORASPEN) for nonlinear diffusion problems, where Robin transmission conditions are used to communicate subdomain errors. We find out that for the problems with large heterogeneities, the Robin parameter has a significant impact to the convergence behavior when subdomain boundaries cut through the discontinuities. Therefore, we perform an algebraic analysis for a linear diffusion model problem with piecewise constant diffusion coefficients in the second main part. We carefully discuss two possible choices of Robin parameters on the artificial interfaces and derive asymptotic expressions of both the optimal Robin parameter and the convergence rate for each choice at the discrete level. Finally, in the third main part, we study the time-dependent nonequilibrium Richards equation, which can be used to model preferential flow in physics. We semi-discretize the problem in time, and then apply ORASPEN for the resulting elliptic problems with the Robin parameter studied in the second part.

This dissertation aims to apply non-zero attitude and position setpoint tracking to a quadrotor aircraft, achieved by solving the problem of a quadrotor’s inherent underactuation. The introduction of extra actuation aims to mechanically accommodate for stable tracking of non-zero state trajectories. The requirement of the project is to design, model, simulate and control a novel quadrotor platform which can articulate all six degrees of rotational and translational freedom (6-DOF) by redirecting and vectoring each propeller’s individually produced thrust. Considering the extended articulation, the proposal is to add an additional two axes (degrees) of actuation to each propeller on a traditional quadrotor frame. Each lift propeller can be independently pitched or rolled relative to the body frame. Such an adaptation, to what is an otherwise well understood aircraft, produces an over-actuated control problem. Being first and foremost a control engineering project, the focus of this work is plant model identification and control solution of the proposed aircraft design. A higher-level setpoint tracking control loop designs a generalized plant input (net forces and torques) to act on the vehicle. An allocation rule then distributes that virtual input in solving for explicit actuator servo positions and rotational propeller speeds. The dissertation is structured as follows: First a schedule of relevant existing works is reviewed in Ch:1 following an introduction to the project. Thereafter the prototype’s design is detailed in Ch:2, however only the final outcome of the design stage is presented. Following that, kinematics associated with generalized rigid body motion are derived in Ch:3 and subsequently expanded to incorporate any aerodynamic and multibody nonlinearities which may arise as a result of the aircraft’s configuration (changes). Higher-level state tracking control design is applied in Ch:4 whilst lower-level control allocation rules are then proposed in Ch:5. Next, a comprehensive simulation is constructed in Ch:6, based on the plant dynamics derived in order to test and compare the proposed controller techniques. Finally a conclusion on the design(s) proposed and results achieved is presented in Ch:7. Throughout the research, physical tests and simulations are used to corroborate proposed models or theorems. It was decided to omit flight tests of the platform due to time constraints, those aspects of the project remain open to further investigation. The subsequent embedded systems design stemming from the proposed control plant is outlined in the latter of Ch:2, Sec:2.4. Such implementations are not investigated here but design proposals are suggested. The primary outcome of the investigation is ascertaining the practicality and feasibility of such a design, most importantly whether or not the complexity of the mechanical design is an acceptable compromise for the additional degrees of control actuation introduced. Control derivations and the prototype design presented here are by no means optimal nor the most exhaustive solutions, focus is placed on the whole system and not just a single aspect of it.

The FANTOM consortium has generated a large gene expression dataset of different cell lines and tissue cultures using the single-molecule sequencing technology of HeliscopeCAGE. This provides a unique opportunity to investigate novel associations between gene expression over time and different cell types. Here, we create a MatLab wrapper for a powerful and computationally intensive set of statistics known as Maximal Information Coefficient, and then calculate this statistic for a large, comprehensive dataset containing gene expression of a variety of differentiating tissues. We then distinguish between linear and nonlinear associations, and then create gene association networks. Following this analysis, we are then able to identify clusters of linear gene associations that then associate nonlinearly with other clusters of linearity, providing insight to much more complex connections between gene expression patterns than previously anticipated.