The vital signs monitoring data of an infant receiving intensive care are a rich source of information about its health condition. One major concern about the state of health of such patients is the onset of neonatal sepsis, a life-threatening bloodstream infection. As early signs are subtle and current diagnosis procedures involve slow laboratory testing, sepsis detection based on the monitored physiological dynamics is a clinically significant task. This challenging problem can be thoroughly modelled as real-time inference within a machine learning framework. In this thesis, we develop probabilistic dynamical models centred around the goal of providing useful predictions about the onset of neonatal sepsis. This research is characterised by the careful incorporation of domain knowledge for the purpose of extracting the infant’s true physiology from the monitoring data. We make two main contributions. The first one is the formulation of sepsis detection as learning and inference in an Auto-Regressive Hidden Markov Model (AR-HMM). The model investigates the extent to which physiological events observed in the patient’s monitoring traces could be used for the early detection of neonatal sepsis. In addition, the proposed approach involves exact marginalisation over missing data at inference time. When applying the ARHMM on a real-world dataset, we found that it can produce effective predictions about the onset of sepsis. Second, both sepsis and clinical event detection are formulated as learning and inference in a Hierarchical Switching Linear Dynamical System (HSLDS). The HSLDS models dynamical systems where complex interactions between modes of operation can be represented as a twolevel hidden discrete hierarchical structure. For neonatal condition monitoring, the lower layer models clinical events and is controlled by upper layer variables with semantics sepsis/nonsepsis. The model parameterisation and estimation procedures are adapted to the specifics of physiological monitoring data. We demonstrate that the performance of the HSLDS for the detection of sepsis is not statistically different from the AR-HMM, despite the fact that the latter model is given “ground truth” annotations of the patient’s physiology.

Recent studies demonstrate that mechanical deformation of small volume systems can be significantly different from those of the bulk. One such interesting length scale dependent property is the increase in the yield stress with decrease in diameter of micrometer rods, particularly when the diameter is below a micrometer. Intermittent flow may also result when the diameter of the rods is decreased below a certain value. The second such property is the intermittent plastic deformation during nano-indentation experiments. Here again, the instability manifests due to smallness of the sample size, in the form of force fluctuations or displacement bursts. The third such length scale dependent property manifests as ’smaller is stronger’ property in indentation experiments on thin films, commonly called as the indentation size effect (ISE). More specifically, the ISE refers to the increase in the hardness with decreasing indentation depth, particularly below a fraction of a micrometer depth of indentation. The purpose of this thesis is to extend nonlinear dynamical approach to plastic deformation originally introduced by Anantha krishna and coworkers in early 1980’s to nano and micro-indentation process. More specifically, we address three distinct problems : (a) intermittent force/load fluctuations during displacement controlled mode of nano-indentation, (b) displacement bursts during load controlled mode of nano-indentation and (c) devising an alternate framework for the indentation size effect. In this thesis, we demonstrate that our approach predicts not just all the generic features of nano-and micro-indentation and the ISE, the predicted numbers also match with experiments. Nano-indentation experiments are usually carried-out either in a displacement controlled (DC) mode or load controlled (LC) mode. The indenter tip radius typically ranges from few tens of nanometer to few hundreds of nanometers-meters. Therefore, the indented volume is so small that the probability of finding a dislocation is close to zero. This implies that dislocations must be nucleated for further plastic deformation to proceed. This is responsible for triggering intermittent flow as indentation proceeds. While several load drops are seen beyond the elastic limit in the DC controlled experiments, several displacement jumps are seen in the LC experiments. In both cases, the stress corresponding to load maximum on the elastic branch is close to the theoretical yield stress of an ideal crystal, a feature attributed to the absence of dislocations in the indented volume. Hardness is defined as the ratio of the load to the imprint area after unloading and is conventionally measured by unloading the indenter from desired loads to measure the residual plastic imprint area. Then, the hardness so calculated is found to increase with decreasing indentation depth. However, such size dependent effects cannot be explained on the basis of conventional continuum plasticity theories since all mechanical properties are independent of length scales. Early theories suggest that strong strain gradients exist under the indenter that require geometrically necessary dislocations (GNDs) to relax the strain gradients. In an effort to explain the the size effect, these theories introduce a length scale corresponding to the strain gradients. One other feature predicted by subsequent models of the ISE is the linear relation between the square of the hardness and the inverse of the indentation depth. Early investigations on the ISE did recognize that GNDs were required to accommodate strain gradients and that the hardness H is determined by the sum of the statistically stored dislocation (SSD) and GND densities. Following these steps, Nix and Gao derived an expression for the hardness as a function of the indentation depth z. The relevant variables are the SSD and GND densities. An expression