Thesis (M. Sc) --University of Limpopo, 1999 / refer to ducument

Thesis (M.Sc. (Physics)) --University of Limpopo, 2005 / Self-consistent electronic structure calculations have been performed on ordered cubic-based magnesium-lithium (Mgx-Li1−x) alloys spanning the concentration range 0 ≤ x ≤ 1, using an ab initio plane wave pseudopotential (PWP) method. The first principle pseudopotential planewave approach is used within the local density approximation (LDA) and generalized-gradient approximation (GGA)of the density functional theory (DFT) framework. We have calculated the binding energy curves and the systematic trends in various cohesive and elastic properties at zero temperature, as a function of Li concentration. The calculated equilibrium lattice parameters show a large deviation from Vegard’s rule in the Li-rich region whilst the bulk moduli decrease monotonically with increase in Li concentration. The heats of formation for different ground state superstructures predict that the DO3, B2 and DO22 structures would be the most stable at absolute zero amongst various phases having the Mg3Li, MgLi and MgLi3 compositions, respectively. This stability is reflected in the electronic density of states (DOS). Because of the special significance of the isotropic bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio for technological and engineering applications, we have also calculated these quantities from the elastic constants. The elastic constants indicate the softness of the material as more Li is added with the bcc-based phases becoming mechanically less stable for Li concentration less than 50%. Our results show good agreement within the estimated uncertainty with both experimental and previous theoretical results. / The National Research Foundation (NRF), South Africa-Royal Society (RS), Great Britain collaboration and Council for the Scientific and Industrial Research (CSIR)

Measurements are carried out for dendrite tip growth of succinonitrile-acetone alloys solidifying freely in an undercooled melt. The current experimental investigation is conducted using the equiaxed dendritic solidification experiment (EDSE). This setup allows for precise measurements of the dendrite tip velocity, radius and shape for a range of undercoolings and solute concentrations. The collected data are compared to available theories of free dendritic growth, such as the Lipton-Glicksman-Kurz and Li-Beckermann models. It is found that for dilute succinonitrile-acetone alloys, the measured dendrite tip Péclet numbers agree well with previous theories of free dendritic growth, if the effects of melt convection are taken into account. The tip selection parameter deviates significantly from the pure succinonitrile value and is inversely related to the applied undercooling. Besides, the selection parameter shows no dependence on the solute concentration. These results are consistent with phase-field simulations and preceding experimental investigations. In addition, scaling relationships for the sidebranching shape were obtained in terms of the dendritic envelope, projection area and contour length. These new scaling relations agree well with previous measurements in pure succinonitrile dendrites by Li and Beckermann.

Smoothing techniques are designed to improve the accuracy of equating functions. The main purpose of this dissertation was to propose a new statistic (CS) and compare it to existing model selection strategies in selecting smoothing parameters for polynomial loglinear presmoothing (C) and cubic spline postsmoothing (S) for mixed-format tests under a random groups design. For polynomial loglinear presmoothing, CS was compared to seven existing model selection strategies in selecting the C parameters: likelihood ratio chi-square test (G2), Pearson chi-square test (PC), likelihood ratio chi-square difference test (G2diff), Pearson chi-square difference test (PCdiff), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Consistent Akaike Information Criterion (CAIC). For cubic spline postsmoothing, CS was compared to the ± 1 standard error of equating (± 1 SEE) rule. In this dissertation, both the pseudo-test data, Biology long and short, and Environmental Science long and short, and the simulated data were used to evaluate the performance of the CS statistic and the existing model selection strategies. For both types of data, sample sizes of 500, 1000, 2000, and 3000 were investigated. In addition, No Equating Needed conditions and Equating Needed conditions were investigated for the simulated data. For polynomial loglinear presmoothing, mean absolute difference (MAD), average squared bias (ASB), average squared error (ASE), and mean squared errors (MSE) were computed to evaluate the performance of all model selection strategies based on three sets of criteria: cumulative relative frequency distribution (CRFD), relative frequency distribution (RFD), and the equipercentile equating relationship. For cubic spline postsmoothing, the evaluation of different model selection procedures was only based on the MAD, ASB, ASE, and MSE of equipercentile equating. The main findings based on the pseudo-test data and simulated data were as follows: (1) As sample sizes increased, the average C values increased and the average S values decreased for all model selection strategies. (2) For polynomial loglinear presmoothing, compared to the results without smoothing, all model selection strategies always introduced bias of RFD and significantly reduced the standard errors and mean squared errors of RFD; only AIC reduced the MSE of CRFD and MSE of equipercentile equating across all sample sizes and all test forms; the best CS procedure tended to yield an equivalent or smaller MSE of equipercentile equating than the AIC and G2diff statistics. (3) For cubic spline postsmoothing, both the ± 1 SEE rule and the CS procedure tended to perform reasonably well in reducing the ASE and MSE of equipercentile equating. (4) Among all existing model selection strategies, the ±1 SEE rule in postsmoothing tended to perform better than any of the seven existing model selection strategies in presmoothing in terms of the reduction of random error and total error; (5) pseudo-test data and the simulated data tended to yield similar results. The limitations of the study and possible future research are discussed in the dissertation.

