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This treatise investigated mathematical word problems (MWPs) and their implementation in Foundation Phase classrooms. Factors influencing the implementation of MWPs, with specific reference to the teachers and learners involved, emerged. Direct and indirect factors influencing the implementation of MWPs were acknowledged. Student teachers‟ reflections on classroom practices experienced during their teaching practice training period for their initial teaching qualification inspired me as lecturer to embark on my own journey of inquiry and study the phenomenon above. As this study was undertaken in South Africa, the need arose to take into consideration the changes that have occurred since 1994. Observations of how democratic values and desires feature, or do not feature, when engaging with the phenomenon had to be considered. This study also aimed to emphasise inequalities in everyday practice. The discovery of “good practice” (Cooper 2010:170) contributed towards addressing the factors that emerged as influencing the implementation of MWPs. Jansens (2009:170) book Knowledge in the blood presents compelling reasons for disclosing the state of current practice and seeks alternatives to promote the required change in mathematics teaching, with one of the perspectives on mathematics education being the emphasis on implementing MWPs in the Foundation Phase. Teachers often extend their own preferences into practice and emphasise their “knowledge in the blood” as their view of good practice. Learners‟ needs and learner diversity are often overlooked. Learners‟ assessment scores, both nationally and internationally, have revealed more negative facts. These low scores have often been, and often still are, news flashes, contributing to a negative view of teachers and education. In order to address the widespread sentiment that there is “no hope for teachers” (Jansen 2011:19), and to avoid a recycling of negativity, “good practice” (Cooper 2010:170) is key to success. This study aimed to discover hope for teachers and learners.

The doped perovskite manganite La1-xCaxMnO3 (0<x<1) has been extensively studied due to the interactions between the electronic, magnetic and crystal lattices, and the wide range of phases that can coexist. The region of greatest interest in the bulk material is around x~0.5, where there is often mesoscopic phase coexistence between a ferromagnetic metal (FM) and an antiferromagnetic insulator (AF). The first part of the dissertation describes a systematic study on a series of La1-xCaxMnO3 films deposited onto SrTiO3 (001) by pulsed laser deposition with compositions in the range 0.40<x<0.45. From electrical transport and magnetisation measurements, the limit of metallic behaviour was found to be x=0.41 whereas ferromagnetism was seen up to x=0.45. Although the transition temperatures of 150-200 K were comparable with the bulk material, the saturation moment at 20 K was about 40% of the fully spin-aligned value, which suggests the possibility of a phase separated mixture of FM and AF regions. The deviation from the bulk behaviour is thought to be due to substrate-induced strain altering the crystal symmetry and making the cubic ferromagnetic state less favourable. In the remainder of this work, the nature of phase separation in 60 nm La0.59Ca0.41MnO3 and La0.60Ca0.40MnO3 films is investigated. The effect of an external magnetic field is studied. A high-field magnetoresistance (Δρ/ρB=0) of 41% in fields of 400 mT was observed for a La0.60Ca0.40MnO3 film, which, while not as large as the values previously reported in the literature, is still significant. The magnetic history of the films was found to be very significant, with the zero-field resistivity depending on the highest field applied. The isothermal time dependence of the resistivity was found to be exponential, with a time constant in the range 100-1000 s. Possible mechanisms for the MR effect and the dependence on magnetic history are discussed.