for the GND density was obtained by assuming that the GNDs are contained within a hemispherical volume of mean contact radius. The authors derive an expression for the hardness H as a function of indentation depth z given by [ HH 0 ]2 = 1+ zz ∗ . The intercept H0 represents the hardness arising only from SSDs and corresponds to the hardness in the limit of large sample size. The slope z ∗ can be identified as the length scale below which the ISE becomes significant. The authors showed that this linear relation was in excellent agreement with the published results of McElhaney et al for cold rolled polycrystalline copper and single crystals of copper, and single crystals of silver by Ma and Clarke. Subsequent investigations showed that the linear relationship between H2 verses 1/z breaks down at small indentation depths. Much insight into nano-indentation process has come from three distinct types of studies. First, early studies using bubble raft indentation and later studies using colloidal crystals (soft matter equivalent of the crystalline phase) allowed visualization of dislocation nucleation mechanism. Second, more recently, in-situ transmission electron microscope studies of nano-indentation experiments have been useful in understanding the dislocation nucleation mechanism in real materials. Third, considerable theoretical understanding has come largely from various types of simulation studies such as molecular dynamics (MD) simulations, dis¬location dynamics simulations and multiscale modeling simulations (using MD together with dislocation dynamics simulations). A major advantage of simulation methods is their ability to include a range of dislocation mechanisms participating in the evolution of dislocation microstructure starting from the nucleation of a dislocation, its multiplication, formation of locks, junctions etc. However, this advantage is offset by the serious limitations set by short time scales inherent to the above mentioned simulations and the limited size of simulated volumes that can be implemented. Thus, simulation approaches cannot impose experimental parameters such as the indentation rates or radius of the indenter and thickness of the sample, for example in MD simulations. Indeed, the imposed deformation rates are often several orders of magnitude higher than the experimental rates. Consequently, the predicted values of force, indentation depth etc., differ considerably from those reported by experiments. For these reasons, the relevance of these simulations to real materials has been questioned. While several simulations, particularly MD simulation predict several force drops, there are no simulations that predict displacement jumps seen in LC mode experiments. The inability of simulation methods to adopt experimental parameters and the mismatch of the predicted numbers with experiments is main motivation for devising an alternate framework to simulations that can adopt experimental parameters and predict numbers that are comparable to experiments. The basic premise of our approach is that describing time evolution of the relevant variables should be adequate to capture most generic features of nano and micro-indentation phenomenon. In the particular case under study, this point of view is based on the following observation. While one knows that dislocations are the basic defects responsible for plastic deformation occurring inside the sample, the load-indentation depth curve does not include any information about the spatial location of dislocation activity inside the sample. In fact, the measured load and displacement are sample averaged response of the dislocation activity in the sample. This suggests that it should be adequate to use sample averaged dislocation densities to obtain load-indentation depth curve. Keeping this in mind, we devise a method for calculating the contribution from plastic deformation arising from dislocation activity in the entire sample. This is done by setting up rate equations for the relevant sample averaged dislocation densities. The first problem we consider is the force/load fluctuations in displacement controlled nano-indentation. We devise a novel approach that combines the power of nonlinear dynamics with the evolution equations for the mobile and forest dislocation densities. Since the force serrations result from plastic deformation occurring inside the sample, we devise a method for calculating this contribution by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities. The approach follows closely the steps used in the Anantha krishna (AK) model for the Portevin-Le Chatelier (PLC) effect. The model includes nucleation, multiplication and propagation of dislocation loops in the time evolution equation for the mobile dislocation density. We also include other well known dislocation transformation mechanisms to forest dislocation. Several of these dislocation mechanisms are drawn from the AK model for the PLC effect. To illustrate the ability of the model to predict force fluctuations that match experiments, we use the work of Kiely at that employs a spherical indenter. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rate, the radius the indenter etc. The model predicts all the generic features of nano-indentation such as the Hertzian elastic branch followed by several force drops of decreasing magnitudes, and residual plas¬ticity after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted values for all the quantities are close to those reported by experiments. Our model allows us to address the indentation-size effect including the ambiguity in defining the hardness in the force drop dominated regime. At large indentation depths where the load drops disappear, the hardness shows decreasing trend, though marginal. The second problem we consider is the load controlled mode of indentation where sev¬eral displacement jumps of decreasing magnitudes are seen. Even though, the LC mode is routinely used in nano-indentation experiments, there are no models or simulations that predict the generic features of force-displacement curves, in particular, the existence of sev¬eral