Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Dans le cadre des études de neutronique menées pour réacteurs de GEN-IV, les nouveaux outils de calcul des cœurs de réacteur sont implémentés dans l’ensemble du code APOLLO3® pour la partie déterministe. Ces méthodes de calculs s’appuient sur des données nucléaires discrétisée en énergie (appelées multi-groupes et généralement produites par des codes déterministes eux aussi) et doivent être validées et qualifiées par rapport à des calculs basés sur la méthode de référence Monte-Carlo. L’objectif de cette thèse est de mettre au point une technique alternative de production des propriétés nucléaires multi-groupes par un code de Monte-Carlo (TRIPOLI-4®). Dans un premier temps, après avoir réalisé des tests sur les fonctionnalités existantes de l’homogénéisation et de la condensation avec des précisions meilleures accessibles aujourd’hui, des incohérences sont mises en évidence. De nouveaux estimateurs de paramètres multi-groupes ont été développés et validés pour le code TRIPOLI-4®à l’aide de ce code lui-même, puisqu’il dispose de la possibilité d’utiliser ses propres productions de données multi-groupes dans un calcul de cœur. Ensuite, la prise en compte de l’anisotropie de la diffusion nécessaire pour un bon traitement de l’anisotropie introduite par des fuites des neutrons a été étudiée. Une technique de correction de la diagonale de la matrice de la section efficace de transfert par diffusion à l’ordre P1 (nommée technique IGSC et basée sur une évaluation du courant des neutrons par une technique introduite par Todorova) est développée. Une amélioration de la technique IGSC dans la situation où les propriétés matérielles du réacteur changent drastiquement en espace est apportée. La solution est basée sur l’utilisation d’un nouveau courant qui est projeté sur l’axe X et plus représentatif dans la nouvelle situation que celui utilisant les approximations de Todorova, mais valable seulement en géométrie 1D. A la fin, un modèle de fuite B1 homogène est implémenté dans le code TRIPOLI-4® afin de produire des sections efficaces multi-groupes avec un spectre critique calculé avec l’approximation du mode fondamental. Ce modèle de fuite est analysé et validé rigoureusement en comparant avec les autres codes : Serpent et ECCO ; ainsi qu’avec un cas analytique.L’ensemble de ces développements dans TRIPOLI-4® permet de produire des sections efficaces multi-groupes qui peuvent être utilisées dans le code de calcul de cœur SNATCH de la plateforme PARIS. Ce dernier utilise la théorie du transport qui est indispensable pour la nouvelle filière à neutrons rapides. Les principales conclusions sont : -Le code de réseau en Monte-Carlo est une voie intéressante (surtout pour éviter les difficultés de l’autoprotection, de l’anisotropie limitée à un certain ordre du développement en polynômes de Legendre, du traitement des géométries exactes 3D), pour valider les codes déterministes comme ECCO ou APOLLO3® ou pour produire des données pour les codes déterministes ou Monte-Carlo multi-groupes.-Les résultats obtenus pour le moment avec les données produites par TRIPOLI-4® sont comparables mais n’ont pas encore vraiment montré d’avantage par rapport à ceux obtenus avec des données issues de codes déterministes tel qu’ECCO. / In the framework of the Generation IV reactors neutronic research, new core calculation tools are implemented in the code system APOLLO3® for the deterministic part. These calculation methods are based on the discretization concept of nuclear energy data (named multi-group and are generally produced by deterministic codes) and should be validated and qualified with respect to some Monte-Carlo reference calculations. This thesis aims to develop an alternative technique of producing multi-group nuclear properties by a Monte-Carlo code (TRIPOLI-4®).At first, after having tested the existing homogenization and condensation functionalities with better precision obtained nowadays, some inconsistencies are revealed. Several new multi-group parameters estimators are developed and validated for TRIPOLI-4® code with the aid of itself, since it has the possibility to use the multi-group constants in a core calculation.Secondly, the scattering anisotropy effect which is necessary for handling neutron leakage case is studied. A correction technique concerning the diagonal line of the first order moment of the scattering matrix is proposed. This is named the IGSC technique and is based on the usage of an approximate current which is introduced by Todorova. An improvement of this IGSC technique is then presented for the geometries which hold an important heterogeneity property. This improvement uses a more accurate current quantity which is the projection on the abscissa X. The later current can represent the real situation better but is limited to 1D geometries.Finally, a B1 leakage model is implemented in the TRIPOLI-4® code for generating multi-group cross sections with a fundamental mode based critical spectrum. This leakage model is analyzed and validated rigorously by the comparison with other codes: Serpent and ECCO, as well as an analytical case.The whole development work introduced in TRIPLI-4® code allows producing multi-group constants which can then be used in the core calculation solver SNATCH in the PARIS code platform. The latter uses the transport theory which is indispensable for the new generation fast reactors analysis. The principal conclusions are as follows:-The Monte-Carlo assembly calculation code is an interesting way (in the sense of avoiding the difficulties in the self-shielding calculation, the limited order development of anisotropy parameters, the exact 3D geometries) to validate the deterministic codes like ECCO or APOLLO3® and to produce the multi-group constants for deterministic or Monte-Carlo multi-group calculation codes. -The results obtained for the moment with the multi-group constants calculated by TRIPOLI-4 code are comparable with those produced from ECCO, but did not show remarkable advantages.

