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The BACOLI package is a numerical software package for solving parabolic partial differential equations in one spatial dimension. It implements a B-spline collocation method for the spatial discretization of a system of partial differential equations. The resultant ordinary differential equations together with the boundary conditions form a system of differential-algebraic equations. The differential-algebraic equations are then solved using the DASSL solver. The BACOLI software package features adaptive error control in the temporal and spatial domains. The estimate of the temporal error is controlled through the DASSL solver. The estimate of the spatial error is controlled based on the difference between two solutions computed in the BACOLI software package. This difference gives an estimation of the error. If this error estimate does not meet the user-supplied tolerance, then the spatial mesh is changed. The BACOLI software package can only solve parabolic partial differential equations that depend on spatial derivatives. In this thesis, the BACOLI software package is modified to solve a broader spectrum of problems. In fact, after some modifications, the extended BACOLI software package can solve systems of parabolic partial differential equations and time-dependent equations that do not depend on spatial derivatives. We apply this extended software package to solve the monodomain model of cardiac electrophysiology. The monodomain model is a multi-scale mathematical model for the evolution of the electrical potential in cardiac tissue that couples the ionic currents at the cellular scale with their propagation at the tissue scale. Because of their local nature, the mathematical models of a single cell have no dependency on spatial derivatives whereas the models at the tissue level do. The heart models considered in our numerical experiments use various cardiac cell models. We find that solving the heart models through the extended BACOLI software package, in some cases, leads to a speed-up in comparison with the Chaste software package, which is a powerful, widely used, and well-respected software package for heart simulation.

The work presented within this dissertation focusses on the development of affinite element method (FEM) model for the microwave absorption and heat transfer within a microwave combination washer dryer (MCWD). FEM will be used to aid in the implementation of more advanced fluid dynamics such as laminar or turbulent flow, that may be present within the system. The intended use of the model is to aid a South African based company in the development of a control system for the MCWD. The model development presented focusses on the washing cycle of the MCWD and will therefore not take into account the drying cycle of the system. The target of the microwave heating within the model will be distilled water as the dielectric constant of water is a know quantity. Various literature sources on microwave absorption and heat transfer models can be found, but none specific to the topic of the combination washer dryer. By reviewing literature from various sources, the finite element method was selected as the modelling technique and the COMSOL® software package was selected as the tool for developing the model. A model for the MCWD will be developed within the COMSOL® environment which in turn implements FEM as a technique to solve the model. The model development is broken into nine stages. Stage one start by modelling the heat transfer within the washing drum. Each consecutive stage expands the model by adding features or model domains. Model verification takes place in parallel to the development by verifying each stage before moving to the next stage. The stage eight and nine models, which represent a full three dimensional model of the system, are selected to be validated as the final models. Stage eight models the system without an enclosure and makes use of convective cooling boundary conditions on the boundary of the air enclosed within the system enclosure. Stage stage nine models the system with the aluminium enclosure of the system and also implements convective cooling boundary conditions on the outer boundary of the aluminium. The boundary between the enclosed air and aluminium enclosure is implemented as a normal convective heat transfer boundary between a gas and solid. Data capturing is done using the dSpace® platform. Sensors to log the microwave power and system temperature are selected and optimal placement of the sensors is evaluated. The capturing platform is interfaced to the sensors by an in-house developed signal conditioning board. Model validation is completed by comparing the response of the model to the practical system. Numerous simulations are completed to select the optimal configuration of the model that provides the optimal response. The stage eight model was found to be more accurate then the stage nine model with respect to the difference between the simulated and expected response over the whole domain of the transient temperature response. A further method implemented to easily compare the results of various simulations is by comparing the average absolute temperature of the response over the whole domain of the transient response. The average absolute temperature is calculated by taking absolute difference between the expected results and the model response at each time step within the response domain and then to average the absolute difference. This enables the comparison of two responses using two values. Needles to say this method should not be used alone and should be used in conjunction with a comparison over the full response domain. Use of the average absolute temperature difference is aimed at filtering the results from a selection of results which warrants a more in depth investigation. Using a comparison of the average absolute temperature difference of the target in the 500 W model, it was found that their respective values are 2:92 °C and 11:36 °C. The stage eight model computation time was far less than the stage nine model and is therefore recommended for further development. The final conclusion was made that the stage eight model represents the system fairly accurately at this stage and warrants further development by expanding the model to account for the drying cycle of the MCWD. The term fairy accurate is used to describe the results as further improvement of the model is definitely possible with regards to the accuracy of the transient response of the system. Further improvement of the model response may be possible by implementing a smaller mesh size or launching an in depth study on the effect of the various material thermal properties on the response of the system during various stages. For instance below a certain temperature the response closely represents the expected response and above that temperature the response various greatly from the expected response. Future work on the model include, to change the target from distilled water to an actual representation of the textiles intended to be washed within the MCWD. This will require a study into how the various parameters such as the density and dielectric constant, of the heterogeneous mixtures of textiles and water, can be combined for use into the model. As a next step in the expansion of the model, the model can be configured to account for the drying cycle of the system which will require the model to account for the phase changes that the water will undergo. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013.