displacement jumps of decreasing magnitudes. The basic reason for this is the inability of these methods to impose constant load rate during displacement jumps. We then show that an extension of the model for the DC mode predicts all the generic features when the model is appropriately coupled to an equation defining the load rate. Following the model for DC mode, we retain the system of coupled nonlinear time evolution equations for mobile and forest dislocation densities that includes nucleation, multiplication, and propagation threshold mechanisms for mobile dislocations, and other dislocation transformation mechanisms. The commonly used Berkovich indenter is considered. The equations are then coupled to the force rate equation. We demonstrate that the model predicts all the generic features of the LC mode nano-indentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes, and residual plasticity after unloading for a range of model parameter values. In this range, the predicted values of the load, displacement jumps etc., are similar to those found in experiments. Further, optimized set of parameter values can be easily determined that provide a good fit to the load-indentation depth curve of Gouldstone et al for single crystals of Aluminum. The stress corresponding to the maximum force on the Berkovich elastic branch is close to the theoretical yield stress. We also elucidate the ambiguity in defining hardness at nanometer scales where the displacement jumps dominate. The approach also provides insights into several open questions. The third problem we consider is the indentation size effect. The conventional definition of hardness is that it is the ratio of the load to the residual imprint area. The latter is determined by the residual plastic indentation depth through area-depth relation. Yet, the residual plastic indentation depth that is a measure of dislocation mobility, never enters into most hardness models. Rather, the conventional hardness models are based on the Taylor relation for the flow stress that characterizes the resistance to dislocation motion. This is a complimentary property to mobility. Our idea is to provide an alternate way of explaining the indentation size effect by devising a framework that directly calculates the residual plastic indentation depth by integrating the Orowan expression for the plastic strain rate. Following our general approach to plasticity problems, we set-up a system of coupled nonlinear time evolution equations for the mobile, forest (or the SSD) and GND densities. The model includes dislocation multiplication and other well known dislocation transformation mechanisms among the three types of dislocations. The main contributing factor for the evolution of the GND density is determined by the mean strain gradient and the number of sites in the contact area that can activate dislocation loops of a certain size. The equations are then coupled to the load rate equation. The ability of the approach is illustrated by adopting experimental parameters such as the indentation rates, the geometrical quantities defining the Berkovich indenter including the nominal tip radius and other parameters. The hardness is obtained by calculating the residual plastic indentation depth after unloading by integrating the Orowan expression for the plastic strain rate. We demonstrate that the model predicts all features of the indentation size effect, namely, the increase in the hardness with decreasing indentation depth and the linear relation between the square of the hardness and inverse of the indentation depth, for all but 200nm, for a range of parameter values. The model also predicts deviation from the linear relation of H2 as a function of 1/z for smaller depths consistent with experiments. We also show that it is straightforward to obtain optimized parameter values that give a good fit to polycrystalline cold-worked copper and single crystals of silver. Our approach provides an alternate way of understanding the hardness and indentation size effect on the basis of the Orowan equation for plastic flow. This approach must be contrasted with most models of hardness that use the SSD and GND densities as parameters. The thesis is organized as follows. The first Chapter is devoted to background material that covers physical aspects of different kinds of plastic deformation relevant for the thesis. These include the conventional yield phenomenon and the intermittent plastic deformation in bulk materials in alloys exhibiting the Portevin-Le Chatelier (PLC) effect. We then provide background material on nano-and micro-indentation, both experimental aspects and the current status of the DC controlled and LC controlled modes of nano-indentation. Results of simulation methods are briefly summarized. The chapter also provides a survey of hardness models and the indentation size effect. A critical survey of experiments on dislocation microsructure that contradict / support certain predictions of the NixGao model. The current status of numerical simulations are also given. The second Chapter is devoted to introducing the basic steps in modeling plastic deformation using nonlinear dynamical approach. In particular, we describe how the time evolution equations are constructed based on known dislocation mechanisms such as nucleation, multiplication formations of junctions etc. We then consider a model for the continuous yield phenomenon that involves only the mobile and forest densities coupled to constant strain rate condition. This problem is considered in some detail to illustrate how the approach can be used for modeling nano-indentation and indentation size effect. The third Chapter deals with a model for displacement controlled nano-indentation. The fourth Chapter is devoted to adopting these equation to the load controlled mode of nano¬indentation. The fifth Chapter is devoted to modeling the indentation size effect based on calculating residual plastic indentation depth after unloading by using the Orowan’s expression for the plastic strain rate. We conclude the thesis with a Summary, Discussion and Conclusions.

