# Masters Degrees (Physics)

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Item Theoretical and experimental investigations of the Kerr Effect and Cotton-Mouton Effect.(2008) Janse Van Rensburg, Angela Louise.; Couling, Vincent William.Mr T. J. Sono, an MSc student during the period January 2001 to January 2003, developed an apparatus to measure the pressure and temperature dependence of the electric-field induced birefringence (or electro-optic Kerr effect) in gases. Mr Sono obtained experimental results for dimethyl ether at a wavelength of 632.8 nm resulting in polarizability tensor components, first and second Kerr hyperpolarizabilities, and second Kerr-effect virial coefficients for this particular molecular species. One of the primary concerns of this thesis has been to obtain new measured Kerr-effect data for dimethyl ether and for trifluoromethane over a range of temperature. The cell has been calibrated using hydrogen as a primary standard, and has been carefully aligned to avoid multiple reflections of the incident laser beam off the closely-spaced electrode surfaces. The data has been analyzed to extract values of the polarizability anisotropy and the second Kerr hyperpolarizability for these molecules. In addition, precise values for the second Kerr-effect virial coefficients have been obtained from measurements of the Kerr effect a function of pressure. The molecular-tensor theory of the second Kerr-effect virial coefficient BK is reviewed. This theory describes the effects of intermolecular interactions on the molar Kerr constant, and it has been used to compute BK for dimethyl ether and trifluoromethane over the experimental temperature range. Agreement between experiment and theory is generally good. BK for ammonia has also been calculated, and compared to recent measured data found in the literature. The theory of the Cotton-Mouton effect (the magnetic analogue of the Kerr-effect) in a dilute gas is reviewed, and a new molecular-tensor theory describing the effects of molecular pair-interactions is developed. Calculations for a test molecule, namely chloromethane, indicate that density-dependent effects for this molecule are extremely tiny (of the order of 1% for typical experimental pressures). This new theory could be profitably used in selecting molecules which might demonstrate a larger effect which might be more readily measured in the laboratory.Item The effect of the f-component of the pseudopotential on selected properties of 5d transition metal systems(2008) Cunnama, DanielCohesive 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.Item Transverse modes in porro prism resonators(2008) Burger, Liesl.This dissertation consists of two main sections. The first is a review of laser resonators using spherical mirrors, and incorporates a physical optics numerical model of a Fabry-Perot laser resonator without gain. The output of this model, which includes spot sizes, loss, and transverse mode formation, is compared to the parameters calculated using published analytical results. This comparison serves as a verification of the numerical methods used, as well as a frame of reference for the model of a Porro prism resonator which follows in the second section. The second section proposes a new method for analysing Porro prism resonators. The analysis incorporates both geometric as well as physical optics concepts, with the prisms modelled as rotating elements with amplitude and phase distortions. This yields expressions for the orientation of the loss at the apex of each prism, and as well as the number of petals in the “petal-pattern” beam structure commonly observed from Porro prism lasers. These expressions are included in a numerical model, which is first used to verify the development of the characteristic petal-pattern. Next, the numerical model is used to investigate the development of the beam structure, in both time and space, in crossed Porro resonators with a range of Fresnel numbers and stability parameters. This leads to some new insight into the transverse modes of these lasers.Item Monte Carlo simulations in open quantum systems.(2007) Van Ryn, Nicholas.; Petruccione, Francesco.The motivation for this Masters thesis is to develop numerical algorithms to study the dynamical evolution of non-Markovian open quantum systems. Such systems are of importance if one is interested in modeling solid state systems which are candidates for the qubit - the quantum analog of the binary digit. Such an example may be a trapped spin onto which is encoded a chosen spin state. In reality, such a spin is never completely isolated from the environment, and so from a practical point of view it is of interest to study the dynamics of this interaction between some open system with an environment. The goal here is to create a computer program to simulate this behaviour of all density matrix elements for the open system numerically. Many interesting quantum systems, spin chains as an example, do not behave as a Markovian process, and it is sometimes difficult or perhaps indeed impossible to derive exact analytical solutions. As such, the