3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item The application of the attainable region analysis in comminution.(2008-06-09T10:03:28Z) Khumalo, NgangezweABSTRACT This work applies the concepts of the attainable region for process synthesis in comminution. The attainable region analysis has been successfully applied for process synthesis of reactor networks. The Attainable Region is defined as the set of all possible output states for a constrained or unconstrained system of fundamental processes (Horn, 1964). A basic procedure for constructing the attainable region for the fundamental processes of reaction and mixing has been postulated in reaction engineering (Glasser et al., 1987). This procedure has been followed in this work to construct the candidate attainable region for size reduction processes as found in a size reduction environment. A population balance model has been used to characterise the evolution of particle size distributions from a comminution event. Herbst and Fuerstenau (1973) postulated the dependency of grinding on the specific energy. A specific energy dependent population balance model was used for the theoretical simulations and for the fitting of experimental data. A new method of presenting particle size distributions as points in the Euclidian space was postulated in place of the traditional cumulative distribution. This allows successive product particle size distributions to be connected forming a trajectory over which the objective function can be evaluated. The curve connects products from successive batch grinding stages forming a pseudo-continuous process. Breakage, mixing and classification were identified as the fundamental processes of interest for comminution. Agglomeration was not considered in any of the examples. Mathematical models were used to describe each fundamental process, i.e. breakage, mixing and classification, and an The application of the attainable region analysis in comminution Abstract algorithm developed that could calculate the evolution of product particle size distributions. A convex candidate attainable region was found from which process synthesis and optimisation solutions could be drawn in two dimensional Euclidian space. As required from Attainable Region Theory, the interior of the bounded region is filled by trajectories of higher energy requirements or mixing between two boundary optimal points. Experimental validation of the proposed application of the attainable region analysis results in comminution was performed. Mono-sized feed particles were broken in a laboratory ball mill and the products were successfully fitted using a population balance model. It was shown that the breakage process trajectories were convex and they follow first order grinding kinetics at long grind times. The candidate attainable region was determined for an objective function to maximise the mass fraction in the median size class 2. It was proved that the same specific energy input produces identical products. The kinematic and loading conditions are supposed to be chosen as a subsequent event after the required specific energy is identified. Finally the fundamental process of classification was added to the system of breakage and mixing. The attainable regions analysis affords the opportunity to quantify exactly the reduction in energy consumption due to classification in a comminution circuit, thus giving optimal targets. Classification showed the potential to extend the candidate attainable region for a fixed specific energy input. The boundary of the attainable region is interpreted as pieces of equipment and optimum process conditions. This solves both the original process synthesis and successive optimisation problems.Item Apprenticing undergraduate history students into interpretative practice through local history(2007-03-01T13:33:46Z) Ludlow, Elizabeth HelenThis research report investigates the development of undergraduate history students’ knowledgeability and identity as historians. Drawing on a sociological paradigm, it examines the classification of the discipline or practice of history that informs undergraduate history teaching at a sample of three South African universities. It suggests that most undergraduate courses focus on and aim to apprentice students into a partial experience of the practice of history – the adjudicative task of the historian. The report then presents findings from an analysis of student feedback on their participation in an extended local history assignment. The analysis of student work draws upon socio-cultural notions of situated learning and the community of practice. This analysis suggests that as an instance of situated learning, the local history engagement enhances students’ understanding of the interpretative task of the historian and their own identity as constructors of history. The findings also suggest that there are implications for curriculum development in undergraduate history programmes.Item Approaching real time dynamic signature verification from a systems and control perspective.(2006-10-31T08:35:35Z) Gu, Yialgorithm. The origins of handwriting idiosyncrasies and habituation are explained using systems theory, and it is shown that the 2/3 power law governing biomechanics motion also applies to handwriting. This leads to the conclusion that it is possible to derive handwriting velocity profiles from a static image, and that a successful forgery of a signature is only possible in the event of the forger being able to generate a signature using natural ballistic motion. It is also shown that significant portion of the underlying dynamic system governing the generation of handwritten signatures can be inferred by deriving time segmented transfer function models of the x and y co-ordinate velocity profiles of a signature. The prototype algorithm consequently developed uses x and y components of pen-tip velocity profiles (vx[n] and vy[n]) to create signature representations based on autoregression-with-exogenous-input (ARX) models. Verification is accomplished using a similarity measure based on the results of a k-step ahead predictor and 5 complementary metrics. Using 350 signatures collected from 21 signers, the system’s false acceptance (FAR) and false rejection (FRR) rates were 2.19% and 27.05% respectively. This high FRR is a result of measurement inadequacies, and it is believed that the algorithm’s FRR is approximately 18%.