No description available.

<p dir="ltr">The increasing availability of spatio-temporal information in the form of detailed time-resolved images sampled at very high framing rates has resulted in a search for mathematical techniques capable of extracting and relaying the pertinent underlying physics governing complex flows. Analysis relying on the usage of a solitary spectral, correlation, or modal decomposition techniques to identify dynamically significant information from large datasets may give an incomplete description of these phenomena. Moreover, fully resolved spatio-temporal measurements of these complex flow fields are needed for a complete and accurate description across a wide spectrum of length and time scales. The primary goals of this dissertation are address these challenges in two key aspects: (1) to improve and demonstrate the novel application of complementary data analysis and modal decomposition techniques to quantify the dynamics of flow systems that exhibit intricate patterns and behaviors in both space and time, and (2) to make advancements in achieving and characterizing high-resolution and high-speed quantitative measurements of turbulent mixing fields.</p><p dir="ltr">In the first goal, two canonical flow fields are considered, including an acoustically excited co-axial jet and a bluff-body stabilized flame. The local susceptibility of a nonreacting, cryogenic, coaxial-jet, rocket injector to transverse acoustics is characterized by applying dynamical systems theory in conjunction with complementary wavelet-based spectral decomposition to high-speed backlit images of flow field. The local coupling of the jet with external acoustics is studied as a function of the relative momentum flux ratio between the outer and inner jets, giving a quantitative description of the dynamical response of each jet to external acoustics as a function of the downstream distance from the nozzle.</p><p dir="ltr">Bluff bodies are a common feature in the design of propulsion systems owing to their ability to act as flame holders. The reacting wake behind the bluff body consists of a recirculation bubble laden with hot-products and wrapped between separated shear layers. The wake region of a bluff body is systematically investigated utilizing a technique known as robust dynamic mode decomposition (DMD) to discern the onset of the thermoacoustic instability mode, which is highly detrimental to aerospace propulsion systems. The approach enables quantification of the spatial distribution and behavior of coherent structures observed from different flows as a function of the equivalence ratio.</p><p dir="ltr">As modal decomposition techniques employ a certain degree of averaging in time, a novel space-and-time local filtering technique utilizing the well-defined characteristics of wavelets is introduced with a goal of temporally resolving the spatial evolution of irregular flow instabilities associated with specific frequencies. This provides insight into the existence of transient sub-modal characteristics representing intermittencies within seemingly stable modes. The flow fields obtained from the same two canonical flows are interrogated to demonstrate the utility of the technique. It has been shown that temporally resolved flow features obtained from wavelet filtering satisfactorily track the same modal featured derived from DMD, but reveal sub-modal spatial distortions or local non-stationarity of specific modal frequencies on a frame-by-frame basis.</p><p dir="ltr">Finally, to improve the ability to study the dynamical behavior of complex flows across the full range of spatio-temporal scales present, advancements are reported in the spatial and temporal quantitative measurement of the scalar quantities in turbulent mixing fields utilizing 100 kHz planar laser-induced fluorescence (PLIF) and Rayleigh scattering imaging of acetone. The imaging system provided a resolution of 55 µm with a field-of-view mapping of 18.5 µm/pixel on the camera sensor, which is three times better spatial resolution than the previous reported work to-date for similar flow fields that were investigated at 1/10^th the current measurement rate. The power spectra of instantaneous mixture fraction fluctuations adhere to Kolmogorov's well-established -5/3 law, showing that the technique captures a significant range of dissipation scales. This observation underscores the ability to study mixing dynamics throughout the turbulent by fully resolving scalar fluctuations up to 30 kHz. This enhanced spatio-temporal resolution allows for a more detailed investigation of the dynamical behavior of turbulent flows with complex modal interactions down to the smallest diffusion limited mixing scales.</p>