techniques used in this thesis are aimed at describing non-Markovian processes in a way that approaches the exact solution. The study begins by introducing the reader to important concepts and results in the general study of both closed and open quantum systems. Differences in the treatment of the two types of systems are pointed out, and the necessary standard equations used generally are presented. Additionally, two different techniques are explained for the study of open quantum systems, namely the density matrix approach and the stochastic wavefunction approach. Important results from these two methods are presented and the section ends by convincing the reader of their equivalence. The second chapter begins with an example of an open quantum system which exhibits non-Markovian behaviour. The model of the spin star system is described and important results are given from references. This chapter introduces the reader to the model, conceptually explaining the system, and going on to show its exact analytical behaviour. This basic model, with minor changes, will be used throughout this study and the physics, interactions and symmetries, does not really change. This study then shows how one can use the stochastic wavefunction method to solve the dynamics of the spin star model. This chapter follows with deriving stochastic equations for the same system as the preceding chapter, and using these equations a numerical algorithm is developed, the results of which provide a good comparison between the exact analytical and exact numerical techniques. As a further example, a similar but slightly more complex system is studied in exactly the same manner, with the only important difference being that the open quantum system to be modeled is now a spin-one particle. Important differences in the results are pointed out and explained, and important similarities are highlighted. In presenting the results of this second simulation, shortcomings of the numerical technique and areas of applicability are discussed. In the final chapter the author considers using this numerical technique's ability to completely map the dynamics for a density matrix to investigate a measure of quantumness for an open system. This research has been submitted for publication to a peer reviewed journal.Item The fluorescent tube-lamp integrating chamber.(2008) Durrheim, C. R.The objective of this project is to design a facility that will characterize the electrical and optical properties of both tubular and the more recent compact fluorescent tubes. The first stage of this project, which is the subject of this dissertation, was to design, build, test, and model a cylindrical light integrating chamber. An integrating chamber capable of measuring 2-metre long fluorescent tubes was built at the University of KwaZulu-Natal, South Africa. To approximate an infinitely long tube, precisely mounted planar mirrors were placed at opposite ends of the cylinder. The reflectance of diffusive reflective paint and mirrors enter into calculations and were investigated experimentally using a Jarrel-Ash optical spectrometer. The light flux was finally measured for various chamber lengths and compared with a mathematical model. Total light power output from the lamp was calculated and compared with the electrical power input, and the lamp efficiency deduced. Accurate calculations required that the light field surrounding a cylindrical diffuse source be modeled mathematically. The reflection coefficients of the mirrors were not unity and the equations had to be modified to include this effect. The mathematical model was solved using a combination of analytical and numerical techniques. The model results were compared with measurements. The final result includes a mathematical description of the integrating chamber, and a flux-density plot of the space surrounding the fluorescent tube.Item Equilibrium properties of some high-temperature superconductors.(2007) Mbela, Kalengay.An important fundamental problem in the understanding of the high-Tc superconducting systems is the determination of their equilibrium magnetization behaviour, in particular their constitutive Brev(H) orMrev(H) behavior. Single crystal specimens of these materials are typically small (order of micron/millimeter), and are generally in the form of platelets. Their superconductivity properties are, moreover, highly anisotropic. The magnetization [M(H0)] curves in these systems also manifest a hysteresis due to vortex pinning, and, at fields below the lower critical field Hc1, due to a “geometry” effect, which results from a non-uniform internal field distribution in the platelet specimen geometry in a perpendicular applied magnetic field H0. In the present work a brief review of the field is given and a treatment (due to Doyle and Labusch) of the problem is described in some detail, and is used in the analysis of magnetization data [M(H0)] on single-crystal platelet specimens of the YBCO and BSCCO high-Tc superconducting systems. The treatment, which is based on a rigorous theoretical analysis of a quasi-static arbitrary distribution of