3. Electronic Theses and Dissertations (ETDs) - All submissions

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    Mathematical models for the transmission dynamics of bovine schistosomiasis with contaminated environment
    (2020) Kadaleka, Solomon
    Schistosomiasis is a chronically debilitating infection of humans and animals, caused by different species of blood flukes. The main purpose of this thesis is to gain some insights into the transmission dynamics of the disease by exploring the role of contaminated environment. We first propose and rigorously analyze a generic deterministic mathematical model with snail and bovine hosts as a system of non-linear ordinary differential equations. Second, we extend our generic model to incorporate humans and control measures, namely treatment of humans and bovines and mollusciciding of the contaminated environment. The basic reproduction number R0 of the two proposed models is computed and used to theoretically investigate the existence and stability of the models’ steady states. By constructing a suitable Lyapunov function, we prove the global stability of the endemic equilibria. Sensitivity analysis is performed to determine the relative importance of model parameters to disease transmission. The basic reproduction number is most sensitive to model parameters biased towards the contaminated: the bovine recruitment rate, the fecal output parameter, the snail-Miracidia effective contact rate and the cercariae to miracidia survival probability. Pontrayagin’s Maximum Principle is used for the optimal control analysis in order to determine the strategies which yield optimal results in controlling the spread of schistosomiasis. Analytical results are supported with numerical simulation using Matlab, Maple and Mathematica software. Numerical simulations indicate that mollusciciding proves to be more effective in containing the spread of the disease in humans and bovines, however a combined application of treatment of infected bovines and humans and mollusciciding will be most effective in controlling the spread of schistosomiasis. Finally, uncertainty analysis on the non-dimensional system parameters is graphically represented using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques
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    A DFT based study of the gold-water interface
    (2019-10) Masike, Tshegofatso Titus
    A gold/water interface has been investigated with the DFT-based self-consistentcharge density-functional tight-binding (SCC-DFTB) method using a full cell model with periodic boundary conditions. Born-Oppenheimer molecular-dynamics simulations for water on the surfaces of two Au60 electrode slabs were computed. We have demonstrated the applicability of this method to study the structural and dynamical properties of the gold/water interface in a system with periodic-boundary conditions. The results of the simulation clearly show a dependency on the charged electrodes by means of the orientation of the water molecules and the ensuing polarisation of the cell. However, it was also shown that this polarisating e ect is con ned almost exclusively to rst few angstroms away from the electrode . This is indicative of the rather short-range screening behaviour of water. The present study is a feasibility study of models with periodic-boundary conditions and beckons further analysis of metal/electrolyte interfaces on a dependable atomic scale, using periodic boundary conditions.
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    Supersymmetric quantum mechanics and path integrals
    (2017) Ayad Mohamed Ali, Ahmed
    Supersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. In this dissertation, we review the basics formulation of supersymmetric quantum mechanics starting with introducing the concepts of supercharges and superalgebra. We show that, if there is a supersymmetric state, it is the zero-energy ground state. If such a state exists, the supersymmetry is unbroken otherwise it is broken. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. In fact, supersymmetry may be broken spontaneously at any order of perturbation theory, or dynamically due to non-perturbative e ects. The goal of this dissertation is to study the methods of supersymmetry breaking. For this purpose, a special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. Then we explain that perturbation theory gives us incorrect results for both the ground state wave function as well as the energy spectrum and it fails to give an explanation to the supersymmetry breaking. Later in the dissertation, a review of the uses of instantons in quantum mechanics is given. In particular, instantons are used to compute the tunneling e ects within the path integral approach to quantum mechanics. As a result, we give evidence that the instantons, which are a non-perturbative e ect in quantum mechanics and can not be seen in perturbation theory, leads to calculate the corrections to the ground state energy and provides a possible explanation for the supersymmetry breaking.
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    Flow of a thin ribbon of molten glass on a bath of molten tin
    (2016) Sangweni, Zinhle Brighty
    The equations for the flow of a thin lm of molten glass on a bath of molten tin are extended to the case in which the viscosity of the molten glass depends on the temperature. The continuity equation for an incompressible fluid, the Navier-Stokes equation and the energy balance equation are written in the lubrication (thin fluid lm) approximation. The kinematic boundary condition and the boundary conditions for the normal and tangential stress and the normal heat flux are derived on the upper and lower surfaces of the glass ribbon. It is found for the lubrication approximation that only one equation is obtained for four unknowns which are the two horizontal velocity components, the absolute temperature difference and the thickness of the molten glass rib- bon. The remaining three equations are obtained by taking the calculation to the next order in the square of the ratio of the thickness to length of the glass ribbon. The kinematic edge condition and the edge conditions for the normal and tangential stress and the normal heat flux are derived. The four edge conditions and the boundary conditions at the inlet and outlet give the boundary conditions for the four partial differential equations. It is not the aim of the dissertation to solve the boundary value problem which has been derived, either numerically or analytically.
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    Development of a condition monitoring philosophy for a pulverised fuel vertical spindle mill
    (2016) Govender, André
    The quantity and particle size distribution of pulverised coal supplied to combustion equipment downstream of coal pulverising plants are critical to achieving safe, reliable and efficient combustion. These two key performance indicators are largely dependent on the mechanical condition of the pulveriser. This study aimed to address the shortfalls associated with conventional time-based monitoring techniques by developing a comprehensive online pulveriser condition monitoring philosophy. A steady-state Mill Mass and Energy Balance (MMEB) model was developed from first principles for a commercial-scale coal pulveriser to predict the raw coal mass flow rate through the pulveriser. The MMEB model proved to be consistently accurate, predicting the coal mass flow rates to within 5 % of experimental data. The model proved to be dependent on several pulveriser process variables, some of which are not measured on a continuous basis. Therefore, the model can only function effectively on an industrial scale if it is supplemented with the necessary experiments to quantify unmeasured variables. Moreover, a Computational Fluid Dynamic (CFD) model based on the physical geometry of a coal pulveriser used in the power generation industry was developed to predict the static pressure drop across major internal components of the pulveriser as a function of the air flow through the pulveriser. Validation of the CFD model was assessed through the intensity of the correlation demonstrated between the experimentally determined and numerically calculated static pressure profiles. In this regard, an overall incongruity of less than 5 % was achieved. Candidate damage scenarios were simulated to assess the viability of employing the static pressure measurements as a means of detecting changes in mechanical pulveriser condition. Application of the validated pulveriser CFD model proved to be highly advantageous in identifying worn pulveriser components through statistical analysis of the static pressure drop measured across specific components, thereby demonstrating a significant benefit for industrial application.
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