This thesis focuses on Fast Radio Bursts (FRBs) and presents computational techniques that can be used to understand these enigmatic events and the Universe around them. Chapter 1 provides a theoretical overview of FRBs; providing a foundation for the chapters that follow. Chapter 2 details current understandings by providing a review of FRB properties and progenitor theories. In Chapter 3, we implement non-parametric techniques to measure the elusive baryonic halo of the Milky Way. We show that even with a limited data set, FRBs and an appropriate set of statistical tools can provide reasonable constraints on the dispersion measure of the Milky Way halo. Further, we expect that a modest increase in data (from fewer than 100 FRB detections to over 1000) will significantly tighten constraints, demonstrating that the technique we present may offer a valuable complement to other analyses in the near future. In Chapter 4, we study the fine time-frequency structure of the most famous FRB: FRB 121102. Here, we use autocorrelation functions to maximise the structure of 11 pulses detected with the MeerKAT radio telescope. The study is motivated by the low time-resolution of MeerKAT data, which presents a challenge to more traditional techniques. The burst profiles that are unveiled offer unique insight into the local environment of the FRB, including a possible deviation from the expected cold plasma dispersion relationship. The pulse features and their possible physical mechanisms are critically discussed in a bid to uncover the nature and origin of these transients.

The dynamics of many biological processes rely on an interplay between spatial transport and chemical reactions. In particular, spatial dynamics can play a critical role in the successful functioning of cellular signaling processes, where as basic a prop- erty as cell shape can significantly influence the behavior of signaling pathways. The inside of cells is a complex spatial environment, filled with organelles, filaments and proteins. We investigate the question of how cell signaling pathways function robustly in the presence of such spatial heterogeneity for the most basic of chemical signals. Due to the noisy environment of a cell, particle-based stochastic reaction-diffusion models are a widely used approach for studying such cellular processes, explicitly modeling the diffusion of, and reactions between, individual molecules. However, the computational expense of such methods can greatly limit the size of chemical systems that can be studied. To overcome this challenge, we rigorously derive coarse-grained deterministic partial integro-differential equation models that provide a mean field ap- proximation to the particle-based stochastic reaction-diffusion model. Relationships between the mean field models and standard reaction-diffusion partial differential equation models are further investigated for general biochemical reaction systems. Comparisons between these models are illustrated through mathematical analysis and numerical examples.

Bibliography: leaves 81-85. / This work investigates strategies for the transfer of energy technologies so as to develop the necessary capability for adapting and adopting such technologies in the recipient country using the transfer of hydropower technology to Lesotho as a case study. The work reviewed the literature on this subject as a background to the development of a technology transfer framework that formed the basis of the analysis. The framework was tested using the Muela hydropower project in Lesotho. Existing mini-hydropower projects in Lesotho were also reviewed to identify possible lessons from them regarding objective of this study.

Includes bibliographical references. / The central objective of this project was to develop a package of energy education workshops for secondary schools. The package contains nine energy workshops. Each workshop comprises a teacher's guide and a student worksheet. The package production process included choosing an education methodology, reviewing energy themes for selection as workshop topics and evaluating the energy workshop package. This dissertation provides insight into the processes of producing this package. My participation in the Community Education Resource's Masters programme introduced he goal of producing university resources in formats which are accessible to a broader audience. Energy themes for the workshops were drawn from a review of existing resources, particularly those f the Energy for Development Research Centre, and were selected for their relevance to energy as an agent of development, energy production and environmental concerns, energy policy formulation and vocational interest.

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In multilingual countries, proficiency in more than one language can benefit individuals and society. For this reason, many universities, especially those with medical faculties, promote the learning of additional languages. Stellenbosch University's Faculty of Medicine and Health Sciences (SUFMHS) offers an isiXhosa Clinical Communication (XCC) course as part of some undergraduate courses. This study explores the use of clickers, a student response system (SRS). The study aims to answer the following research questions: How do students engage with the Student Response System (clickers) in an isiXhosa Clinical Communication course in Higher Education settings? This core question is followed by this subsidiary research question: To what extent can the use of clickers enhance students' clinical communicative competence in isiXhosa as a second additional language? The participants were 51 female first year Occupational Therapy (OT) students. They answered multiple choice questions (MCQs) using their mobile phones as clickers as a formative assessment procedure. The researcher observed the students from the moment they started answering the MCQs until the post-test classroom discussions had ended. The students' MCQ responses were polled and then displayed in the form of histograms. Additional data were collected by means of a post-intervention questionnaire, from focus group discussions and with informal staff interviews. The immediate feedback seemed to enhance content consolidation, student self-assessment and constructive peer comparison. For these reasons the study found that the use of clickers could enhance student-lecturer and student-student engagement. An important additional finding is that the use of students' personal mobile devices, rather than commercial clickers, contributed to the success of the intervention. It does seem though that, in order to be used maximally, clickers should be incorporated in the teaching pedagogy from the onset, rather than being primarily utilised as a resource to enhance teaching interventions.