vortices in a specimen of arbitrary shape (Labusch and Doyle ), predicts the quasi-static magnetization behavior M(H) of the specimen, and allows for the inclusion of explicit relations for the equilibrium “constitutive” Brev(H, T), and for the bulk vortex pinning force density Pv(B). An analytical formula for Brev(H, T) in terms of the fundamental characteristic properties ?ij(T) (the anisotropic Ginsburg -Landau parameter) and the critical field Hc(T) (or the lower critical field Hc1(T)) is obtained from an accurate model fit to a numerical solution of the non-linear Ginsburg-Landau equation (Labusch and Doyle ). For the determination of ? and Hc c1, (i.e. the G-L parameter and the lower critical field along the crystalline c- axis of platelet specimens) from M(H0, T) experimental isotherms (where H0 is the magnetic field applied along the c-axis -the thin dimension of the platelet specimens), a computer algorithm, which incorporates the above treatments, was used. In order to obtain a fit between theoretical model results (of the numerical algorithm for equilibrium behavior) and the experimental M(H0, T) data, experimentally obtained hysteresis curves were averaged by taking the mean values of M(H0) for H0 increasing and decreasing over the entire M(H0) loop. This data was then normalized by Hc1(T) for both M and H0, with Hc1(T) and ?(T) being used as fitting parameters.Item Applications of Lie symmetry analysis to the quantum Brownian motion model.(2008) Naicker, Viroshan.Lie symmetry group methods provide a useful tool for the analysis of differential equations in a variety of areas in physics and applied mathematics. The nature of symmetry is that it provides information on properties which remain invariant under transformation. In differential equations this invariance provides a route toward complete integrations, reductions, linearisations and analytical solutions which can evade standard techniques of analysis. In this thesis we study two problems in quantum mechanics from a symmetry perspective: We consider for pedagogical purposes the linear time dependent Schrodinger equation in a potential and provide a symmetry analysis of the resulting equations. Thereafter, as an original contribution, we study the group theoretic properties of the density matrix equation for the quantum Brownian motion of a free particle interacting with a bath of harmonic oscillators. We provide a number of canonical reductions of the system to equations of reduced dimensionality as well as several complete integrations.Item Towards practical quantum cryptography.(2009) Mirza, Abdul R.The information society that presides today is dependent on the communication industry to facilitate unintelligible data transfers between authenticated parties. Such requirements have, to date, taken advantage of security based on the mathematical complexities of certain algorithms. However, the advancement of computing power and the advent of the quantum computer together with the vulnerability of this scheme to mathematical progress have prompted the introduction of quantum cryptography. This process, through the laws of quantum physics, ensures provably secure data communication. Quantum cryptography provides physical protection to individual bits of information thus providing a hardware implemented solution. The implementation of this theoretical concept requires much practical innovation for transparent deployment into current cryptographic solutions. This thesis introduces the concept of quantum cryptography in a practical perspective. It raises a few core concerns with the present quantum cryptographic technology and provides some solutions towards the practical deployment of commercially feasible quantum cryptographic systems. The thesis commences with an introduction to classical cryptography focussing on key management protocols. This is followed by the presentation of the basic concepts of Quantum Key Distribution (QKD) together with an explanation of some QKD protocols and parameter required to classify such protocols. Chapter 2 discusses the theoretical and practical aspects of quantum channels in particular optical fibre. The primary challenges of transferring classical and quantum data along these channels are mentioned together with some solutions. A description of experimental usage with present QKD solutions is presented in Chapter 3. An investigation into highly efficient QKD protocols follows illustrating effective post-distribution processing for increasing the efficiency of the BB84 protocol. Chapter 4 begins with the limitations of present day QKD systems and explicates Quantum Networks as a possible solution. An introduction to classical networking theory is first presented after which some quantum network architectures based on passive optical networks are illustrated. Finally the proposed Quantum City project in conjunction with the eThekwini Municipality is explained. The realization of this project is intended to be complete by the third quarter of 2008 effectively making Durban into the first Quantum City in the world.Item Vacuum vessels in tension.