The work presented within this dissertation focusses on the development of affinite element method (FEM) model for the microwave absorption and heat transfer within a microwave combination washer dryer (MCWD). FEM will be used to aid in the implementation of more advanced fluid dynamics such as laminar or turbulent flow, that may be present within the system. The intended use of the model is to aid a South African based company in the development of a control system for the MCWD. The model development presented focusses on the washing cycle of the MCWD and will therefore not take into account the drying cycle of the system. The target of the microwave heating within the model will be distilled water as the dielectric constant of water is a know quantity. Various literature sources on microwave absorption and heat transfer models can be found, but none specific to the topic of the combination washer dryer. By reviewing literature from various sources, the finite element method was selected as the modelling technique and the COMSOL® software package was selected as the tool for developing the model. A model for the MCWD will be developed within the COMSOL® environment which in turn implements FEM as a technique to solve the model. The model development is broken into nine stages. Stage one start by modelling the heat transfer within the washing drum. Each consecutive stage expands the model by adding features or model domains. Model verification takes place in parallel to the development by verifying each stage before moving to the next stage. The stage eight and nine models, which represent a full three dimensional model of the system, are selected to be validated as the final models. Stage eight models the system without an enclosure and makes use of convective cooling boundary conditions on the boundary of the air enclosed within the system enclosure. Stage stage nine models the system with the aluminium enclosure of the system and also implements convective cooling boundary conditions on the outer boundary of the aluminium. The boundary between the enclosed air and aluminium enclosure is implemented as a normal convective heat transfer boundary between a gas and solid. Data capturing is done using the dSpace® platform. Sensors to log the microwave power and system temperature are selected and optimal placement of the sensors is evaluated. The capturing platform is interfaced to the sensors by an in-house developed signal conditioning board. Model validation is completed by comparing the response of the model to the practical system. Numerous simulations are completed to select the optimal configuration of the model that provides the optimal response. The stage eight model was found to be more accurate then the stage nine model with respect to the difference between the simulated and expected response over the whole domain of the transient temperature response. A further method implemented to easily compare the results of various simulations is by comparing the average absolute temperature of the response over the whole domain of the transient response. The average absolute temperature is calculated by taking absolute difference between the expected results and the model response at each time step within the response domain and then to average the absolute difference. This enables the comparison of two responses using two values. Needles to say this method should not be used alone and should be used in conjunction with a comparison over the full response domain. Use of the average absolute temperature difference is aimed at filtering the results from a selection of results which warrants a more in depth investigation. Using a comparison of the average absolute temperature difference of the target in the 500 W model, it was found that their respective values are 2:92 °C and 11:36 °C. The stage eight model computation time was far less than the stage nine model and is therefore recommended for further development. The final conclusion was made that the stage eight model represents the system fairly accurately at this stage and warrants further development by expanding the model to account for the drying cycle of the MCWD. The term fairy accurate is used to describe the results as further improvement of the model is definitely possible with regards to the accuracy of the transient response of the system. Further improvement of the model response may be possible by implementing a smaller mesh size or launching an in depth study on the effect of the various material thermal properties on the response of the system during various stages. For instance below a certain temperature the response closely represents the expected response and above that temperature the response various greatly from the expected response. Future work on the model include, to change the target from distilled water to an actual representation of the textiles intended to be washed within the MCWD. This will require a study into how the various parameters such as the density and dielectric constant, of the heterogeneous mixtures of textiles and water, can be combined for use into the model. As a next step in the expansion of the model, the model can be configured to account for the drying cycle of the system which will require the model to account for the phase changes that the water will undergo. / Thesis (MIng (Computer and Electronic Engineering))--North-West University, Potchefstroom Campus, 2013.