We consider the heat equation forced by a space-time white noise and with periodic boundary conditions in one dimension. The equation is discretized in space using four different methods; spectral collocation, spectral truncation, finite differences, and finite elements. For each of these methods we derive a space-time white noise approximation and a formula for the covariance structure of the solution to the discretized equation. The convergence rates are analyzed for each of the methods as the spatial discretization becomes arbitrarily fine and this is confirmed numerically. Dirichlet and Neumann boundary conditions are also considered. We then derive covariance structure formulas for the two dimensional stochastic heat equation using each of the different methods. In two dimensions the solution does not have a finite variance and the formulas for the covariance structure using different methods does not agree in the limit. This means we must analyze the convergence in a different way than the one dimensional problem. To understand this difference in the solution as the spatial dimension increases, we find the Sobolev space in which the approximate solution converges to the solution in one and two dimensions. This result is then generalized to n dimensions. This gives a precise statement about the regularity of the solution as the spatial dimension increases. Finally, we consider a generalization of the stochastic heat equation where the forcing term is the spatial derivative of a space-time white noise. For this equation we derive formulas for the covariance structure of the discretized equation using the spectral truncation and finite difference method. Numerical simulation results are presented and some qualitative comparisons between these two methods are made. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2015. / April 8, 2015. / Space-Time White Noise, Stochastic Heat Equation / Includes bibliographical references. / Xiaoming Wang, Professor Co-Directing Dissertation; Brian Ewald, Professor Co-Directing Dissertation; Laura Reina, University Representative; Philip L. Bowers, Committee Member; Bettye Anne Case, Committee Member; Giray Okten, Committee Member.

The sensitivity analysis of options is as important as pricing in option theory since it is used for hedging strategies, hence for risk management purposes. This dissertation presents new sensitivities for options when the underlying follows an exponential Lévy process, specifically Variance Gamma and Normal Inverse Gaussian processes. The calculation of these sensitivities is based on a finite dimensional Malliavin calculus and the centered finite difference method via Monte-Carlo simulations. We give explicit formulas that are used directly in Monte-Carlo simulations. By using simulations, we show that a localized version of the Malliavin estimator outperforms others including the centered finite difference estimator for the call and digital options under Variance Gamma and Normal Inverse Gaussian processes driven option pricing models. In order to compare the performance of these methods we use an inverse Fourier transform method to calculate the exact values of the sensitivities of European call and digital options written on S&P 500 index. Our results show that a variation of localized Malliavin calculus approach gives a robust estimator while the convergence of centered finite difference method in Monte-Carlo simulations varies with different Greeks and new sensitivities that we introduce. We also discuss an approximation method for the Variance Gamma process. We introduce new random number generators for the path wise simulations of the approximating process. We improve convergence results for a type of sensitivity by using a mixed Malliavin calculus on the increments of the approximating process. / A Dissertation Submitted to the Department of Mathematics in Partial FulfiLlment of the Requirements for the Degree of Doctor of Philosophy. / Summer Semester, 2010. / April 12, 2010. / Centered Finite Difference, Monte-Carlo simulations, FFT, Malliavin calculus, Inverse Fourier Transform method, Normal Inverse Gaussian process, Approximation of Lévy processes, Variance Gamma process, Greeks / Includes bibliographical references. / Craig A. Nolder, Professor Directing Thesis; Fred Huffer, University Representative; Bettye Anne Case, Committee Member; David Kopriva, Committee Member; Giray Okten, Committee Member; Jack Quine, Committee Member.

Bibliography: leaves 79-81. / Glasses with various compositions, falling in the CaO-AI20rSi02 and MgO-CaOAI20rSi02 systems were made, using pulverised fuel ash and silica, hydrated lime, kaolin and magnesium carbonate. Titania or ferric oxide and chromia were used as nucleants. Various crystallisation heat treatments were carried out and the nucleation and crystallisation behaviour was studied. A minimum MgO:CaO was found to be necessary for bulk nucleation to occur. The activation energy for viscous flow decreased with increased MgO:CaO ratios. This was accompanied by an increase in the surface crystal growth rates and a decrease in the activation energy for surface crystal growth. Titania also lowered the activation energies for viscous flow and surface crystal growth and caused an increase in the surface crystal growth rates.

Bibliography: leaves 86-89. / An information database built through regular planned surveys in a comprehensive manner is the objective of this study. A foundation for periodic up-date of household energy is necessary and requires a proper institutional or structural set up that gives priority to household energy issues. This study explores the fundamental need to shift away from the current ad hoc surveys to a more reliable, systematic, comprehensive and financially effective way of conducting household energy surveys to generate household energy information that is representative of national picture and which supports effective planning and policy-making. Promotion of the importance of the household energy sector in terms of social equity and improved living standards is vital for investors, developers, financiers and policy-makers and planners to improve the sector. Thus the study addresses the appropriate way of obtaining comprehensive household energy information and harmonized data collection methodology through cooperation in information exchange amongst African countries to achieve comparability of data for a common African energy database.