(1999) McKenzie, Edric Roy.; Michaelis, Max M.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.Item Feasibility study of ionospheric tomography using HF radar(2010-09-09) Nambala, Fred JoeThis thesis gives an outline of the ionosphere and studies that were conducted to investigateItem Modelling the interaction between human immunodeficiency virus, mycobacterium tuberculosis and the human immune system, including the effects of drug therapy.(2007) Ramkissoon, Santosh.; Matthews, Alan Peter.; Mwambi, Henry G.Tuberculosis (TB) is the leading cause of death in individuals infected with human immunodeficiency virus (HIV) in several African countries, including South Africa. HIV-positive individuals do not have the immune system resources to keep TB in check and are as much as 30 times more likely to develop active TB than people who are HIV-negative. Many people infected with HIV develop TB as the first manifestation of AIDS and TB accelerates disease progression in HIV-positive individuals. HIV and TB pathogenesis are thus inextricably intertwined so that it is necessary for medical practitioners to have an understanding of the dynamics and treatment of HIV-TB coinfection. At present the question remains as to whether the best time for coinfected individuals to start antiretroviral treatment for HIV is at the beginning, the peak, or after the completion of the TB treatment phase. This dissertation was undertaken with the aim of obtaining some clarity on this question by creating a mathematical model of HIV-TB coinfection and its treatment. This needs an understanding of the biological interactions; therefore the dissertation begins with a discussion of the biological mechanisms of HIV, the human immune system, TB and the drug therapies for each disease. Thereafter a brief introduction to mathematical modelling reviews basic HIV models, which are then modified to include HIV drug therapy. Analyses and simulations of these models were carried out, which yielded some insights into the dynamics of HIV and HIV therapy. Finally HIV-TB coinfection is introduced by reviewing a previously developed model. Based on all the models reviewed, a model for coinfection is developed which includes treatment for HIV and TB. Numerical simulations suggest that, if HIV disease progression is at an advanced stage of the immune system collapsing towards AIDS, with low T-cell count and high viral load, it is necessary to treat for both diseases simultaneously to ensure a positive survival prognosis for the coinfected individual. However, if disease progression is in the early stages of AIDS, with T-cell count and viral load beginning to display signs of the immune system collapse but still at reasonable levels relative to advanced stages, it need not be necessary to treat both diseases simultaneously. TB can be treated first, and upon completion HIV treatment can be initiated thus sparing the coinfected individual from the compounded side-effects and drug-drug interactions which usually result from simultaneous treatment.Item An investigation of ultra low frequency (ULF) pulsations using radar data and solar wind data.(2010-09-10) Mthembu, Sibusiso H.An investigation of Ultra Low Frequency (ULF) pulsations was conducted using dataItem Computational studies of percolation : determination of the cluster number scaling function for lattices in 2 dimensions.(2010-09-30) Nduwayo, Léonard.The main aim of this work is to study percolation theory on regular two dimensionalItem Extracellular potentials from action potentials of anatomically realistic neurons and neuronal populations.(2005) Cavero, Miguel.; Chetty, Nithaya.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.Item Figure rotation of dark halos in cold dark matter simulations.(2005) Bryan, Sarah.; Cress, Catherine M.We have simulated structure formation on cosmological-scales using N-body simulations run on the University of KwaZulu-Natal's cluster of computers and have used these simulations to investigate aspects of galaxy evolution. In particular, we focus on the rotation of dark matter halos identified in Cold Dark Matter (CDM) simulations. These halos are typical of those thought to surround galaxies. Understanding their morphology and kinematics will help with the interpretation of observations and will constrain models of galaxy formation and evolution. We have determined the mass function of our simulated halos and shown that this agrees well with other simulations and theoretical predictions of this function. We have also explored the evolution of the mass function with redshift, which clearly shows hierarchical structure formation. In considering the angular momentum of our sample of halos, we have found the spin distribution to be well fit by a log normal distribution. After removing all halos that have either recently undergone major mergers or contain a significant amount of substructure from our sample, 75% of the remaining halos were found to undergo coherent rotation over periods of three gigayears. The pattern speeds were found to follow a log normal distribution, with an average value of 0.13h radians per gigayear. The most rapidly rotating halo detected was found to have a pattern speed of 0.41h radians per gigayear. Many halos showed alignment between their rotation and minor axes. We found no correlation between halo properties, such as total mass, and the pattern speed. While the speeds observed were not sufficient to cause spiral structure, the rotation could be relevant for understanding other observations of galaxies.Item Characterization and improvement of a direct solar radiation detector.