Continuous weak measurement provide a convenient way to gather information about a quantum system without the need to prepare huge ensembles of identical systems as required by standard quantum measurement theory. Even though weak measurement alter the dynamics of the wave function slightly, they nevertheless are a good tool to monitor the dynamics of the wave function in real time in the presence of certain perturbations, for example, sudden momentum kicks due to collisions with particles of a surrounding gas. With weak measurement it is possible to monitor the dynamics of the wave function without knowing it initially. The continuous monitoring can be employed to influence the dynamics by means of feedback. This thesis focuses on the numeric simulation of the continuous monitoring of the position of a free massive particle as well as a particle bound in the following one-dimensional potentials: harmonic and double well. The monitoring scheme involves estimating the wave function of the hydrogen atom initially and then applying the results of the weak measurement its position to update the estimate through a numerically simulated stochastic evolution. We also simulate evolution of the true wave function. The key highlights of this thesis include: discussion of an alternative way to derive the stochastic differential equations that govern the evolution of the true and estimated wave functions of the system, as well as the explanation of the second order numerical scheme. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.

Tensional Vacuum Vessels (TVV) are vessels constructed such that the walls are placed in tension rather than in compression as is the case with conventional vacuum vessels. TVVs have the advantage of being cost-effective, light weight in construction, and potentially portable. Tensional vessels have already been designed with regard to submarine applications. However, the use of this principle with regard to vacuum applications is believed to be novel. TVVs have two interlinked thin walled shells instead of the traditional single thick wall of conventional design. These shells are placed in tension by pressurising the intermediate space. This thesis outlines the theory of tensional vessels and describes the performance of a number of experimental chambers developed during this investigation. The fundamental theory of the TVV is outlined and developed in more detail with regard to cylindrical vessels. These include vessels constructed from longitudinal and circumferential tubes. The basic theory for any TVV can be derived from the equilibrium condition. This states that the force due to the gauge pressure on the outer shell must be greater than or equal to the force due to the absolute pressure on the inner shell. If the inward force predominates implosion will occur. Materials science considerations are also taken into account. If the tension in the walls exceeds that required for yield, the vessel will deform. The use of novel tensile materials is also explored. TVVs are potentially inflatable and theory is developed with regard to the possibility of buoyant vessels. The first experiments were based on earlier work performed at this institution with cylindrical TVVs constructed from longitudinal tubes. The tubes employed were soft drink cans which were sealed together with putty. The work described in this thesis outlines the development of larger versions and the instabilities which developed are noted. High vacuum experiments performed through the inclusion of a guard vessel are then described. This is followed by a further description of experiments performed with this basic tensional wall design in an attempt to gain a better understanding of its properties. These vessels were smaller and were gas pressurised in order to allow for increased flexibility with regard to pressure and volume variation. It is found that the compressional elements of such vessels cannot be ignored. A series of cylindrical TVVs with the walls constructed from circumferential tubes is then described, including high vacuum experiments, also performed through the inclusion of a guard vessel. The initial experiments were small in scale and made use of small bicycle tyres as the TVV walls. Larger vessels were then built, the walls being constructed from car tyres. These vessels are also inflatable and more stable than those constructed from longitudinal tubes. Also, the compressional elements do not play as great a role in these vessels. A fully tensional cylindrical vessel is then described which includes tensional end plates. Experiments performed with large bowls as the end plates are outlined. The theory of the deformation of a circular plate is also given including finite element analysis. Finally, a further novel vacuum vessel design is proposed. This is the spinning vacuum vessel. Proof of principle experiments are performed on a small scale vessel (a soft drink can with its interior reinforced with putty) which yields promising results. / Thesis (M.Sc.)-University of Natal, 1999.

Extracellular potentials due to firing of action potentials are computed around cortical neurons and populations of cortical neurons. These extracellular potentials are calculated as a sum of contributions from ionic currents passing through the cell membrane at various locations using Maxwell's equations in the quasi-static limit. These transmembrane currents are found from simulations of anatomically reconstructed cortical neurons implemented as multi-compartmental models in the simulation tool NEURON. Extracellular signatures of action potentials of single neurons are calculated both in the immediate vicinity of the neuron somas and along vertical axes. For the neuronal populations only vertical axis distributions are considered. The vertical-axis calculations were performed to investigate the contributions of action potential firing to laminar-electrode recordings. Results for high-pass (750 - 3000 Hz) filtered potentials are also given to mimic multi-unit activity (MUA) recordings. Extracellular traces from single neurons and populations (both synchronous and asynchronous) of neurons are shown for three different neuron types: layer 3 pyramid, layer 4 stellate and layer 5 pyramid cell. The layer 3 cell shows a 'closed-field' configuration, while the layer 5 pyramid demonstrates an 'open-field' appearance for singe neuron simulations which is less apparent in population simulations. The layer 4 stellate cell seems to fall somewhere in between the open- and closed-field scenarios. Comparing single neuron and synchronous populations, the amplitudes of the extracellular traces increase as population radii increase, though the shapes are generally similar. Asynchronous populations produce small amplitudes due to a time convolution of various neuron contributions. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2005