Systems biology is an emergent field focused on developing a system-level understanding of biological systems. In the last decade advances in genomics, transcriptomics and proteomics have gathered a remarkable amount data enabling the possibility of a system-level analysis to be grounded at a molecular level. The reverse-engineering of biochemical networks from experimental data has become a central focus in systems biology. A variety of methods have been proposed for the study and identification of the system's structure and/or dynamics. The objective of this dissertation is to introduce and propose solutions to some of the challenges inherent in reverse-engineering of biological systems. First, previously developed reverse engineering algorithms are studied and compared using data from a simulated network. This study draws attention to the necessity for a uniform benchmark that enables an ob jective comparison and performance evaluation of reverse engineering methods. Since several reverse-engineering algorithms require discrete data as input (e.g. dynamic Bayesian network methods, Boolean networks), discretization methods are being used for this purpose. Through a comparison of the performance of two network inference algorithms that use discrete data (from several different discretization methods) in this work, it has been shown that data discretization is an important step in applying network inference methods to experimental data. Next, a reverse-engineering algorithm is proposed within the framework of polynomial dynamical systems over finite fields. This algorithm is built for the identification of the underlying network structure and dynamics; it uses as input gene expression data and, when available, a priori knowledge of the system. An evolutionary algorithm is used as the heuristic search method for an exploration of the solution space. Computational algebra tools delimit the search space, enabling also a description of model complexity. The performance and robustness of the algorithm are explored via an artificial network of the segment polarity genes in the D. melanogaster. Once a mathematical model has been built, it can be used to run simulations of the biological system under study. Comparison of simulated dynamics with experimental measurements can help refine the model or provide insight into qualitative properties of the systems dynamical behavior. Within this work, we propose an efficient algorithm to describe the phase space, in particular to compute the number and length of all limit cycles of linear systems over a general finite field. This research has been partially supported by NIH Grant Nr. RO1GM068947-01. / Ph. D.

Doctor of Philosophy / Department of Mathematics / Alexander G. Ramm / Several methods for a stable solution to the equation $F(u)=f$ have been developed. Here $F:H\to H$ is an operator in a Hilbert space $H$, and we assume that noisy data $f_\delta$, $\|f_\delta-f\|\le \delta$, are given in place of the exact data $f$. When $F$ is a linear bounded operator, two versions of the Dynamical Systems Method (DSM) with stopping rules of Discrepancy Principle type are proposed and justified mathematically. When $F$ is a non-linear monotone operator, various versions of the DSM are studied. A Discrepancy Principle for solving the equation is formulated and justified. Several versions of the DSM for solving the equation are formulated. These methods consist of a Newton-type method, a gradient-type method, and a simple iteration method. A priori and a posteriori choices of stopping rules for these methods are proposed and justified. Convergence of the solutions, obtained by these methods, to the minimal norm solution to the equation $F(u)=f$ is proved. Iterative schemes with a posteriori choices of stopping rule corresponding to the proposed DSM are formulated. Convergence of these iterative schemes to a solution to the equation $F(u)=f$ is proved. This dissertation consists of six chapters which are based on joint papers by the author and his advisor Prof. Alexander G. Ramm. These papers are published in different journals. The first two chapters deal with equations with linear and bounded operators and the last four chapters deal with non-linear equations with monotone operators.