(2004) Macome, Marcelino Adriano.; McPherson, Michael.A low-cost Direct Solar Radiation Detector (DSRD) was developed in house in the Department of Physics at the University of KwaZulu-Natal (Westville). A main use of this instrument is to gather solar energy data that are to be used in the design of systems that concentrate and convert solar energy into thermal energy (concentrating solar thermal energy systems). These data are compiled into a database from which the efficiency and potential use of many solar systems can be based. It was required that the detector was fully characterized with respect to spectral range, polar (angular) response and environmental stability. Based on this analysis it was also required to investigate possible ways of improving the detector. An Eppley Normal Incidence Pyrheliometer (NIP) mounted on an Eppley Sun Tracker (ST) was used as a reference instrument. The ST is a power driven tracker with an axis parallel to the Earth's axis of rotation. The NIP and DSRD were mounted together on the tracker in order to correlate their responses and also to calibrate the DSRD. The results indicate that the modified DSRD works better in that it follows the reference instrument. The correlation between the NIP data and the DSRD data is better with the value of correlation factor close to unity and the root mean square error value close to zero. This means that the modifications carried out on the detector have improved the low cost in-house detector and hence the quality of data collected.Item Experimental investigation of waves breaking over a bar in the surf zone.(2005) Pillay, Ursula Monica.; Govender, Kessie.Experiments on regular two dimensional waves breaking over an artificial sand bar were conducted in a glass walled flume to facilitate an investigation of the hydrodynamic processes that evolve in the surf zone. The instantaneous time averaged velocities and the velocity flow fields have been measured using digital video imaging and analysis techniques. The instantaneous velocity flow fields were then processed, resulting in the phase-ensemble-averaged velocities, time averaged velocities and energy and momentum fluxes. The time averaged velocities above the trough level have been found to be much higher than those below. After wave breaking, kinetic energy and momentum flux are shown to increase, reaching a peak value and decreasing thereafter. An estimate of the relative density of the fluid in the wave crests was obtained by comparing the forward and reverse velocity fluxes. Other surf zone physical parameters such as the free surface displacements, wave heights across the flume and potential energies have been derived from the resistive wave gauge measurements. A spectral analysis of the water level time series was conducted and the energy growth in each spectral component was examined. It was noticed that there is a transfer of energy from the primary frequency of the wave maker to higher harmonics. Also, wave breaking has little effect on the amplitudes of the harmonic components. The roller and aeration areas were also computed. Two methods of estimating the roller area have been explored and these are the analysis of the wave gauge measurements of the surface elevation and the analysis of the video images. There was agreement between the results obtained and those published in the literature.Item Kinematics and dynamics of the elliptical galaxy NGC 5266.(2005) Pakzad, Sabrina L.; Cress, Catherine M.In studies of triaxial elliptical galaxies, one of the least observationally studied phenomena is figure rotation. Figure rotation has important consequences for the orbital structure and could explain the survival of steep nuclear cusps. For this project, we thus wish to investigate the possibility of measuring the figure rotation of an elliptical galaxy for which the geometry is approximately known using the Tremaine-Weinberg (TW) method. Originally meant for measuring the pattern speed of barred disk galaxies, we test the validity of the method using NGC 5266, a minor-axis dust-lane elliptical. In the process, the galaxy's line-of-sight velocity distribution (LOSVD) is measured along several slit positions. Measurements of the velocity v, velocity dispersion a, skewness /J3, and kurtosis h^ are derived using the Fourier Correlation Quotient method and a Gauss-Hermite series. This work represents the most detailed stellar kinematic measurements of NGC 5266 to date and confirm that it is one of the fastest rotating elliptical galaxies known today (Varnas et al. 1987). We find a maximum velocity of about 167 km s_1 at both a PA of 274° and 304°. This is compared to a maximum of 212 ± 7kms~1 at a PA of 287° found elsewhere (Varnas et al. 1987). The TW method yields significantly different values for the pattern speed. These vary between -19 and 22kms Wcsec"1. The discrepancy between the results casts doubt on the ability to straightforwardly apply the TW method to elliptical systems, but the study provides some insight into how the method may be more successfully implemented in the future.Item Measurement of the Kerr electro-optic effect by induced birefringence.