We analyze a simplified mathematical model of the complete degradation of monochlorophenol. The model takes form of a system of six ordinary differential equations, the dynamics of which can be reduced to the dynamics of a three-dimensional system on the invariant set. We extend the previous analysis by considering multiple substrate inflow. We also focus on the bifurcations occurring in the system and their biological meaning. / Thesis / Master of Science (MSc)

The Oxygen Steelmaking process is used to refine pig iron produced in the blast furnace to produce liquid steel for further refining in secondary steelmaking processes. The main advantages of the process are its autogenous nature, wherein the heat is generated through the refining reactions itself, and the refining is completed in a relatively short time (typically 15-25 mins). Achieving the desired end-point composition of refined steel is essential to avoid re-blows, which lead to delays in downstream processes and an increase in steel production costs. Improving process control through regular monitoring and a better understanding of the process is thus very critical. Multiple reaction interfaces are formed between various phases (slag, metal, gas), at extremely high temperatures and this makes the monitoring of the process through sampling and observation difficult and expensive. Consequently, mathematical modelling has been used as a tool to improve the understanding of the process and propose developments in operation. Numerous models have been developed in the past; however, these models do not address several open questions regarding the detailed reaction mechanisms and the contributions from different reaction zones inside the Basic Oxygen Furnace. The current work aimed to fill this gap. In this work, four prominent reaction zones, namely; impact, slag-metal bulk, cavity, and emulsion zones were identified. A more mechanistic approach involving process variables has been used to decrease the level of empiricism. With regards to the impact and the slag-metal bulk zones, the velocity of flow of metal (or surface-renewal) at the interfaces of these zones are calculated by taking into the momentum induced by the top-jets and bottom-stirring plumes. This study found that these zones contribute negligibly to overall refining in the oxygen steelmaking process. In the case of the emulsion zone, a very rigorous description of all aspects (external and internal decarburization, bloating behavior, and trajectory) pertaining to the life cycle of a single metal droplet in slag has been achieved. The emulsion zone is found to contribute 5 to 75 % of decarburization during various times of blow. The cavity zone model represents the first reported effort to predict the refining behavior of metal droplets that are exposed to oxygen jets within the lance cavities. The model incorporated the mass transfer, reaction equilibria, and kinetics of the reactions. It is predicted that this zone plays a critical role in the removal of silicon and FeO formation in the early part of the blow and removal of carbon throughout the blow. Several significant insights with regards to improvement in the operation of the oxygen steelmaking process are derived from each sub-models. The integration of these models will guide the steelmaker to improve their practices so that they can achieve better consistency in the end-point composition of refined steel and reduce re-blows. / Thesis / Doctor of Philosophy (PhD)