Cohesive energies, bulk moduli, and equilibrium lattice constants have been calculated for the 5d transition atoms (Hf, Ta, W, Re, Os, Ir and Pt) in face–centred cubic crystal lattices. We have used the ab initio pseudopotential method for the total energy calculations within the local density approximation. Two calculations have been performed for each element, one using only the s, p and d angular momentum components and another including the s, p and d components as well as the unoccupied 5f orbital in the ionic pseudopotentials. The pseudo–wave functions and charge densities of the valence electrons have been represented by a basis of plane waves. For the 5d metals the changes in the electronic structure of the solid are small and they produce small changes in the bulk properties. / Thesis (M.Sc.) - University of KwaZulu-Natal, Pietermaritzburg, 2008.

The continuous monitoring of beaches and structures near, or in the surf-zone, has become a vital task from an environmental and economic standpoint. Specifically, the Durban beaches are continually nourished with sand that is dredged south of the Durban Harbour mouth. Constant monitoring is essential to control the erosion and accretion of these beaches. Currently, infrequent and labour-intensive manual surveys are being used to fulfil this task. This dissertation describes the techniques used to process and validate surf-zone video images to extract information, which is equivalent but more frequent and cost effective to that obtained using manual surveying methods. The emphasis is on the extraction of accurate hourly waterlines by analysing video images obtained from Coastal Imaging stations located at Addington Beach and North Beach in Durban, South Africa and the measurement of rip currents in the surf-zone from video images together with the validation of these results. The implementation of a neural network incorporating non-local image pixel data is more reliable than previously used methods, for example, grayscale thresholding or the delta-discriminator. Grayscale thresholding relies on the difference between the water and the sand pixel intensities. The delta-discriminator incorporates hue-saturation-lightness (HSL) values to improve the discrimination between water and sand. These methods could not, however, overcome the problem of varying seasonal and diurnal light intensities and require the prior choice of threshold values. The use of non-local data, such as the average RGB-values, in addition to individual pixel values as inputs to a neural network is shown to give better results in changing ambient lighting conditions. Wavelet and Fourier analysis of the temporal nature of the breaking waves in the surf-zone is also used to calculate more accurate waterlines. These extracted waterlines are validated by data collected from manual surveys. The use of Digital Correlation Image Velocimetry (DCIV) has been proven as a successful method in tracing velocity flow fields in a fluid medium. Typically, the medium is populated with distinct seeds that are tracked through successive video frames using a cross-correlation technique. It is shown that DCIV can be used in surf-zone images to measure surface rip currents by tracking the structure of the advected foam. This technique was validated by simultaneously tracking a large number of yellow corks scattered on the water surface. / Thesis (M.Sc.)-University of Natal, Durban, 2001.

The molecular theory of the second light-scattering virial coefficient Bp describing the effects of interacting pairs of molecules on the depolarization ratio p of Rayleigh-scattered light is reviewed, both for interacting linear and nonlinear molecules. The molecular tensor theory of Bp for nonlinear molecules is extended for the first time to include in the scattered intensity p those contributions arising from field gradient effects and induced quadrupole moments in the molecular interactions. The expressions for contributions to Bp are evaluated numerically for the nonlinear polar molecule dimethyl ether. We have used an existing light-scattering apparatus to investigate the pressure-dependence of the depolarization ratio p for dimethyl ether, allowing Bp to be extracted. The measured value is compared with the calculated value, theory and experiment being found to agree to within 9%. This success in modelling Bp for dimethyl ether spurred us on to extend our investigation to the second Kerr-effect virial coefficient BK • The molecular-tensor theory of BK for nonlinear molecules is reviewed, and is applied in this work to dimethyl ether. The calculated BK values generally lie within the uncertainty limits of the available measured data over their full range of temperatures. We have used a recently-commissioned Kerr cell to undertake our own measurement of BK for dimethyl ether at room temperature. This value is in good agreement with the findings of our molecular model, and is in reasonable agreement with the other measured data. This thesis serves to reaffirm recent claims that comprehensive dipole-induced-dipole theories of molecular interaction effects explain the observed phenomena adequately provided one works to higher orders in the molecular tensors so that the series of contributing terms has converged to a meaningful numerical result, and provided the full symmetry of the molecules is allowed for. / Thesis (M.Sc.) - University of Natal, Pietermaritzburg, 2000.

