A bearing chamber may be modelled as a horizontal cylinder, stationary or rotating about its axis, with a film of fluid coating the inside of the cylinder wall. The impact of droplets from a two-phase flow in the core of the chamber drives the motion of the oil film. In this thesis we develop a model for the film based on conservation of mass and momentum across the interface between the film and the core, droplet-laden flow. We derive a fourth-order partial differential equation for the film thickness which can be applied to a range of droplet parameters. Solution of this equation is primarily numerical, but approximating it by a cubic also provides useful analytical results. The equation for film thickness contains terms omitted by previous models of the bearing chamber. In particular, we show that terms due to the azimuthal component of droplet motion have a significant effect on film profiles, as they tend to destabilise shock solutions. A dominance of surface tension over the azimuthal droplet momentum is critical for stable steady shock solutions to exist. We consider the effect of the droplet impact being non-uniform about the cylinder, and the positioning of a sink to remove the mass added to the film by the droplets. We will also examine the underlying flow in the film, with particular note of recirculation regions and the residence time of the fluid in the chamber. These factors may be key to the effectiveness of the fluid as a coolant. We also show that Marangoni stresses on the film surface, one of the effects of heating the cylinder, can be modelled using the same film equation and also has a destabilizing effect.

We study the Hamiltonian dynamics for a system of two colliding point particles coupled to (2+1)-dimensional gravity with a negative cosmological constant by anchoring the dynamics of the system to its spatial infinity. We reduce the Chern-Simons formulation of the gravitational action, finding the reduced Hamiltonian for three special cases of the particle masses, in a phase space chart coordinatised by the geodesic distance between the two particles and its conjugate momentum. The dimension of the reduced phase space is two. At the threshold of black hole formation, the black hole mass depends linearly on the momentum, in agreement with previous analysis in a holonomy-based phase space chart. We use the reduced action to compute the semiclassical probability amplitude of two particles to tunnel out of the black hole, finding that the imaginary part of the action is equal to the Bekenstein-Hawking entropy of the hole. We also study the form that conformal field theory (CFT) correlation functions take in coset spaces of (2, C). We realise the (2, C) twistor space T in two distinct but equivalent ways, deriving some important facts about this space, and we also give one representation of another coset space B. We examine the form of CFT correlation functions in T, B and two other related spaces using techniques from representation theory and make a number of comments on the twistor transform for T.

This study focused on finding a balance between equality and diversity as seemingly opposites, in order to ensure realisation of cultural, linguistic and religious rights in education. In order to reach this goal, it was imperative to illustrate the meaning of the concepts equality, discrimination, culture and diversity in education. Unfolding the meaning of these concepts, as well as determining the scope of the learner's right to culture-specific education, the finding was that equality does not mean identical treatment of all, but rather it implies that a person has the right to be culturally distinguished. The objective of the empirical research was to determine to which extent the learner's cultural, linguistic and religious rights are catered for in schools, also to determine what the educational leaders' attitude is with regard to the subject. The population existed of school principals of public schools in the N3 district in Gauteng of which a sample of 80 principals was randomly chosen. The research was conducted by means of a questionnaire. In conclusion, some of the findings of this study are as follows: The attitude of the principals is in favour of culture specific education, but they do not favour an opinion that such education should lead to seperation of groups. The principals are in favour of mother tongue education and feel that such education will be more effective than education in a foreign language, though they see the implementation of a majority policy as a practicable solution. Principals agree that religion should play a prominent role in education. Cultural differences are being catered for by school cultural activities. Language and religious needs of minority groups are however not accommodated because of the implementation of a majority principle. Educational leaders should be equipped with knowledge and skills to effectively accommodate the cultural, linguistic and religious rights of learners. Respect for cultural identity should be cultivated by means of informing leaders, parents and teachers of mutual fundamental rights and duties. The practicability of education in the previously disadvantaged languages should be researched. This should be done concerning the different training methods and the need for training with regard to knowledge and skills that will enable educational leaders to effectively accommodate the cultural, linguistic and religious rights of the learners. / Thesis (M.Ed.)--Potchefstroom University for Christian Higher Education, 2002