The complex and coupled physical processes taking place in the atmosphere, ocean and land surface are described in Global Circulation Models (GCMs). These models have become the main tools to simulate climate variability and project future climate change. GCMs have the potential to give physically reliable estimates of climate change at global, continental or regional scales, but their projections are currently of too course horizontal resolution to capture the smaller scale features of climate and climate change. This situation stems from the fact that GCM simulations, which are effectively three-dimensional simulations of the coupled atmosphere-ocean-land system, are computationally extremely expensive. Therefore, downscaling techniques are utilised to do perform simulations over preselected areas that are of sufficiently detailed to represent the climate features at the meso-scale. Dynamic regional climate models (RCMs), based on the same laws of physics as GCMs but applied at high resolution over areas of interest, have become the main tools to project regional climate change. The research presented here utilises the Conformal-Cubic Atmospheric Model (CCAM), a variable-resolution global atmospheric model that can be applied in stretched-grid mode to function as a regional climate model. As is the case with RCMs, CCAM has the potential to improve climate simulations along rough topography and coastal areas when applied at high spatial resolution, whilst side-stepping the lateral boundary condition problems experienced by typical limited-area RCMs. CCAM has been developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia. The objective in the study is to test capability of a regional climate model, CCAM, to realistically simulate cumulus convection at different spatial scales over regions with steep topography, such as the eastern escarpment of South Africa. Since both GCMs and RCMs are known to have large biases and shortcomings in simulating rainfall over the steep eastern escarpment of southern Africa and in particular Lesotho, the paper “Model simulations of rainfall over southern Africa and its eastern escarpment” (Chapter 3) has a focus on verifying model performance over this region. In the paper the CCAM simulations include six 200 km resolution Atmospheric Model Intercomparison Project (AMIP) simulations that are forced with sea surface temperatures and one 50 km resolution National Centre for Environmental Prediction (NCEP) reanalysis simulation that is forced with sea surface temperatures and synoptic scale atmospheric forcings. These simulations are verified against rain gauge data sets and satellite rainfall estimates. The results reveal that at these resolutions the model is capable of simulating the key synoptic-scale features of southern African rainfall patterns. However, rainfall totals are often drastically overestimated. A key aspect of model performance is the representation of the diurnal cycle in convection. For the case of South Africa, the realistic representation of the complex patterns of rainfall over regions of steep topography is also of particular importance. At a larger spatial scale, the model also needs to be capable of representing the west-east rainfall gradient found over South Africa. The ability of CCAM to simulate the diurnal cycle in rainfall as well as the complex spatial patterns of rainfall over eastern South Africa is analysed in “High Resolution Rainfall Modelling over the Eastern Escarpment of South Africa” (Chapter 4). The simulations described in the paper have been performed at 8km resolutions in the horizontal and span a thirty-year long period. These are the highest resolution climate simulations obtained to date for the southern African region, and were obtained through the downscaling reanalysis data of the European Centre for Medium-range Weather Forecasting (ECMWF). The simulations provide a test of the robustness of the CCAM convective rainfall parameterisations when applied at high spatial resolution, in particular in representing the complex rainfall patterns of the eastern escarpment of South Africa. / M (Geography and Environmental Management), North-West University, Potchefstroom Campus, 2015

The complex and coupled physical processes taking place in the atmosphere, ocean and land surface are described in Global Circulation Models (GCMs). These models have become the main tools to simulate climate variability and project future climate change. GCMs have the potential to give physically reliable estimates of climate change at global, continental or regional scales, but their projections are currently of too course horizontal resolution to capture the smaller scale features of climate and climate change. This situation stems from the fact that GCM simulations, which are effectively three-dimensional simulations of the coupled atmosphere-ocean-land system, are computationally extremely expensive. Therefore, downscaling techniques are utilised to do perform simulations over preselected areas that are of sufficiently detailed to represent the climate features at the meso-scale. Dynamic regional climate models (RCMs), based on the same laws of physics as GCMs but applied at high resolution over areas of interest, have become the main tools to project regional climate change. The research presented here utilises the Conformal-Cubic Atmospheric Model (CCAM), a variable-resolution