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This thesis proposes and develops a novel optic configuration, Kerr phase-interrogator, which investigates the phase-shift between two sinusoidally modulated optical signals (SMOS) utilizing Kerr effect. The Kerr phase-interrogator gives birth to an entirely new technique for measuring the phase-shift between two light-waves. Taking advantage of all-optical signal processing, ultrafast responses, and being free from the coherent properties of a laser source, the Kerr phase-interrogator based technique for measuring the phase-shift is a promising novel approach for monitoring and sensing applications. The thesis begins with theoretically demonstrating the operation of Kerr phase-interrogator. As the core of optical process occurs in Kerr phase-interrogator, nonlinear interactions between two SMOSs in the Kerr medium are theoretically analyzed utilizing the models of nonlinear phase-modulation and four-wave mixing (FWM). The phase-modulation-based model is intuitive and allows for conceptual understanding of the operation of the Kerr phase-interrogator. However, this model does not account for the impact of chromatic-dispersion (CD) of the Kerr medium on the operation of the Kerr phase-interrogator. Compared with the former model, the FWM-based model is essential for acquiring insight into Kerr phase-interrogator, and can explain the CD impact of the Kerr medium. The analytical solution of the power of the first order sideband as a result of the nonlinear interaction is obtained in both theoretical models. The obtained solution shows sinusoidal dependence of the power on the phase-shift of the SMOSs. Utilizing this sinusoidal dependence, the phase-shift of two SMOSs can be acquired by measuring the power of the first-order sideband. Birefringence and CD are critical factors that affect the nonlinear interactions and thus impact the operation of Kerr phase-interrogator. In this work, vector analysis is performed on the nonlinear interaction between two SMOSs in a Kerr medium with randomly varying birefringence, and the effect of polarization-states of SMOSs on the operation of Kerr phase-interrogator is investigated. Impact of CD of Kerr medium on the operation of Kerr phase-interrogator is theoretically investigated using theory of FWM and is experimentally verified. Four typical applications, which comprehensively reflect the advantages of Kerr phase-interrogator, are proposed and experimentally demonstrated in this thesis. First, we present a novel approach for measurements of CD in long optical fibers using a Kerr phase-interrogator. The Kerr phase-interrogator measures the phase variation of a SMOS induced by CD in a fiber under test as the laser carrier wavelength is varied. This approach takes advantage of all-optical signal-processing based on Kerr effect to acquire the phase variation, and consequently removes the requirement of complex electrical signal-processors in existing techniques of CD measurement. CD measurement for several fibers is experimentally demonstrated. Second, a novel temperature sensor that utilizes temperature dependence of reflection group-delay in a linearly chirped fiber Bragg grating is presented. The reflection group-delay of chirped grating changes with temperature leading to a variation in the phase of a SMOS reflected from the grating. A Kerr phase-interrogator converts the phase-variation into power variation allowing for temperature sensing with a resolution of 0.0089 oC and a sensitivity of 1.122 rad/oC. Third, a Kerr phase-interrogator is applied for implementation of real-time CD monitoring. CD induces a phase-shift between two SMOSs carried by two different wavelengths. A Kerr phase-interrogator converts the phase-shift into power variation and CD monitoring is achieved by measurement of the power variation in real time with a resolution of 0.196 ps/nm. This application takes advantages of ultrafast response of Kerr phase-interrogator and achieves the real-time monitoring. Lastly, a novel approach for incoherent optical frequency-domain reflectometry based on a Kerr phase-interrogator is presented. The novel approach eliminates the limitation of finite coherent length of the light source, and achieves measurement of long-range distance beyond the coherent length of the light source. Long-range detection of reflection points as far as 151 km at a spatial-resolution of 11.2 cm is experimentally demonstrated.

This study entails an investigation of a novel moment closure, originally constructed for rarefied-gas prediction, to the modelling of inert, dilute, disperse, particle flows. Such flows are important in many engineering situations. As one example, in internal-combustion engines, fuel is often injected as a spray of tiny droplets and, during combustion, a cloud of tiny soot particles can be formed. These particle phases are often difficult to model, especially when particles display a range of velocities at each location in space. Lagrangian methods are often too costly and many Eulerian field-based methods suffer from model deficiencies and mathematical artifacts. Often, Eulerian formulations assume that all particles at a location and time have the same velocity. This assumption leads to nonphysical results, including an inability to predict particle paths crossing and a limited number of boundary conditions that can be applied. The typical multi-phase situation of many particles is, in many ways, similar to that of a gas compressed of a huge number of atoms or molecules. It is therefore expected that powerful techniques from the kinetic theory of gases could be applied. This work explores the advantages of using a modern fourteen-moment model, originally derived for rarefied gases, to predict multi-phase flows. Details regarding the derivation, the mathematical structure, and physical behaviour of the resulting model are explained. Finally, a numerical implementation is presented and results for several flow problems that are designed to demonstrate the fundamental behaviour of the models are presented. Comparisons are made with other classical models.