Abstract available in PDF file. / Thesis (Ph.D.)-University of Natal, 1979.

The synthesis, structure and physical properties of a series of Mnx(Co, Mg)₁ˍxFe₂O₄, (Mg, Sr)₀.₂ Mn₀.₁Co₀.₇Fe₂O₄ and Mg₀.₅Mn₀.₅(RE)₀.₁Fe₁.₉O₄ (where RE are rare earth elements) nanoferrites have been studied. These compounds were synthesized at low reaction temperature of about 200 ⁰C using the glycol-thermal method. The starting materials were high-purity metal chlorides or nitrates which were precipitated by NH₄OH and KOH respectively. In addition, MnxCo₁₋xFe₂O₄ (x = 0, 0.5 and 1) samples were produced directly from high-purity metal oxides by high-energy ball milling technique. Single-phase cubic spinel structure and nanoparticle structure of the synthesized samples were confirmed by X-ray diffraction (XRD) and transmission electron microscope (TEM). The results show that the produced powders of the asprepared samples have average grain sizes ranging from 7 to 16 nm. Filtering the precipitates by Whatman glass microfiber filters (GF/F) appears to be important in obtaining the small particle sizes. We suspect higher stability of the MnxCo₁₋xFe₂O₄ at x = 0 and 0.5 where complete symmetry in the proportion of the atoms on tetrahedral (A) and octahedral (B) sites would tend to favour larger nanoparticles. The evolutions of the magnetic properties as a function of composition, annealing temperature under air and argon atmospheres or measuring temperature have been investigated by ⁵⁷Fe Mössbauer spectroscopy, vibration sample magnetometer (VSM) and superconducting quantum interference device (SQUID). Significant changes in magnetic properties are observed across the composition ranges studied. The Mössbauer spectra indicate ferrimagnetic, superparamagnetic and paramagnetic behaviours of the compounds. The results show evidence of transformation from single-domain to multi-domain structure with thermal annealing in our samples. Temperature dependence of magnetization shows differences between field cooling (FC) and zero field cooling (ZFC) which we attribute to spin-freezing and thermal relaxation for typical nanoparticles. Significant increase in coercive field with reduction in measuring temperature is obtained in Co- based compounds. Mn₀.₅Co₀.₅Fe₂O₄, Sr₀.₂Mn₀.₁Co₀.₇Fe₂O₄ and Mg₀.₂Mn₀.₁Co₀.₇Fe₂O₄ have large coercive fields of 1.45, 3.02 and 10.70 kOe at 4 K compared to 0.17, 0.05 and 0.05 kOe at room temperature respectively. Variation of coercive fields (Hc) with measuri ing temperature for MnxCo₁₋xFe₂O₄ (x = 0.1 and 0.05), (Mg, Sr)₀.₂Mn₀.₁Co₀.₇Fe₂O₄ nanoferrites follow the Kneller's law for uniaxial non-interacting single domain particles of the form Hc(T) = Hc(0)[1-( T/Tβ)α]. The observed temperature dependences are consistent with α = 1/2. We also find evidence of the departure from this law at lower temperature. The temperature dependence of the saturation magnetizations were observed to vary with temperature according to the modified Bloch's law Ms(T) = Ms(0)[1 - ( T/T₀)ᵝ] where β is at least 1.5. This is attributed to the confinement effects of the spin-wave spectrum for magnetic clusters. The equation appears to fit the saturation magnetization data over the entire temperature range with values of β from 2.1 to 2.4 for the samples studied. These results are consistent with the nanoparticle nature of the compounds. In Mg₀.₅Mn₀.₅(RE)₀.₁Fe₁.₉O₄ nanoferrites, the grain sizes, lattice parameters and saturation magnetizations increase with RE substitution which we attribute to larger RE ions substituting smaller Fe ions. The results show evidence of superparamagnetic behaviour of the nanoparticles. The highest grain size and magnetizations are obtained for the Gd substituted sample. We find strong correlation between the saturation magnetizations, grain sizes and microstrains with de Gennes factor G. The correlation with grain sizes and microstrains appear to be unique and characteristic of the nanoparticle nature of the compounds. Bulk samples in the form of pellets were also produced from the as-prepared samples of MnxCo₁₋xFe₂O₄ for resistivity measurements. The temperature dependence of the electrical resistivity for samples sintered from 600 - 1100 ⁰C under argon atmosphere were studied using the four-probe method from room temperature to about 110 ⁰C. Two possible mechanisms for resistivity involving Tˉ¹ and Tˉ¹/² dependences were investigated which we associated with semiconducting and inter-grain conductivity respectively. The Tˉ¹/² dependence is found to fit the data better and predicts higher activation energies. The resistivity was observed to be sensitive to the surface of the pellet being probed and the annealing temperature. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