Myxococcus xanthus, referred to as a 'social bacterium', demonstrates unique behaviors such as coordinated motility, cooperative feeding, and multicellular structure formation. Its complex social behaviors and developmental processes make M. xanthus a model organism for studying bacterial social behaviors and their underlying mechanisms. Much of the social behavior of M. xanthus hinges on coordination of cell motility among bacteria in close proximity. M. xanthus moves on moist solid surfaces, using its Adventurous (A)-motility and Social (S)-motility systems. A striking feature of M. xanthus motility is the periodic reversal of its direction of movement. The reversal frequency is influenced by chemical and mechanical cues in the surrounding environment. The modulation of the reversal frequency upon physical contact between cells is believed to be a key factor in the bacterium's social behaviors, especially in the formation of complex patterns and structures within the cell population. Here I utilized mathematical modeling to study the motility regulation in M. xanthus, focusing on contact-dependent reversal control, mechanosensing response and impact of motility regulation in solitary (single-cell) predation. My goal is to provide experiment-guiding theories and hypotheses for M. xanthus motility regulation, which is essential to fully understand the social behaviors in this bacterium. In Chapter 2, I developed a single-cell model based on a hypothesis that the motility regulation in M. xanthus is mediated by the interplay between the cell polarity regulation pathway and the A-motility machinery. The aim of this model is to elucidate the cellular mechanism governing contact-dependent motility coordination among cells and to understand how contact-dependent responses at the single-cell level contribute to population-level patterns. This model suggests that the A-motility machinery of M. xanthus potentially serves as a 'mechanosensor' that transduces mechanical cues in the environment into a reversal modulation signal. Chapter 3 addresses a puzzling observation: cells with A-motility alone (A+S−) show a dependence of reversal frequency on substrate stiffness that is opposite to what is observed in wild-type cells that possess both motility systems. Specifically, A+S− cells reverse less frequently on harder substrates, whereas wild-type cells reverse more frequently. To elucidate this perplexing phenomenon, I refined the single-cell model developed in Chapter 2 to study the mechanosensing behaviors with or without S-motility. The base model was sufficient to explain the mechanosensing response in A+S− cells. I then proposed possible interactions between the A-motility and S-motility systems that could explain the contrasting responses to substrate stiffness when S-motility is present or absent. This provides a testable prediction for future experimental investigations. The model suggests that the A-motility system in M. xanthus functions as a central hub of mechanosensing-based reversal control, modulating cell reversal in response to environmental mechanical cues. In Chapter 4, I constructed an agent-based model to investigate the optimal motility strategies for nutrient consumption by M. xanthus during its solitary predation. For different nutrient source types and their uptake latencies, the model identifies 'explore', 'inch', and 'fast explore' as the three most effective motility strategies. Variability in velocity and cell reversal period changes the optimal strategies from 'explore' mode to 'revisit' mode and to 'speed-controlled explore' mode, respectively, for massive remains of prey nutrient sources with moderate uptake latency. The experimental observation that solitary M. xanthus cells combined the 'revisit' and 'inch' mode—as predicted by the model for nutrient acquisition respectively from prey remains and macromolecules—suggests that some of the dead preys may not release its cellular contents immediately and that release of molecular nutrients may require multiple digestion cycles. This model provides insights into the functional role of complex motility regulation in M. xanthus during solitary predation. / Doctor of Philosophy / A fundamental question in biology is how a cell responds to physical, chemical and biological stimuli. Such responses are usually mediated by complex coupling between multiple cellular processes. Bacterial motility and its regulation present many excellent examples of this kind. This dissertation focuses on Myxococcus xanthus, a model organism for bacterial social behavior due to the highly coordinated motility of cells in M. xanthus colonies and their functional cooperation. In this dissertation, I built theoretical models to study the motility regulation in M. xanthus, which is essential for understanding the social behaviors and survival in this bacterium. The specific focuses are to comprehend how environmental mechanical cues regulate M. xanthus's motility, and how the observed motility regulation in M. xanthus facilitates its predatory behavior at the single-cell level. The key aspect of this work is to construct a modeling framework to provide coherent explanations for the experimental observations. It is anticipated that the hypotheses generated through modeling will guide new experiments in the field of myxobacterial biology. The findings offer general insights into how bacterial cells sense, respond, and adapt to the chemical, physical, and biological cues.

Natural populations may be managed by humans for a number of reasons, with mathematical modelling playing an increasing role in the planning of such management and control strategies. In an increasingly heterogeneous, or `patchy' landscape, the interactions between distinct groups of individuals must be taken into account to predict meaningful management strategies. Invasive control strategies, involving reduction of populations, such as harvesting or culling have been shown to cause a level of disturbance, or spatial perturbation, to these groups, a factor which is largely ignored in the modelling literature. In this thesis, we present a series of deterministic, differential equation models which are used to investigate the impact of this disturbance in response to control. We address this impact in two scenarios. Firstly, in terms of a harvested population, where extinction must be prevented whilst maximising the yield obtained. Secondly, we address the impact of disturbance in an epidemic model, where the aim of the control strategy is to eradicate an endemic pathogen, or to prevent the invasion of a pathogen into a susceptible population. The movement of individuals between patches is modelled as both a constant rate, and a function which is increasing with population density. Finally, we discuss the 'optimal' control strategy in this context. We find that, whilst a population harvested from a coupled system is able to produce an inflated yield, this coupling can also cause the population to be more resistant to higher harvesting efforts, increasing the effort required to drive the population to extinction. Spatial perturbation raises this extinction threshold further still, providing a survival mechanism not only for the individuals that avoid being killed, but for the population as a whole. With regards to the eradication of disease, we show that disturbance may either raise or lower the pathogen exclusion threshold depending on the particular characteristics of the pathogen. In certain cases, we have shown that spatial perturbation may force a population to be susceptible to an infectious invasion where its natural carrying capacity would prevent this.