Even though the use of renewable energy in electricity generation has significantly increased over time, coal is projected to remain as the primary fuel in electricity generation worldwide in the next decades due to its availability, stability of supply and cost. However, coal-fired power plants are the largest stationary sources of CO2 emissions that contribute to global warming. Several technologies have been developed to mitigate CO2 emissions from coal-fired power plants. Oxy-combustion is a promising pathway to capture CO2 from coal fired power plants that competes favourably with other CO2 capture technology pathways such as post-combustion and pre-combustion. Oxy-combustion has attracted attention because it provides a CO2-enriched flue gas stream which can be further purified using a relatively simple multi-stage compression and cooling processes. Currently, there is no oxy-coal-fired power plant in commercial-scale operation. Thus, the transition towards commercial scale operation is the main challenge for this technology. The CO2 capture and purification unit (CO2CPU) is an important unit in oxy-coal-fired power plants that determine the quality of the CO2 product and energy consumption of the power plants. Several studies published on the CO2CPU process have evaluated the performance of this system at steady state. Insight regarding the dynamic behaviour of the CO2CPU process is very limited and a mechanistic dynamic model of the CO2CPU is not available in open literature. Thus, research on dynamic modelling and control system development is still required to demonstrate the operability and controllability of this technology. This study aims to develop, test and validate a dynamic model of the CO2CPU for oxy-coal-fired power plants. Detailed mathematical models of each unit operation in the CO2CPU are provided in this study. The main challenge was to develop a dynamic model of a multi-stream heat exchanger that involves multiple process streams and encounters both condensing and boiling two phase flows. A dynamic model that is not computationally intensive, to slow down the entire CO2CPU plant model, and that can predict reasonable fluid temperatures in the multi-stream heat exchanger was developed in this study. The proposed multi-stream heat exchanger model was based on a shell and tube configuration that considers only axial changes in flow, i.e., a 1D model. Likewise, the two phase region in this unit was modelled using a homogenous model, which is a simplified discretized two-phase flow model that reduces the computational effort and complexity of the multi-stream heat exchanger process model. The homogenous model takes into account the changes in the fluid properties in the two phase region to calculate the heat transfer coefficients of the multi-stream heat exchanger models. To the author???s knowledge, the model presented in this study represents the first mechanistic process model that describes the transient behaviour of a CO2CPU for oxy-fired power plant. Two design configurations of the CO2CPU were considered in this study, i.e. the Air Products??? CO2CPU and the CanmetENERGY???s proprietary CO2CPU (CanCO2). Both plants are designed based on a two-stage flash separation process. The CanCO2 is an extended design of the Air Products??? CO2CPU. The presence of an external recycle stream , recycling a portion of the CO2 rich effluent gas stream from the first flash drum to the compressor train, in the CanCO2 is a major distinction between the two CO2CPU configurations and enhances the CO2 capture rate for the CanCO2 process. Nevertheless, the addition of this recycle stream makes the CanCO2 plant model convergence more challenging than the Air Products??? CO2CPU since it adds natural feedback into the system. A systematic procedure to perform the process integration of all the unit operations considered in the CO2CPU flowsheets was developed and presented in this study. Stand-alone unit operation models were developed, coded and then connected together one at a time. Dynamic models of the Air Products??? CO2CPU and the CanCO2 were developed and validated at steady state using design data. Reasonable agreement between the developed models and the design data were obtained for both CO2CPU configurations. Several dynamic tests were performed to gain insight into the transient behaviour of the CO2CPU. The results obtained from the transient analyses clearly demonstrate that both CO2CPU plants are highly nonlinear processes. The CO2 recovery and the CO2 product purity obtained from the base case of both plants are similar, approximately at 89 wt% and 95 mol% respectively. The operating conditions of the first flash drum were found to play a key role on the CO2CPU performance of both plants. In addition, both models indicate that the CO2 recovery is more sensitive to the operating conditions than that of the CO2 product purity. The CO2 purity is more sensitive to the flue gas composition and responds to all changes performed in this study faster than the CO2 recovery. Because of the recycle stream, the CanCO2 response to all changes is slower than the Air Products??? CO2CPU. Nevertheless, the use of a recycle stream improves the CO2 recovery and increases the number of manipulated variables in the CanCO2, thus this system has more alternative control structures than the Air Products??? CO2CPU. The models developed in this study can be extended to include the controllability analysis and the control structure design for the CO2CPU; and the integration of oxy-boiler, steam cycle and also air separation unit (ASU) into a complete dynamic model of the oxy-fired power plant that will be very useful for oxyfuel combustion technology scale-up.

The objective of this dissertation is to extend the use of spatial predictive modelling for use by biosecurity agencies to help prevent the introductions of new and emerging invasive plants (i.e., pests). A critical review of international and national policy instruments found that they did not effectively articulate how spatial predictive modelling could be incorporated into the biosecurity toolbox. To determine how spatial predictive modelling could be extended I modelled the potential distribution of Tamarix and Lythrum salicaria in Prairie Canada using a genetic algorithm. New seasonal growth data was used to interpolate a growing degree-day’s risk surface for L. salicaria. Models were developed using suites of predictive variables as well as different data partitioning methods and evaluated using different performance measures. Expert evaluation was found to important in final model selection. The results indicated that both invasive plants have yet to reach their potential distribution in Prairie Canada. The spatial models can be used to direct risk-based surveillance efforts and to support biosecurity policy decisions. The results of this dissertation conclude that spatial predictive modelling is an informative tool that needs to be incorporated into the biosecurity toolbox. A phytosanitary standard is proposed to guide toolbox development.