Text in Afrikaans / Real empowerment of school learners requires preparing them for the age of technology. This empowerment can be achieved by developing their higher-order thinking skills. This is clearly the intention of the proposed South African FET National Curriculum Statements Grades 10 to 12 (Schools). This research shows that one method of developing higher-order thinking skills is to adopt an integrated curriculum approach. The research is based on the assumption that an integrated curriculum approach will produce learners with a more integrated knowledge structure which will help them to solve problems requiring higher-order thinking skills. These assumptions are realistic because the empirical results of several comparative research studies show that an integrated curriculum helps to improve learners' ability to use higher-order thinking skills in solving nonroutine problems. The curriculum mentions four kinds of integration, namely integration across different subject areas, integration of mathematics with the real world, integration of algebraic and geometric concepts, and integration into and the use of dynamic geometry software in the learning and teaching of geometry. This research shows that from a psychological, pedagogical, mathematical and historical perspective, the theme conic sections can be used as an integrating factor in the new proposed FET mathematics curriculum. Conics are a powerful tool for making the new proposed curriculum more integrated. Conics can be used as an integrating factor in the FET band by means of mathematical exploration, visualisation, relating learners' experiences of various parts of mathematics to one another, relating mathematics to the rest of the learners' experiences and also applying conics to solve real-life problems. / Mathematical Sciences / D.Phil. (Wiskundeonderwys)

Le genre Angraecum est un groupe d’orchidées tropicales qui compte environ 221 espèces réparties en Afrique subsaharienne, dans l’ouest de l’Océan Indien, et au Sri Lanka. Plus de la moitié des espèces se trouvent à Madagascar, dont au moins 90% sont endémiques à l’île. L’étude systématique et taxonomique du genre Angraecum a toujours été problématique à cause de sa grande diversité morphologique. Pour faciliter la classification, des sections ont été établies dont la plus connue est celle de Garay (1973), qui regroupe les espèces sous 19 sections. Plusieurs analyses phylogénétiques avaient montré que le genre Angraecum et les sections de Garay ne sont pas monophylétiques. Cependant, aucune révision systématique n’a été apportée à cause du faible échantillonnage dans ces analyses. En incorporant un plus grand nombre d'espèces et en ajoutant d’autres caractères morphologiques dans l’analyse, nous avons apporté une plus grande résolution à la reconstruction phylogénétique du groupe. Cette résolution concerne surtout les nœuds plus profonds qui représentent les différents clades à l’intérieur d'Angraecum, qui correspondent à des sections naturelles. A partir de ces clades, nous avons redéfini 14 sections monophylétiques toute en reconnaissant cinq nouvelles. Grâce à cette nouvelle phylogénie d'Angraecum, nous avons pu étudier la diversification du genre et de la sous-tribu Angraecinae en utilisant des méthodes macroévolutives, notamment les roles joués par les traits floraux dans la spéciation, tout en l'interprétant grâce aux histoires géologique et paléoclimatique. Le modèle de diversification chez les Angraecinae semble avoir été celui communément rencontré dans les forêts tropicales humides, c’est-à-dire une diversification par accumulation graduelle d’espèces à travers le temps et non pas une radiation adaptative rapide, comme souvent observée chez des lignées animales malgaches. Plusieurs caractères morphologiques jouent un rôle important dans la diversification des espèces d'Angraecum. Le début de la diversification d'Angraecum à Madagascar coïncide avec le mouvement progressif de l’île vers le nord, l’établissement de la mousson dans la partie nord de l’île durant le Miocène, et l’expansion de la forêt tropicale malgache pendant cette période. Notre étude de l’histoire biogéographique des Angraecinae suggère une origine malgache de la sous-tribu et du genre Angraecum. On observe de la dispersion à longue distance à