School of Mathematics and Statistics - Theses
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ItemA Variational Approach to Solving Differential Equations on a Quantum Computer( 2021)As quantum computing technology continues to develop, quantum algorithms have the potential to outperform classical algorithms in future for certain computational tasks. One of these potential applications of quantum computing is numerically solving differential equations and integral equations. In this thesis the variational quantum linear solver algorithm (VQLS) proposed by Bravo-Prieto et al. is adapted to solve the Laplace and Poisson equations, ordinary differential equation initial value problems (IVPs) with both constant and function coefficients, and a Fredholm integral equation of the second type. As this thesis demonstrates, variational quantum algorithms for solving differential equations and integral equations such as VQLS are highly promising for use on Noisy Intermediate-Scale Quantum (NISQ) devices. The quantum circuit components of the VQLS algorithm were simulated using IBM Quantum's statevector simulator with the optimized solution circuits implemented on the IBM Quantum Guadalupe device (in most cases). A discussion of errors and convergence is also included. The application of VQLS to these differential equations and integral equations is novel and, to my knowledge, work using VQLS to solve the Poisson equation has only recently been published once by authors Liu et al. which was conducted concurrently and independently of this research.
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ItemTransport equations and boundary conditions for oscillatory rarefied gas flows( 2018)A wide range of flow phenomena in everyday life can be modelled accurately using classical continuum theory: the Navier-Stokes equations with associated no-slip conditions. However, oscillatory flows generated by nanoscale devices violate the basic assumptions underpinning continuum theory. Study of such flows, under the assumption of small perturbations from equilibrium, requires analysis of the unsteady Boltzmann equation. At sufficiently high oscillation frequencies, the resulting flow can result in wave propagation. This thesis presents a rigorous asymptotic analysis of slightly rarefied wave motion. Particular emphasis is placed on the boundary layer structure, transport equations and associated slip boundary conditions, valid for a general curved oscillating boundary with a velocity-independent body force.
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ItemEvaluating the constructivist potential of the multimedia software "Stage struck" in drama education( 2005-01)This project compares the educational aims of the designers of the educational title “Stage Struck” with those of two separate groups in the process of learning and teaching; namely the aims of teachers and students. This method of comparing the observations of two key stakeholder groups with the objectives of the designer is part of an instrument proposed by Squires and McDougall (1994) called the Perspectives Interaction Paradigm. This instrument diverges from traditional models of software evaluation in that it has encompassed multiple points of view in the determination of whether a piece of software is useful in educational environments. This project hypothesizes that the Squires/McDougall approach shows how software can be utilized in ways that can be complimentary or contrary to the intentions of designers. It is for this reason and the multi-pronged method of data collection that the instrument is considered a more appropriate tool for the project than other evaluative checklists. “Stage Struck” has been chosen because a number of items in the education literature indicate clearly articulated aims that the software be used in a manner befitting constructivist approach. Using interviews with two teachers and observations of two students within the scope of the controlled setting, this project will identify where and why aims are transformed/modified and how the expectations of the educational merit of “Stage Struck” correspond or fail to correspond.
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ItemFlowshop sequencing: a graphic approach( 1990-03)This thesis is concerned with flowshop sequencing which seeks to arrange a variety of different jobs in a sequence which minimizes the total time for the completion of all jobs.