Silicon Carbide has been a semiconductor material of interest as a high power and temperature replacement for Silicon (Si) in harsh environments due to the higher thermal conductivity and chemical stability of SiC. The cost, however, to produce this material is quite high. There are also defects in the substrate material (SiC) that penetrate into the active devices layers which are known device killers. Silicon is a material that provides a low cost substrate material for epitaxial growth and does not contain the defects that SiC substrates have. However, the large (~22%) lattice mismatch between Si and SiC creates dislocations at the SiC/Si interface and defects in the SiC epitaxial layer. These defects result in high leakage currents in 3C-SiC/Si devices. The main focus of the this research was to reduce or eliminate these defects using novel Si substrates. First a 3C-SiC on Si baseline process was developed under atmospheric pressure conditions consisting of 3 steps - an in-situ hydrogen etch to remove the native oxide, a carbonization step to convert the Si surface to SiC, and finally a growth step to thicken the SiC layer to the desired value. This process was then modified to establish a high-quality, low-pressure 3C-SiC CVD growth process. This LPCVD process was then used to grow 3C-SiC on numerous novel Si substrates, including porous Si, porous 3C-SiC "free-standing" substrates and SOI substrates which consisted on thin Si films bonded to poly-crystalline SiC plates. The results of these experiments are presented along with suggestions for future work so that device-grade films of 3C-SiC can be developed for various applications.

Doctor of Philosophy (PhD) / For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models.

<p>This thesis studies path generation for industrial robots of six degrees of freedom. A path is defined by connection of simple geometrical objects like arcs and straight lines. About each point at which the objects connect, a region, henceforth called a zone, is defined in which deviation from the defined path is permitted. The zone allows the robot to follow the path at a constant speed, but the acceleration needed may vary. </p><p>Some means of calculating the zone path as to make the acceleration continuous will be presented. In joint space the path is described by the use of cubic splines. The transformation of the Cartesian path to paths in joint space will be examined. Discontinuities in the second order derivatives will appear between the splines. </p><p>A few examples of different zone path calculations will be presented where the resulting spline functions are compared with respect to their first and second order derivatives. An investigation of the number of spline functions needed when, given an upper limit of deviation, the transformation back to Cartesian coordinates is made.</p>

Two extensions to the proper orthogonal decomposition (POD) technique are considered for steady transonic aerodynamic applications. The first is to couple the POD approach with a cubic spline interpolation procedure in order to develop fast, low-order models that accurately capture the variation in parameters, such as the angle of attack or inflow Mach number. The second extension is a POD technique for the reconstruction of incomplete or inaccurate aerodynamic data. First, missing flow field data is constructed with an existing POD basis constructed from complete aerodynamic data. Second, a technique is used to develop a complete snapshots from an incomplete set of aerodynamic snapshots. / Singapore-MIT Alliance (SMA)

In the study of the Degasperis-Procesi dierential equation, an eigenvalue problem called the cubic string occurs. This is a third order generalization of the second order problem describing the eigenmodes of a vibrating string. In this thesis we study the eigenfunctions of the cubic string for discrete and continuous mass distributions, using the theory of total positivity, via a combinatorial approach with planar networks.

c-BN has been in focus for several years due to its interesting properties. The possibility for large area CVD is a requirement for the realization of these different properties in various applications. Unfortunately, there are at present severe problems in the CVD growth of c-BN. The purpose with this research project has been to theoretically investigate, using DFT calculations, the possibility for a layer-by-layer CVD growth of c-BN. It could be established that, PEALD, using a BF3-H2-NH3-F2 pulse cycle and a diamond substrate, is a promising method for deposition of c-BN films. The gaseous species will decompose in the plasma and form BFx, H, NHx, and F species (x = 0, 1, 2, 3). The H and F radicals will uphold the cubic structure by completely hydrogenate, or fluorinate, the growing surface. However, surface radical sites will appear during the growth process as a result of atomic H, or F, abstraction reactions. The addition of NHx growth species (x = 0, 1, 2) to B radical sites, and BFx growth species (x = 0, 1, 2) to N radical sites, will then result in a continuous growth of c-BN.