partir de Madagascar vers le reste du monde dans le genre Angraecum. La forêt tropicale humide du Nord Est de Madagascar est le point de départ de la diversification des espèces d'Angraecum. Le premier événement de dispersion a débuté à l’intérieur de l’île vers la fin du Miocène. Cet évènement est marqué par une migration du Nord Est vers le centre de Madagascar. Par ailleurs, la majorité des événements de dispersion à longue distance se sont produits durant le Pliocène-Pléistocène à partir soit du centre, soit du Nord Est de l'île. On assiste à des migrations indépendantes vers l’Afrique de l’est et les Comores d’une part, et vers les Mascareignes d’autre part. Un seul événement fondateur ayant conduit à l’apparition de la section Hadrangis est observé dans les Mascareignes. La saison cyclonique joue un rôle significatif dans la dispersion à longue distance des graines d’orchidées, comparée aux vents dominants qui soufflent dans la région ouest de l’Océan Indien, notamment l’alizé et la mousson. La similarité des niches écologiques a facilité l’expansion des espèces d'Angraecum dans les Comores et les Mascareignes. / Angraecum is a group of tropical orchids that includes ca. 221 species distributed in Sub-Saharan Africa, the western Indian Ocean region, and Sri Lanka. At least half of the species are found in Madagascar, 90% being endemic to the island. Taxonomic studies of Angraecum have always been problematic because of the great morphological diversity of the group. To facilitate classification, sections have been proposed, the best-known system to date being that of Garay (1973) that subdivides the genus into 19 sections. Previous phylogenetic studies had shown that genus Angraecum and Garay’s sections are not monophyletic. However, no systematic review was made because of a reduced species sample in these analyses. Using a greater sampling from Madagascar and adding morphological characters to the analyses, we brought greater resolution to the phylogenetic reconstruction of the group. This resolution mainly concerns the deeper nodes representing different clades within Angraecum, which basically correspond to natural sections. By using these clades, we redefined 14 sections and recognized five new ones. Using this phylogeny of Angraecum, we evaluated species diversification using macroevolutionary methods, essentially the effect of floral traits in speciation. The great diversity of Angraecum species in Madagascar, the high endemicity, and the geology and paleoclimate histories allowed us to evaluate diversification patterns within the genus as well as sub-tribe Angraecinae. The model of diversification in Angraecinae follows that of most tropical rain forest taxa, which results from the gradual accumulation of species through time and not from a rapid adaptive radiation, as is often the case for Malagasy fauna lineages. Several morphological characters are involved in the diversification of Angraecum. The beginning of Angraecum diversification in Madagascar coincided with the progressive movement of the island northwards, the establishment of a monsoon regime in the northern part of the island during the Miocene, and the expansion of the Malagasy rainforest during that period. Our historical biogeographic study of Angraecinae suggests a Malagasy origin of the subtribe Angraecinae and Angraecum. We observed out-of Madagascar long-distance dispersal in Angraecum. The north-eastern Malagasy rainforest is the center of species radiation for the genus. The first dispersal event within the island started in the late Miocene. This event was a migration from the north to the central highland. The majority of long-distance dispersal events outside Madagascar occurred during the Pliocene-Pleistocene, originating from either the center or the North East of the island. There were multiple independent dispersals to East Africa and the Comoros, and to the Mascarenes. A single founder-effect event in section Hadrangis is observed in the Mascarenes. The cyclonic seasons play a significant role in long-distance dispersal of orchid seeds, as compared to prevailing winds in the western Indian Ocean region, essentially trade wind and monsoon. Ecological niche similarity favored the expansion of Angraecum species in the Comoros and Mascarene archipelagos.