This thesis describes the optimisation of the growth of bulk cubic GaN with low hexagonal content and with the intention of making it a commercial substrate for device applications. The optimised material was then applied for fabrication of cubic AlxGa1-xN/GaN based double barrier resonant tunnelling diode (DBRTD) devices. The devices with a clear negative differential resistance (NDR) and high reproducibility are demonstrated. In the early part of this project, we reported a study on cubic GaN material with the variation of III/V ratio, growth rate and wafer position. Using PL and XRD measurements, we found that all these factors influence the increase of hexagonal inclusions in cubic GaN, leading to poor quality in cubic nitride growth. This problem however is more significant when the thickness of cubic GaN is increased. From the calibration work, a ~50μm cubic GaN layer has been grown for the first time with a low average proportion of hexagonal inclusions of around 10% and just few percent at the interface of cubic GaN and GaAs substrate. Thus, the interface would be the most suitable surface for further growth. Next, we investigated the fundamental properties of cubic GaN using picosecond acoustic measurements. In this material, the sound velocity is found to be 6.9±0.1 kms-1, elastic constant = 285±8GPa and the refractive index at 400nm = 2.63±0.04. Comparison with hexagonal GaN films indicated that these parameter values differ considerably in different symmetry of GaN. These show the usefulness of our layers for determination of the basic properties of cubic GaN using a wide range of techniques. From the Hall transport measurement, the electrical properties of undoped cubic GaN samples depend on growth conditions and thickness. In this work, we successfully demonstrated p-type cubic GaN:Mn using C-doping and n-type behaviour from Si-doped cubic GaN. However, these samples have high electron density but low mobility as the residual impurities and intrinsic defects were found to be higher inside the samples. We extended the technology of growing cubic GaN to cubic AlxGa1-xN. A number of cubic AlxGa1-xN samples with different Al content, x were grown and characterised by PL measurement. We found that the hexagonal PL starts to dominate when x is increased, even for thin samples. This could be due to the problems of maintaining cubic AlxGa1-xN growth. It could also be due to the miscibility gap between AlN and GaN. More results and data are required to explain this behaviour. In this thesis, we demonstrated potential cubic GaN substrates for device applications for the first time. The study on bulk cubic GaN showed that the interface between the cubic GaN and the GaAs substrate has only few percent of hexagonal content. Thus, the surface that was in contact with GaAs is the most suitable surface for further processing and growth. Due to the effect of strain, As inclusions and defects were already formed on the surface. By polishing the surface for ~2 hours, these problems were minimised and the surface still had low hexagonal content. In this work, the first working InGaN LED device grown on a polished free-standing cubic GaN substrate has been demonstrated. Our polished cubic GaN substrates also improve the quality of the grown device as been measured by luminescence and I-V characteristics. In the last part of this thesis, we investigated the potential of cubic GaN for developing cubic AlxGa1-xN/GaN DBRTD devices. In the first stage of this work, the I-V characteristics of the cubic tunnel devices were calculated for various band offset, well width, barrier composition and barrier thickness parameters. From this work, optimal designs of cubic AlxGa1-xN/GaN tunnel diodes that could be fabricated and characterised were proposed. The result was then used as a starting point for the growth of cubic AlxGa1-xN/GaN DBRTD. A number of cubic AlxGa1-xN/GaN tunnel devices with different structural parameters were grown. Some devices showed a clear NDR effect but not all of them are reproducible due to breakdown of the device. This factor may also contribute to the irreproducibility of wurtzite (hexagonal) nitride based tunnel diodes in addition to the problem related to charge trapping.

Various aspects of three-dimensional spin foam models for quantum gravity are discussed. Spin foam models and graphical calculus are introduced via the Ponzano-Regge model for 3d gravity and some important properties of this model are described. The asymptotic formula for the 6j symbol found by Ponzano and Regge is generalised to include the Ponzano-Regge amplitude for triangulations of handlebodies. Some simple observables are computed in a model for fermions coupled to 3d gravity. The result is a sum over spin foam models with certain vertex amplitudes which are described. An explicit example is given and the vertex amplitudes expressed in terms of 6j symbols. Finally, a group field theory for this spin foam model is described.

This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are be useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through spacetime. We employ the use of Bogoliubov transformations to describe the effects of changing acceleration. We investigate how entanglement can be generated within a single cavity and the protocol of quantum teleportation is affected by non-uniform motion. The second set of results investigate how the Dirac field can be confined to a cavity for quantum information purposes. By again considering Bogoliubov transformations, we thoroughly investigate how the entanglement shared between two cavities is affected by non-uniform motion. In particular, we investigate the role of the Dirac fields charge in entanglement effects. We finally analyse a \one-way-trip" of one of the entangled cavities. It is shown that different types of Dirac field states are more robust against motion than others. The final results looks at using our second notion of localisation, Unruh-DeWitt detectors. We investigate how allowing for a \non-point-like" spatial profile of the Unruh-DeWitt detector affects how it interacts with a quantum field around it. By engineering suitable detector-field interactions, we use techniques from symplectic geometry to compute the dynamics of a quantum state beyond commonly used perturbation theory. Further, the use of Unruh-DeWitt detectors in generating entanglement between two distinct cavities will be investigated.