The study of outer radiation belt dynamics has been ongoing for over 5 decades. Outer radiation belt dropouts involve the rapid lost of electron fluxes at the main phase of a storm and subsequent recovery. The characteristics of the dropouts are many and varied. This study examines the Geosynchronous Earth Orbit (GEO) and the ionospheric responses during Stream Interface (SI) andMagnetic Cloud (MC) events, using a combination of ground based and satellite instruments. SI- and MC-driven dropout events were inspected from summary plots of the Synchronous Orbit Particle Analyser (SOPA) instruments from the year 1996 to 2007. Comprehensive studies were done on six selected events. Analysis of the data from the instruments indicate that SIs and MCs are important lost drivers with significant differences in GEO and ionospheric environment. To validate the data and test for consistent response of the events, the Superposed Epoch Analysis (SEA) technique was used. The ground based measurements also revealed how the absorption peaks in the ionosphere correlated with dropouts and geophysical activity. Ionospheric absorption during SI associated dropouts was enhanced for 5 < L < 6, while significant peaks in ionospheric absorption extended to lower L during MC driven dropouts. Wave-particle interactions and southward Interplanetary Magnetic Field (IMF-Bz) are apparent causes for the precipitation. This analysis showed that, within the confines of the selected events, SI driven dropouts were more dominant at the declining phase of the solar cycle while the MC driven dropouts were more dominant during solar maximum. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.

Whistlers are naturally occurring Very Low Frequency (VLF) phenomena which are the result of lightning-radiated electromagnetic waves propagating in Earth’s plasma environment. Major research into whistlers and their generation began in 1951 and since then much has been discovered about them. This has allowed whistlers to be used as magnetospheric probes. Many issues concerning whistlers are still disputed, however, such as the relationship between the lightning location and the conjugate point of the receiver. A correlation between whistlers detected by the DEMETER satellite above South Africa and lightning located by WWLLN was used to determine the source region for these whistlers. The whistlers were found to originate from lightning strokes as far away as 10000 km. This result is statistically significant. During the course of this research an interesting observation of chorus was made on Marion Island. Since this was the first observation of chorus made on the sub-antarctic Marion Island, conditions surrounding the event were studied in great detail. This led to several interesting observations about the nature of this observation. In particular, during the evolution of the emission, it transformed to hiss, which makes this observation relevant to recent results suggesting that hiss is generated by chorus. It was also found that Marion Island was close to the plasmapause during the observation, which has further implications related to the chorus-hiss relationship. A study of the occurrence of twin whistlers received at Rothera and SANAE IV was conducted. These were whistlers which had propagated from a single ionospheric exit point to both receivers. Rothera and SANAE IV share the same whistler source region, yet the average number of whistlers received at Rothera is an order of magnitude greater than that received at SANAE IV. The twin whistler analysis showed that the most probable reason for this disparity is that whistlers from the source region enter the waveguide preferentially closer to Rothera, making it more likely for them to be received at Rothera than SANAE IV. These results have implications on the nature of sub-ionospheric propagation of whistlers, which is not the same as that of spherics. Finally, a method for tracking tropical cyclones using lightning locations from WWLLN was developed. During the course of this thesis, tropical cyclone Irena was the result of damage on the east coast of South Africa. This presented an opportunity to investigate the ability of WWLLN data to describe the passage of these destructive phenomena near South Africa. The details of this new method are discussed. While the algorithm developed has room for improvement, its performance was tested on the recent tropical cyclone Irina which occurred during 2012. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.