L'étude des noyaux exotiques riches en neutrons est l'un des enjeux actuels majeurs de la physique nucléaire expérimentale. Le spectromètre S ³ , aujourd'hui en construction, pourrait permettre de les produire "en vol" grâce aux hautes intensités de l'accélérateur linéaire de Spiral2. Le mécanisme de réaction utilisé serait celui des collisions profondément inélastiques, pour ses caractéristiques telles que l'échange de nombreux nucléons et l'équilibre en N/Z des produits obtenus. Les recherches sur ce mécanisme, débutées dans les années 1970, bénéficient aujourd'hui des progrès technologiques, en particulier concernant les spectromètres de particules chargées. On a mesuré, pour la première fois sur une gamme de 0° à 35°, les sections efficaces de réactions d2sigma/dOmegadE pour différents noyaux riches en neutrons formés par collisions profondément inélastiques entre un faisceau de ⁴⁸Ca¹ ⁹ ⁺ à 10 A MeV et une cible de ² ³ ⁸U de 170(+-10%) ug/cm ². L'expérience a été réalisée au Ganil, avec le spectromètre Vamos couplé à sept clovers Exogam afin de confirmer l'identification des noyaux produits par leur signature gamma. De plus, un détecteur BaF₂ a permis la mesure de l'intensité du faisceau, essentielle au calcul des sections efficaces absolues. Les distributions angulaires, en énergie et en masse des sections efficaces double différentielles absolues sont présentées pour une large plage de quasi-projectiles. Les résultats sont comparés à ceux donnés par le couplage des modèles DIT (Deep Inelastic Transfers) et Gemini++. Les résultats obtenus montrent une production importante qui laisse envisager ce mécanisme pour la formation de noyaux riches en neutrons. Les modèles sont globalement cohérents avec les résultats et les différences majeures concernent généralement les quasi-projectiles très proches ou au contraire très éloignés du faisceau. Les implications pour la production de faisceau avec S³ sont également discutées. / The study of neutron-rich nuclei is one of the main challenges nowadays in experimental nuclear physics. Thanks to the future high intensity beams delivered by the linear accelerator of Spiral2, the S ³ spectrometer might allow their production using the "in-flight" method. The deep inelastic reaction mechanism might be used due to the important multi-nucleon transfer and the N/Z equilibration. Studies on this topic, started in the seventies, take advantages of the new available devices. We measured, for the first time between 0° and 35° in the laboratory frame, the reactions cross-sections d2sigma/dOmegadE for the neutron-rich nuclei formed by deep inelastic collisions between a 10 A MeV ⁴⁸Ca ¹ ⁹ ⁺ beam and a 170(+-10%) ug/cm² ² ³ ⁸U target. The experiment was performed at Ganil using the Vamos spectrometer coupled to seven Exogam to confirm the nuclei identification using their gamma signature. Moreover, a BaF2 detector was used to extract the beam intensities, essential for the absolute cross sections measurements. Momentum, angular and mass distributions of absolute differential cross-sections are presented for a wide range of quasi-projectiles. The results are compared with those of DIT (Deep Inelastic Transfers) coupled with Gemini++ theoretical calculations. The models are generally consistent with the results. Important differences appear for quasi-projectiles very close and very far from the beam. Relevant implications for S³ beam production are pointed out.

Recent advances in plasma-based propulsion systems have led to the development of electromagnetic Radio-Frequency (RF) plasma generation and acceleration systems, called Helicon Plasma Thrusters (HPT). One of the pioneer companies developing this new type of space propulsion is T4i Technology for Propulsion and Innovation s.p.a., with its cutting-edge project called REGULUS, among which this study has been performed. A crucial part of HPT systems is the acceleration region, where, by the means of a magnetic nozzle, the thermal energy of the plasma is converted into axial acceleration and, in turn, into thrust. This study is focused on the numerically simulation of the plasma dynamics in the acceleration stage, using Xenon gas. A three-dimensional full Particle-In-Cell (PIC) simulation strategy is used to simulate the plume in the magnetic nozzle. The code developed for the plasma simulation is based on the open-source software Spacecraft Plasma Interaction Software (SPIS). The code has been conveniently modified and improved, neutrals and collision processes were added to evaluate their impact on the plasma properties. The features added improved the validity of the results, now one step closer to the physical reality. The code has been proven to be an extremely versatile and powerful tool for optimization and adaptation to different mission scenarios. / De senaste framstegen i plasmaframdrivning har lett till utvecklingen Helicon Plasma Thruster (HPT) som kombinerar elektromagnetisk högfrekvent (RF) plasmakälla och ett accelerationssystem. En av företagen som är pionjärer i att utveckla denna nya framdrivningsteknik är T4i Technology for Propulsion and Innovation s.p.a., med dess banbrytande projekt REGULUS, som detta arbete bygger på. En viktig del av HPT-systemet är accelerationsområde där plasmats termiska energin omvandlas till axiell accelleration i en magnetisk dysa. Denna rapport fokuserar på numeriska modelleringen av plasmadynamiken accelerationsområdet vid användning av Xenongasen. En tredimensionell Particle-In-Cell (PIC) simulering används för att studera plasmautflödet i magnetiska dysan. Koden bygger på den öppna mjukvaran Spacecraft Plasma interaction Software (SPIS). Koden har modifierats och förbättrats, en neutral komponent samt kollisionsprocesser har lagts till och deras påverkan på plasmabeteende har studerats. Dessa nya element förbättrade giltigheten av simulerings-resultaten. Nu ett steg närmre den fysiska verkligheten. Koden är ett mångsidigt och kraftfullt verktyg för optimering och anpassning till olika användningsscenarier.