The growth of graphene on Ni thin films using several different methods is discussed. These methods include no intentional introduction of carbon, immersion in an organic solvent, exposure to carbon-containing gas and a solid state approach by decomposition of molecules. All the methods have produced single layer graphene over a large area. We suggest that the graphene formation without intentional introduction of carbon involves conversion of carbon-containing adsorbates on Si02. This process has been verified by our experiment of graphene growth by decomposition of C6O, in which C60 is deposited on top of Si02 and buried under Ni thin film. Single layer graphene has successfully formed which suggests that the carbon from C60 has diffused and segregated to the top of the Ni surface. So we investigate the effect of outgassing aimed to eliminate adsorbates on Si02. Graphene growth by immersion in an organic solvent was initially performed to investigate the effect of outgassing process, and single layer graphene is formed but is highly defective, as determined by the intensity of the Raman D band. We found that outgassing the Si02 is important to produce single layer graphene, but the defects in graphene are not significantly reduced. Graphene growth method using propylene is carried out to identify the factors that influence the amount of defects and to reduce through optimization of growth parameters. The graphene defects are reduced significantly by varying the annealing temperature and exposure time to propylene. We found that different Ni thickness do not affect the defect formation in graphene but do improve the Ni surface morphology. Graphene growth by decomposition of C60 on Ni thin film produced graphene layers with controlled thickness. This molecular carbon source provides a method of controlling the total dosage of carbon introduced into the film with a high degree of precision. We found that the C60 coverage, annealing temperature, and deposition sequence influence the properties of graphene layers. We also presented preliminary results of graphene enhanced Raman scattering (GERS) of adsorbed PTCDI. We demonstrate that single layer graphene is a very good substrate for Raman enhancement in which the adsorbed molecules can be detected at a small fraction of monolayer coverage. Using the same transfer method typically used for graphene, we managed to transfer PTCDI on graphene from Ni film to Si02. Here we demonstrate the effect of a substrate for graphene which can give rise to the enhancement of a Raman signal of adsorbed molecules.

The project concerned the study of quantum correlations (QC) in compound systems, i.e. statistical correlations more general than entanglement which are predicted by quantum mechanics but not described in any classical scenario. I aimed to understand the technical and operational properties of the measures of QC, their interplay with entanglement quantifiers and the experimental accessibility. In the first part of my research path, after having acquired the conceptual and technical rudiments of the project, I provided solutions for some computational issues: I developed analytical and numerical algorithms for calculating bipartite QC in finite dimensional systems. Then, I tackled the problem of the experimental detection of QC. There is no Hermitian operator associated with entanglement measures, nor with QC ones. However, the information encoded in a density matrix is redundant to quantify them, thus the full knowledge of the state is not required to accomplish the task. I reported the first protocol to measure the QC of an unknown state by means of a limited number of measurements, without performing the tomography of the state. My proposal has been implemented experimentally in a NMR (Nuclear Magnetic Resonance) setting. In the final stage of the project, I explored the foundational and operational merits of QC. I showed that the QC shared by two subsystems yield a genuinely quantum kind of uncertainty on single local observables. The result is a promising evidence of the potential exploitability of separable (unentangled) states for quantum metrology in noisy conditions.

We investigate phenomenologies arising from two distinct sets of modifications introduced in Loop Quantum Cosmology (LQC), namely, the inverse volume and the holonomy corrections. We find scaling solutions in each setting and show they give rise to a period of super-inflation soon after the universe starts expanding. This type of inflation is explicitly shown to resolve the horizon problem with far fewer number of e-foldings compared to the standard inflationary model. Scalar field perturbations are obtained and we demonstrate their near scale invariance in agreement with the latest observations of the Cosmic Microwave Background (CMB). Consideration of tensor perturbations of the metric results in a large blue tilt for these fluctuations, which implies their amplitude will be suppressed by many orders of magnitude on the CMB compared to the predictions of the standard inflation. This LQC result is shared by the ekpyrotic model and the model of a universe sourced by a phantom field. Exploring a correspondence map at the cosmological background level between braneworld cosmologies and the inverse volume corrected LQC, we discover this map not to hold at the level of linear perturbations. This is found to be due to the different behaviour of the rate of the Hubble parameter in the two classes of models. A complete dynamical analysis of Friedmann-Robertson-Walker spacetimes we carry out results in the most general forms of late time attractor scaling solutions. Our examination includes expanding and contracting universes when a scalar field evolves along a positive or a negative potential. Known results in the literature are demonstrated to correspond to certain limits of our solutions.

We investigate the canonical BRST–quantisation and refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling constraints with nonconstant functions on the configuration space. The quantum constraints are implemented by a rigging map that is motivated by a BRST version of group averaging. Two systems are considered. In the first one we avoid topological built–in complications by considering R 4 as phase space, on which a single constraint, linear in momentum is defined and rescaled. Here, the rigging map has a resolution finer than what can be extracted from the formally divergent contributions to the group averaging integral. Three cases emerge, depending on the asymptotics of the scaling function: (i) quantisation is equivalent to that with identity scaling; (ii) quantisation fails, owing to nonexistence of self–adjoint extensions of the constraint operator; (iii) a quantisation ambiguity arises from the self–adjoint extension of the constraint operator, and the resolution of this purely quantum mechanical ambiguity determines the superselection structure of the physical Hilbert space. The second system we consider is a generalisation of the aforementioned model, two constraints linear in momenta are defined on the phase space R 6 and their rescalings are analysed. With a suitable choice of a parametric family of scaling functions, we turn the unscaled abelian gauge algebra either into an algebra of constraints that (1) keeps the abelian property, or, (2) has a nonunimodular behaviour with gauge invariant structure functions, or, (3) contains structure functions depending on the full configuration space. For cases (1) and (2), we show that the BRST version of group averaging defines a proper rigging map in refined algebraic quantisation. In particular, quantisation case (2) becomes the first example known to the author where structure functions in the algebra of constraints are successfully handled in refined algebraic quantisation. Prospects of generalising the analysis to case (3) are discussed.