global atmospheric model that can be applied in stretched-grid mode to function as a regional climate model. As is the case with RCMs, CCAM has the potential to improve climate simulations along rough topography and coastal areas when applied at high spatial resolution, whilst side-stepping the lateral boundary condition problems experienced by typical limited-area RCMs. CCAM has been developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia. The objective in the study is to test capability of a regional climate model, CCAM, to realistically simulate cumulus convection at different spatial scales over regions with steep topography, such as the eastern escarpment of South Africa. Since both GCMs and RCMs are known to have large biases and shortcomings in simulating rainfall over the steep eastern escarpment of southern Africa and in particular Lesotho, the paper “Model simulations of rainfall over southern Africa and its eastern escarpment” (Chapter 3) has a focus on verifying model performance over this region. In the paper the CCAM simulations include six 200 km resolution Atmospheric Model Intercomparison Project (AMIP) simulations that are forced with sea surface temperatures and one 50 km resolution National Centre for Environmental Prediction (NCEP) reanalysis simulation that is forced with sea surface temperatures and synoptic scale atmospheric forcings. These simulations are verified against rain gauge data sets and satellite rainfall estimates. The results reveal that at these resolutions the model is capable of simulating the key synoptic-scale features of southern African rainfall patterns. However, rainfall totals are often drastically overestimated. A key aspect of model performance is the representation of the diurnal cycle in convection. For the case of South Africa, the realistic representation of the complex patterns of rainfall over regions of steep topography is also of particular importance. At a larger spatial scale, the model also needs to be capable of representing the west-east rainfall gradient found over South Africa. The ability of CCAM to simulate the diurnal cycle in rainfall as well as the complex spatial patterns of rainfall over eastern South Africa is analysed in “High Resolution Rainfall Modelling over the Eastern Escarpment of South Africa” (Chapter 4). The simulations described in the paper have been performed at 8km resolutions in the horizontal and span a thirty-year long period. These are the highest resolution climate simulations obtained to date for the southern African region, and were obtained through the downscaling reanalysis data of the European Centre for Medium-range Weather Forecasting (ECMWF). The simulations provide a test of the robustness of the CCAM convective rainfall parameterisations when applied at high spatial resolution, in particular in representing the complex rainfall patterns of the eastern escarpment of South Africa. / M (Geography and Environmental Management), North-West University, Potchefstroom Campus, 2015

Servo control of pneumatic actuators is difficult due to the high compressibility and non-linear flow of air. Friction as well as uncertainties in the parameters and model character-izing dynamics of the pneumatic systems further contribute to control challenges. These drawbacks cause stick-slip motion, larger tracking error and limit cycles, which degrades the control performances. Selection of a controller that satisfies requirements of the per-forming tasks is thus crucial in servo-pneumatic applications. This thesis focuses on the design and experimental evaluation of a model-based, nonlinear controller known as Dy-namical Adaptive Backstepping-Sliding Mode Control (DAB-SMC). Originally designed for chemical process control and applied only in simulations, the DAB-SMC is adopted in this thesis and applied to the new area of servo-pneumatic control of a single-rod, double acting pneumatic cylinder and antagonistic pneumatic artificial muscles (PAMs). The con-troller is further enhanced by augmenting it with LuGre-based friction observers to com-pensate the adverse frictional effect presents in both actuators. Unlike other research works, the actuators are subject to a varying load that influences control operations in two different modes: motion assisting or resisting. The implementation of DAB-SMC for such servo-pneumatic control application is novel. The mass flow rates of compressed air into and out of the actuators are regulated using one of the following valve configurations: a 5/3-way proportional directional valve, two 3/2-way or four 2/2-way Pulse Width Modu-lation (PWM)-controlled valves. Over the entire range of experiments which involve vari-ous operating conditions, the DAB-SMC is observed to track and regulate the reference input trajectories successfully and in a stable manner. Average root mean square error (RMSE) values of tracking for cylinder and PAMs when the compressed air is regulated using the 5/3-way proportional valve are 1.73mm and 0.10°, respectively. In case of regu-lation, the average steady-state error (SSE) values are 0.71mm and 0.04°, respectively. The DAB-SMC exhibits better control performance than the standard PID and classical SMC by at least 33%. The DAB-SMC also demonstrates robustness for up to 78% in un-certainty of load parameter. When the control valve is replaced by the PWM-controlled valves of 3/2-way and 2/2-way configurations, performance is slightly compromised. / May 2016