This PhD thesis concerns language and racism. The aim is to explore how racism is reproduced in interaction in public debates on immigration, integration and refugee policy. From a constructivist pragmatic perspective, language is considered as a practice that composes and makes sense of our social world and all the phenomena and individuals that we perceive in it. Racist discourses discriminate against and privilege people by categorising them according to notions of cultural, ethnical, racial, religious and national differences. The thesis has two main themes: 1) the linguistic reproduction of, and response to, racist discrimination and privileging in interaction, and 2) the role of language in various public arenas, and the norms and conditions for participation in these arenas. The thesis comprises five studies. Study I examines racist discourses and conditions for participation in an online newspaper comments section. Study II examines how the phrase “politically correct” is used and negotiated in the same comments section, and how its usage leads to the reproduction and normalisation of racism. Another comments section is the focus of Study III, in which discriminating and privileging categorisations of Muslims, Islam, Swedes and Sweden are analysed. Study IV examines an anti-racist forum on the social networking site Instagram. In the study, the reproduction of norms of whiteness is analysed, as well as power relations that are evoked, sustained and transformed in interaction. Finally, Study V is an analysis of linguistic, visual and material reproductions of political positions and racist discourses in a debate among party leaders on Swedish television. The thesis demonstrates how normalisation of racism is accomplished in interaction, and how reproduction of hierarchically structured difference and bigoted stereotypes are performed, and challenged, through language. The medium, combined with the user’s speech acts, set up the norms and conditions for participation, and for the discursive processes that reproduce the relations and structures of power.

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The telescoping cantilever beam structure is applied in many different engineering sectors to achieve weight/space optimisation for structural integrity. There has been limited theory and analysis in the public domain of the stresses and deflections involved when applying a load to such a structure. This thesis proposes (a) The Tip Reaction Model, which adapts classical mechanics to predict deflection of a two and a three section steel telescoping cantilever beam; (b) An equation to determine the Critical buckling loads for a given configuration of the two section steel telescoping cantilever beam assembly derived from first principles, in particular the energy methods; and finally (c) the derivation of a design optimization methodology, to tackle localised buckling induced by shear, torsion and a combination of both, in the individual, constituent, hollow rectangular beam sections of the telescopic assembly. Bending stress and shear stress is numerically calculated for the same structure whilst subjected to inline and offset loading. An FEA model of the structure is solved to verify the previous deflection, stress and buckling predictions made numerically. Finally an experimental setup is conducted where deflections and stresses are measured whilst a two section assembly is subjected to various loading and boundary conditions. The results between the predicted theory, FEA and experimental setup are compared and discussed. The overall conclusion is that there is good correlation between the three sets of data.

Platinum-based catalysts for hydrogen fuel-cell applications have progressed greatly with the addition of a second element in either a mixed-alloy or core-shell structure. Not only do they contain a reduced amount of the more expensive platinum metal but they have been shown to demonstrate a significant improvement in catalytic activity. Further improvement of these systems can only be made by careful investigation of such catalyst panoparticles on an atomic scale. These nanoparticles provide a significant characterisation challenge due to their minute size and beam sensitivity. A new method of quantifying the annular dark-field (ADF) scanning transmission electron microscope (STEM) signal on an absolute scale has been developed to address this problem. Experimental images are scaled to a fraction of the incident beam intensity from a detector map. The integrated intensity of each individual atomic column is multiplied by the pixel area to yield a more robust imaging parameter: a scattering cross section, σ. Using this cross section approach and simulated reference data, I show it is possible to count the number of atoms in individual columns. With some prior knowledge of the sample, this makes it possible to reconstruct the 3-dimensional structures of pure platinum nanoparticles. Such an approach has subsequently been extended to bimetallic particles here the elements are close in atomic number, using the platinum-iridium system as an example. In the same way that the cross section can be calculated from ADF image intensity, it is possible to calculate an energy dispersive x-ray (EDX) partial scattering cross section, beneficial especially because of the simplicity of its implementation. In sufficiently thin samples such that the number of x-ray counts is linearly proportional to sample thickness, we can determine element-specific atom counts. Finally, it is possible to combine EDX and ADF cross sections to provide us with quantitative structural and compositional information.