The human immunodeficiency virus (HIV) epidemic is far from over. Antiretroviral therapy (ART) is effective at suppressing viral replication within a patient but it must be taken daily and is life-long. Therefore, the development of a therapy that could induce drug-free remission or constitute a functional cure is a key focus of HIV research. In this thesis I explore three mechanisms which could lead to more individuals being able to control their viraemia in the absence of ART: (1) T-cell immunity, (2) early initiation of ART, and (3) viral evolution. Firstly, a strong HIV-specific T-cell response has been linked to rare cases of spontaneous viral control, but the extent to which this arm of the immune response contributes to viral control is debated. Several types of data are used to answer this question, including the rate at which the virus evolves to escape the CD8+ T-cell response. I study the frequency of incident immune escape in the largest cohort used for this purpose to date. Secondly, some patients, with characteristics dissimilar to spontaneous HIV controllers, are able to control the virus for years after the interruption of ART that was initiated early in infection. I use mathematical models to investigate a new hypothesis for the differing outcomes of early- and late- initiated ART. Thirdly, since HIV is a relatively new infection of humans it is still adapting to its new host. Recent studies suggest that the virus could be evolving towards decreased virulence at the population level. I study whether the widespread administration of ART has the potential to alter the course of virulence evolution and might result in a further attenuated virus. I conclude by discussing the implications of these results for viral control at the individual level and also for population level epidemic control.

Concentrated solar power (CSP) is an efficient means of renewable energy that makes use of solar radiation to produce electricity instead of making use of conventional fossil fuel techniques such as burning coal. The aim of this study is the simulation and characterisation of a CSP plant in order to gain a better understanding of the dominant plant dynamics. Due to the nature of the study, the dissertation is divided into two main parts namely the simulation of a CSP plant model and the characterisation of the plant model. Modelling the CSP plant takes the form of developing an accurate Flownex® model of a 40 MW combined cycle CSP plant. The model includes thermal energy storage as well as making use of a duct burner. The Flownex® model is based on an existing TRNSYS model of the same plant. The Flownex® model is verified and validated, by making use of a bottom-up approach, to ensure that the developed model is in fact correct. The characterisation part of this dissertation involves evaluating the dynamic responses unique to that of a CSP plant as stated in the literature. This involves evaluating the dominant dynamic behaviour, the presence of resonant and anti-resonant modes found within the control bandwidth, and the change in the dynamics of the plant as the plants’ operating points change throughout the day. Once the developed model is validated, characterisation in the form of evaluating the open loop local linear models of the plant is implemented. In order to do so, these models are developed based on model identification processes, which include the use of system identification software such as Matlab® SID Toolbox®. The dominant dynamic behaviour of the plant model, obtained from the developed local linear models, represents that of an over damped second order system that changes as the operating points of the plant change; with the models’ time responses and the bandwidth decreasing and increasing respectively as the thermal energy inputs to the plant increases. The frequency response of the developed local linear models also illustrates the presence of resonant and antiresonant modes found within the control bandwidth of the solar collector field’s temperature response. These modes however are not found to be present in the mechanical power output response of the plant. The use of adaptive control, such as feedforward and gain-scheduled controllers, for the plant should be developed to compensate for the dynamic behaviours associated with that of a CSP plant. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

Concentrated solar power (CSP) is an efficient means of renewable energy that makes use of solar radiation to produce electricity instead of making use of conventional fossil fuel techniques such as burning coal. The aim of this study is the simulation and characterisation of a CSP plant in order to gain a better understanding of the dominant plant dynamics. Due to the nature of the study, the dissertation is divided into two main parts namely the simulation of a CSP plant model and the characterisation of the plant model. Modelling the CSP plant takes the form of developing an accurate Flownex® model of a 40 MW combined cycle CSP plant. The model includes thermal energy storage as well as making use of a duct burner. The Flownex® model is based on an existing TRNSYS model of the same plant. The Flownex® model is verified and validated, by making use of a bottom-up approach, to ensure that the developed model is in fact correct. The characterisation part of this dissertation involves evaluating the dynamic responses unique to that of a CSP plant as stated in the literature. This involves evaluating the dominant dynamic behaviour, the presence of resonant and anti-resonant modes found within the control bandwidth, and the change in the dynamics of the plant as the plants’ operating points change throughout the day. Once the developed model is validated, characterisation in the form of evaluating the open loop local linear models of the plant is implemented. In order to do so, these models are developed based on model identification processes, which include the use of system identification software such as Matlab® SID Toolbox®. The dominant dynamic behaviour of the plant model, obtained from the developed local linear models, represents that of an over damped second order system that changes as the operating points of the plant change; with the models’ time responses and the bandwidth decreasing and increasing respectively as the thermal energy inputs to the plant increases. The frequency response of the developed local linear models also illustrates the presence of resonant and antiresonant modes found within the control bandwidth of the solar collector field’s temperature response. These modes however are not found to be present in the mechanical power output response of the plant. The use of adaptive control, such as feedforward and gain-scheduled controllers, for the plant should be developed to compensate for the dynamic behaviours associated with that of a CSP plant. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