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Biofilms are aggregations of bacteria that can thrive wherever there is a watersurface or water-interface. Sometimes they can be beneficial; for example, biofilms are used in water and waste-water treatment. The filter used to remove contaminants acts as a scaffold for microbial attachment and growth. However, biofilms could have bad effects, especially on a persons health. They can cause chronic diseases and serious infections. The importance of biofilms in industrial and medical settings, is the main reason of the mathematical studies performed up to now, concerning biofilms. Biofilms have been mathematical modelling targets over the last 30 years. The complex structure and growth of biofilms make them difficult to study. Biofilm formation is a multi-stage process and occurs in even the most unlikely of environmental conditions. Models of biofilms vary from the discrete to the continuous; accounting for one-species to multi-species and from one-scale to multi-scale models. A model may even have both discrete and continuous parts. The implication of these differences is that the tools used to model biofilms differ; we present and review some of these models. The aim in this thesis is to model the early initiation of biofilm formation. This stage involves bacterial movement towards a surface and the attachment to the boundary which seeds a biofilm. We use a diffusion equation to describe a bacterial random walk and appropriate boundary conditions to model surface attachment. An analytical solution is obtained which gives the bacterial density as a function of position and time. The model is also analysed for stability. Independent of this model, we also give a reaction diffusion equation for the distribution of sensing molecules, accounting for production by the bacteria and natural degradation. The last model we present is of Keller-Segel type, which couples the dynamics of bacterial movement to that of the sensing molecules. In this case, bacteria perform a biased random walk towards the sensing molecules. The most important part of this chapter is the derivation of the boundary conditions. The adhesion of bacteria to a surface is presented by zero-Dirichlet boundary conditions, while the equation describing sensing molecules at the interface needed particular conditions to be set. Bacteria at the boundary also produce sensing molecules, which may then diffuse and degrade. In order to obtain an equation that includes all these features we assumed that mass is conserved. We conclude with a numerical simulation. / AFRIKAANSE OPSOMMING: Biofilms is die samedromming van bakterieë wat kan floreer waar daar ’n wateroppervlakte of watertussenvlak is. Soms kan hulle voordelig wees, soos byvoorbeeld, biofilms word gebruik in water en afvalwater behandeling. Die filter wat gebruik word om smetstowwe te verwyder, dien as ’n steier vir mikrobiese verbinding en groei. Biofilms kan ook egter slegte gevolge he, veral op ’n persoon se gesondheid. Hulle kan slepende siektes en ernstige infeksies veroorsaak. Die belangrikheid van biofilms in industriële en mediese omgewings, is die hoof rede vir die wiskundige studies wat tot dusver uitgevoer is met betrekking tot biofilms. Biofilms is oor die afgelope 30 jaar al ’n teiken vir wiskundige modellering. Die komplekse struktuur en groei van biofilms maak dit moeilik om hul te bestudeer. Biofilm formasie is ’n multi-fase proses, en gebeur selfs in die mees onwaarskynlikste omgewings. Modelle wat biofilms beskryf wissel van die diskreet tot die kontinu, inkorporeer een of meer spesies, en strek van eentot multi-skaal modelle. ’n Model kan ook oor beide diskreet en kontinue komponente besit. Dit beteken dat die tegnieke wat gebruik word om biofilms te modelleer ook verskil. In hierdie proefskrif verskaf ons ’n oorsig van sommige van hierdie modelle. Die doel in hierdie proefskrif is om die vroeë aanvang van biofilm ontwikkeling te modeleer. Hierdie fase behels ’n bakteriële beweging na ’n oppervlak toe en die aanvanklike aanhegsel wat sal ontkiem in ’n biofilm. Ons gebruik ’n diffusievergelyking om ’n bakteriële kanslopie te beskryf, met geskikte randvoorwaardes. ’n Analities oplossing is verkry wat die bakteriële bevolkingsdigtheid beskryf as ’n funksie van tyd en posisie. Die model is ook onleed om te toets vir stabiliteit. Onafhanklik van die model, gee ons ook ’n reaksiediffusievergelyking vir die beweging van waarnemings-molekules, wat insluit produksie deur die bakterieë en natuurlike afbreking. Die laaste model wat ten toon gestel word is ’n Keller-Segel tipe model, wat die bakteriese en waarnemings-molekule dinamika koppel. In hierdie geval, neem die bakterieë ’n sydige kanslopie agter die waarnemings molekules aan. Die belangrikste deel van hierdie hoofstuk is die afleiding van die randvoorwaardes. Die klewerigheid van die bakterieë tot die oppervlak word vvorgestel deur nul-Dirichlet randvoorwaardes, terwyl die vergelyking wat waarnemingsmolekule gedrag by die koppelvlak beskryf bepaalde voorwaardes nodig het. Bakterieë op die grensvlak produseer ook waarnemings-molekules wat diffundeer en afbreek. Om te verseker dat al hierdie eienskappe omvat is in ’n vergelyking is die aanname gemaak dat massa behoud bly. Ter afsluiting is numeriese simulasie van die model gedoen.