The formation of grain boundary precipitates of the high temperature β phase from the supersaturated ɤ phase has been examined in Ag-5.64 wt.% aluminum alloys at 688°C . Large grained samples were used and the boundary misorientations were determined by X-ray diffraction. At low angle boundaries only primary sideplates formed while above a misorientation of 17° lenticular precipitates were dominant. Precipitate growth was studied on individual grain boundaries using a statistical technique. The lengthening and thickening rates were independent of the grain boundary misorientation indicating that grain boundary diffusion was not significant under these conditions. The precipitates grew with constant shape, with both the length and thickness increasing parabolically with time. By approximating the shape of the precipitate to that of an oblate spheroid growing with constant shape, an equivalent diffusion coefficient was calculated. The value obtained was in good agreement with measurements obtained from diffusion couples. The nature of the quenched β phase was also examined using optical and electron microscopy. The βphase transformed rapidly on cooling, forming a massive [symbol omitted] product or an acicular martensite at higher quenching rates. The structures were very similar to those reported for the Cu-Ga and Cu-Al systems. Many grain boundary precipitates showed unequal growth into the two matrix grains. Measurements of the matrix habit plane suggested that a possible orientation relationship existed between the precipitate and that grain into which no development occurred. In this case the precipitate nucleated in one grain but grew into the opposite grain. Precipitates which developed equally into both grains exhibited no apparent habit relationship with either grain. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

Ce travail porte sur l'étude des états physiques de la cafëine solide, composé bien connu des industries pharmaceutique et agroalimentaire. afin de comprendre la nature de son polymorphisme original et des instabilités associées. Les caractérisations expérimentales ont été menées par DSC, DRX, RMN et relaxation diélectrique. La caractérisation de la mobilité moléculaire des phases anhydres a mis en évidence la présence d'une dynamique complexe extrêmement lente à température ambiante. Deux processus dynamiques analogues sont observés dans les phases 1 et II. notés AI et AII, et un processus plus lent dans la phase l, noté BI. Les transformations entre les phases 1 et II ont été étudiées afin de rechercher les origines des capacités extraordinaires de la caféine à pouvoir être maintenue dans des situations de métastabilité très prononcées. Cette investigation a révélé des processus de transformation inhabituellement lents, influencés par la dynamique moléculaire lente. Les résultats obtenus suggèrent que la cinétique de transformation 1?II est du 1er ordre, qu'elle est contrôlée par la vitesse de germination et que la dynamique par l'intermédiaire du processus BI en est un facteur déterminant. Un modèle cohérent a également été construit pour la transition II?I, il suggère une transformation à partir de la surface. avec une influence particulièrement importante de la microstructure de l'échantillon. Des opérations de broyage ont permis de confirmer l'influence microstructurale de la transition II ?1 et ont révélé que le broyage induit mécaniquement une transformation de la phase 1 vers la phase II, mais aussi de la phase II vers la phase 1 selon l'intensité du broyage. / We present the study of the physical state of solid caffeine, a well-known pharmaceutieal and food-industry compound, ln order to understand its original polymorphism and the associatcd instabilities. Experimental characterisations have been obtaincd by DSC. XRD. NMR and dielcctric relaxation. The study of lhe moleeular mobility of anhydrous phases shows a very slow complex dynamic at room temperature. Two similar dynamical processes are observed in phases 1 and II. called AI, and AII. and a process slower in phase I callcd BI. The phases transformations (from I to II and II to I) have been studied to determine the origin of the extraordinary property of caffeine to be maintained in situation of high metastability. This investigation reveals anomalous slow transformation processes, influenced by the slow molecular mobility. The results suggest a first order I?II transformation kinetic, controlled by the nucleation rate, and directly governed by the BI dynamical process. A coherent model has also been proposed for the II?I transition, suggesting a transformation f'rom the surface, with a high influence of the microstructure. Milling operations confirm the microstructural influence for the II?I transition. It has also been shown that milling induees I?II transformation but also II?I transformation according to the milling intensity.

The proportions of F and OH in synthetic talc, clinohumite, chondro-dite, norbergite, brucite, and sellaite have been determined by X-ray measurement of interplanar spacings. Unit cell refinement has been carried out on intermediate sellaite, approximate composition MgOHF. The compositions of coexisting phases have been determined in forty hydrothermal experiments yielding information on eighteen different chemical equilibria. These data, combined with phase equilibrium and calorimetric data from the literature, have been treated by the method of least squares to produce a thermodynamic model of the system. Computed equilibria based on the model are in good agreement with data on natural assemblages. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

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