(2005) Singh, Ann.; Couling, Vincent William.During the period January 2001 to January 2003, M Sc student Mr Tleyane Jonas Sono developed an apparatus to measure the pressure- and temperature-dependence of the electro-optic Kerr effect (electric-field-induced birefringence) in gases. Mr Sono presented experimental results for dimethyl ether at a wavelength of 632.8 nm, extracting polarizability tensor components, first and second Kerr hyperpolarizabilities, and second Kerr-effect virial coefficients for this molecular species. This thesis has been primarily concerned with a thorough re-investigation of the Keneffect for the dimethyl ether molecule. Of primary concern is the reproducibility of the measured data, which depend upon precise and accurate knowledge of various experimental parameters. These include calibrations of the high-voltage power supply which is used to establish the electric field across the medium, the pressure transducer, the platinum thermistors, as well as the Faraday cell which forms the heart of the compensator. There is also a possibility of the 316-stainless-steel electrodes buckling and warping as they are cycled over ±200°C, leading to variations in the applied field and a consequent hysteresis in the results. In essence, we have been loath to publish our Kerr-effect investigation of dimethyl ether before making a thorough investigation of the reproducibility of our measured data. Here we present our investigations, and compare our new Kerr virial coefficients and the molecular (hyper)polarizability data extracted from them against the previous work of Sono. It will become apparent agreement is excellent, and that the findings for dimethyl ether are now ready for publication. The molecular-tensor theory of the Kerr-effect; including the second Kerr-effect virial coefficient BK, which describes the effects of intermolecular collisions on the molecular Kerr constant; is reviewed. The computed data is compared with the experimental data, yielding good agreement over the full experimental temperature range of 280 to 450 K. Attempts to obtain measured data at 260 K proved fruitless in the present study, though efforts are underway to complete this task.Item Numerical simulation of pressure response in partially completed oil wells.(2002) Strauss, Jonathan Patrick.; Hearne, John W.This work is concerned with the application of finite difference simulation to modelling the pressure response in partially penetrating oil wells. This has relevance to the oil and hydrology industries where pressure behaviour is used to infer the nature of aquifer or reservoir properties, particularly permeability. In the case of partially penetrating wells, the pressure response carries information regarding the magnitude of permeability in the vertical direction, a parameter that can be difficult to measure by other means and one that has a direct influence on both the total volumes of oil that can be recovered and on the rate of recovery. The derivation of the non-linear differential equations that form the basis for multiphase fluid flow in porous media is reviewed and it is shown how they can be converted into a set of finite difference equations. Techniques used to solve these equations are explained, with particular emphasis on the approach followed by the commercial simulation package used in this study. This involves use of Newton's method to linearize the equations followed by application of a pre-conditioned successive minimization technique to solve the resulting linear equations. Finite difference simulation is applied to a hypothetical problem of solving pressure response in a partially penetrating well in an homogenous but anisotropic medium and the results compared with those from analytical solutions. Differences between the results are resolved, demonstrating that the required level of accuracy can be achieved through selective use of sufficiently small grid blocks and time-steps. Residual discrepancies with some of the analytical methods can be traced to differences in the boundary conditions used in their derivation. The simulation method is applied to matching a complex real-life well test with vertical and lateral variation in properties (including fluid saturation). An accurate match can be achieved through judicious adjustment of the problem parameters with the proviso that the vertical permeability needs to be high. This suggests that the recovery mechanism in the oil field concerned can be expected to be highly efficient, something that has recently been confirmed by production results.