After undergoing a study about current engine modelling and mapping approaches as well as the engine modelling requirements for different applications, a major problem found to be present is the extensive and time consuming mapping procedure that every engine has to go through so that all control parameters can be derived from experimental data. To improve this, a cycle-by-cycle modelling approach has been chosen to mathematically represent reciprocating engines starting by a complete dynamics crankshaft mechanism model which forms the base of the complete engine model. This system is modelled taking into account the possibility of a piston pin offset on the mechanism. The derived Valvetrain model is capable of representing a variable valve lift and phasing Valvetrain which can be used while modelling most modern engines. A butterfly type throttle area model is derived as well as its rate of change which is believed to be a key variable for transient engine control. In addition, an approximation throttle model is formulated aiming at real-time applications. Furthermore, the engine inertia is presented as a mathematical model able to be used for any engine. A spark ignition engine simulation (SIES) framework was developed in MATLAB SIMULINK to form the base of a complete high fidelity cycle-by-cycle simulation model with its major target to provide an environment for virtual engine mapping procedures. Some experimental measurements from an actual engine are still required to parameterise the model, which is the reason an engine mapping (EngMap) framework has been developed in LabVIEW, It is shown that all the moving engine components can be represented by a single cyclic variable which can be used for flow model development.

<p>I Australien är vattenresurserna begränsade. För lantbrukare är tillgängligheten på vatten mycket viktig. På grund av det torra klimatet kan inte de Australiensiska bönderna förlita sig på nederbörden. Bevattningssystemen är därför en viktig del i jordbrukningsindustrin.</p><p>Bevattningsområdet i Coleambally ligger i södra New South Wales nära gränsen till staten Victoria. Bevattningsnätet i Coleambally förser ofta bevattningskanalerna med för mycket vatten för att vara säker på att lantbrukarna får den mängd vatten de behöver. På grund av denna tillförsel av överskottvatten går stor mängd av vatten förlorad. Design av ett bättre reglersystem skulle kunna minska den stora förlusten av vatten.</p><p>En matematisk modell beskrivande dynamiken av bevattningssystemet är ett bra redskap vid en design av ett bättre reglersystem. Syftet med det här projektet var att genom systemidentifiering bygga en matematisk modell av bevattningssystemet. Modellen syftade till att beskriva vattennivån i en sträcka av bevattningskanalerna, sträckan i kanalen skulle ha två olika typer av luckor, en typ där vattnet strömmar över luckan och en annan typ där vattnet strömmar under luckan. En modell byggdes genom att parametrar från en vald modellstruktur estimerades från experimentella data. Data samlades under ett experiment som utfördes på en bevattningskanal i Coleambally.</p><p>Resultatet från systemidentifieringen blev en första ordningens output error grey box modell. Modellen visar goda resultat vid validering och bör kunna användas vid design av ett bättre reglersystem. Modellen visar så god överensstämmelse med valideringsdata att den även kan användas för olika fall av simulering.</p> / <p>Water resources in Australia are limited. For a farmer the access to water is crucial and due to the dry climate the farmers in Australia can not rely on precipitation. Irrigation is therefore a very important part of the farming industry.</p><p>The Coleambally Irrigation Area is situated in the southern parts of New South Wales close to the border of Victoria. The Irrigation Network often supplies the irrigation channels with too much water to be sure that the demand of water is satisfied. Due to this over supply a great amount of water gets wasted. Design of a bettercontrol system would be able to reduce the water wastage.</p><p>A mathematical model describing the dynamics of the irrigation system can be used as a tool for the control system design. The aim of this project was to build a mathematical model with the system identification approach. The model should be able to describe the downstream water level of a single pool of an irrigation channel which has both undershot and overshot gates. A model was built by estimating unknown parameters of a chosen model structure from a set of experimental data. The data was collected from an experiment performed on the real irrigation system in Coleambally.</p><p>The result of the system identification was a first order output error grey box model. The model performs well on validation data and may therefore be used for design of a more efficient control system. The model gave such good results that it additionally may be used for various simulation purposes.</p>

<p>The National Curriculum Statement introduced mathematical literacy officially in 2006. Learners in general perform poorly at mathematics in South Africa but there is strong belief that learners should graduate from schools sufficiently literate to deal with the mathematical issues they will encounter in out-of-school situations. Based on this, this study is an investigation of the contexts, which grades 8 &ndash / 10 learners would prefer to engage with mathematics. The aim of this study was thus to investigate mathematical literacy in relation to learners&rsquo / motivations for the contexts they would prefer to deal with in mathematical literacy. The emphasis of the study is to concentrate on learner&rsquo / s written motivations for mathematical contexts. Data were collected using a questionnaire that deals with contexts for mathematics.</p>