This thesis addresses the question of whether the participants of Britain and Ireland’s Next Top Model act as cultural intermediaries. There is a gap in the literature surrounding the role of participants in reality television programs. Through this analysis, I found the ability of the participant-models to act as cultural intermediaries on BINTM is limited because of their lack of experience, knowledge, and skills. Although they develop their skills throughout the program, they are unable to move up the entrenched hierarchy that exists in the program and that is actively maintained by the judges and other program participants. The participant-models’ positions are constantly challenged as they struggle to prove themselves as models. Methodologically, I undertake a discourse analysis of series eight of BINTM and include two other data sources to give my research greater context and validity. By drawing on the work of Bourdieu and more contemporary scholars of cultural intermediaries, I examine how the participant-models struggle to gain cultural capital and briefly act as cultural intermediaries before the authority and status of the judges is reasserted. In order to address issues related to gender, I also draw on the work of feminist scholars who have expanded on the work of Bourdieu. The hierarchy of the program brings to the surface how the ability to act as a cultural intermediary can best be understood in terms of a continuum, and an individual’s position on the continuum is constantly shifting depending on their ability to frame goods, their level of expertise, and their impact on others. In other words, the ability to act as a cultural intermediary changes depending on the level of acquired cultural capital. Based on my findings, I argue that all models are not cultural intermediaries; rather, only the models that have a high status, acknowledged expertise and level of legitimacy are able to act as cultural intermediaries.

One-dimensional steady flow pollutant transport models assume that the river reach modelled has a uniform cross-sectional shape which manifests as a constant average velocity in the model equations. Rarely do rivers meet this criterion. Their channels are seldom uniform in shape, but rather alternate in a quasi-periodic manner between pool and riffle sections. This bedform sequencing imparts a corresponding variation in the average cross-sectional velocity which is not accounted for in constant velocity transport models. The literature points out that the pool and riffle planform may be the reason for the sometimes poor predictions obtained from these models. This thesis confirms that the fluctuation in average cross-sectional velocity caused by the pool and riffle planform does have a marked effect on transport in rivers. The pool and riffle planform promotes an enhanced decay of a pollutant when a first order biochemical reaction is simulated. This effect becomes more pronounced as flow declines. The reason for this is that travel time in a pool and riffle channel is greater than for a uniformly shaped channel. Current one-dimensional models assume a uniform channel and therefore overestimate the velocity of a substance moving downstream. To show this an equation is developed that describes the variation in average cross-sectional velocity along a pool and riffle channel. The parameters of the equation can be easily evaluated for any river. The equation is incorporated into a mass balance analysis and a new form of the river transport model is derived. Analysis shows that the transport of a substance in a pool and riffle channel is governed by travel velocity which is different from the average cross-sectional velocity used in the traditional advection model. Replacing average velocity with travel velocity provides a simple fix for the traditional model. The new transport model is tested on the Athabasca River with excellent results. The variable velocity model successfully simulates the DO dynamics on a 550 kilometre stretch of the river. This suggests that the model has good potential for simulating pollutant transport in other rivers. Since analysis shows that the effect of the pool and riffle planform on contaminant transport is magnified at low flow levels, the model has good potential for use in determining TMDLs for contaminants, because these regulatory levels are set for low flow conditions.

The focus of this thesis is the inclusion of stochasticity into mathematical models of assembly with particular interest to the in vitro polymerisation of intermediate filaments, one of three components of the cytoskeleton. From the chemical master equation (CME), two additional models (the reaction rate equations or RREs and the two-moment approximation equations or 2MA equations) are derived. As analysis of the CME is generally intractable, we present the stochastic simulation algorithm (SSA) as a means of reproducing the most probable state of the CME at a given time. The results from the SSA are compared to simulations of both the RREs and the 2MA equations and we find that the three models are in good agreement. Further, the numerical results are compared to mean lengths and length distributions of experimental data which all models are shown to mimic. Mathematical analyses of the RREs demonstrate the conservation of mass in the system, and the unique positive equilibrium is proven to be globally asymptotically stable. Further, the 2MA equations are also shown to have conservation of mass and to possess an analogous equilibrium to the one found in the case of the RREs. In general, this study illustrates how randomness can be incorporated in polymerisation models and highlights the advantages and disadvantages of the different approaches.

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