In this work, two approaches for computing the near-field distribution around wind turbines are proposed, including: (1) Huygens Principle and (2) the parabolic equation technique. In order to simplify the problem, the cylinder model is utilized to represent the wind turbines and transform the problem into a two-dimensional case. To make Huygens Principle computationally tractable, several approximations are made based on the problem geometry especially modelling the cylinder as a plate. The expression of the electromagnetic field radiated by the equivalent magnetic current can be analytically solved by the error function. To verify the results, FEKO is utilized to simulate the scattering of infinitely long cylinders using periodic boundary condition (PBC). In order to solve the problem of multiple cylinders, a modified method is derived. For more accurate results, the parabolic equation (PE) technique is utilized to solve this problem, which is usually utilized to solve wave propagation problems. In this case, wide-angle approximation is used to solve the parabolic equation, which can obtain accurate results in a region of up to 45 degrees. Although these two approaches are not full-wave simulation, the calculation time is significantly reduced and the error is acceptable. To further verify the computed results by the parabolic equation technique, two commercial transceivers from Time Domain Corporation are used to measure the field distribution behind a finite-length metal pole. The frequency-domain results are obtained from the measured time-domain results using the fast Fourier transform. It is shown that the computed results by the parabolic equation technique agree well with the measurement results. / text

Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The implementation and verification of a recently proposed Huy gens' principle in hollow lossless waveguide is described. The extended Huygens' principle is applicable to the scattering effect of arbitrary obstacles in waveguide and allows the coupling of a volume Finite Element discretization with a quasi Method of Moments surface element approach. A review of the technique is given and expressions for the two port scattering parameters are derived. The implementation is restricted to posts in rectangular waveguide, although the technique may also be applied to general scattering problems in waveguide. Finite Elements for the volume of the obstacle are selected and a basis set is proposed. The elemental finite element matrices are derived for a low and higher order basis set, while the validity of the derivations is established by considering a simple waveguide example. A coupled set of matrix equations is constructed that can be solved for the unknown surface electric and magnetic fields and the volume magnetic fields. A set of test examples is chosen to verify the implementation. The convergence behaviour is examined for two test cases. The dissertation concludes with an evaluation of the technique and recommendations for future work. / AFRIKAANSE OPSOMMING: Die implementasie en verifiëring van 'n onlangs voorgestelde Huygens beginsel in leë golfleier word beskryf. Die uitgebreide beginsel van Huygens is van toepassing op die strooiingseffek van arbitrêre voorwerpe in verlieslose golfleier en beskryf die koppeling tussen 'n volume eindige element diskretisasie met 'n oppervlakelement kwasi-moment metode. 'n Oorsig oor die tegniek word gegee en uitdrukkings vir die tweepoort strooiingsparameters word afgelei. Die implementering word beperk tot penne in reghoekige golfleier, alhoewel die tegniek op algemene golfleier strooiingsprobleme van toepassing is. Eindige elemente word gekies vir die volume van die voorwerp en 'n basisfunksie versameling afgelei van bestaande basisfunksies. Lae en hoë orde element matrikse word afgelei en die geldigheid van die afleidings word nagegaan deur 'n eenvoudige golfleier probleem op te los. 'n Gekoppelde stel matriksvergelykings word opgestel in terme van die onbekende oppervlak elektriese en magnetiese velde. 'n Aantal toetsvoorbeelde word gekies om die implementasie te verifieer. Konvergensiegedrag word ondersoek vir twee toetsgevalle. Die proefskrif sluit af met 'n evaluasie van die tegniek en aanbevelings vir verdere werk.

This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime. The problem is split into five further sub-cases based on the alignment of the Maxwell and Weyl principal spinors of the underlying spacetime. Two of these sub-cases are considered, one of which is proved to be incompatible with Huygens' principle, while for the other, it is shown that Huygens' principle implies that the two principal null congruences of the Weyl tensor are geodesic and shear-free. Furthermore, an unpublished result of McLenaghan regarding symmetric spacetimes of Petrov type D is independently verified. This result suggests the possible existence of counter-examples of the Carminati-McLenaghan conjecture.

In any research program we begin with a hypothesis and when our expected results do not concur with the observed results we must try and understand the dynamics behind the changed process. In this study we were trying to understand the flux between regional groundwater systems, surface waters and sedimentation processes in order to predict the fate of contaminants entering one of the larger bodies of water in the world- Lake Ontario. This lake has increased levels of tritium due to anthropogenic inputs. Our first approach to the problem was to look at tritium fluxes within the system . Hydrological balances were constructed and a series of sediment cores were taken longitudinally and laterally across the lake. The second approach was to quantify the sediment accumulation rate (SAR) within the depositional basins and zones of erosion in order to improve the linkage between erosion control (sedimentation) and the water quality program. In the last chapter the movement of tritium, by molecular diffusion, through the clayey-silts of Lake Ontario is quantified in terms of an effective diffusion coefficient. In these sediments effective diffusion equals molecular diffusion. In a laboratory experiment four cores of lake sediment were spiked with tritium . The resulting concentration gradient changes in the sediment porewaters after six weeks could be modeled by an analytical one- dimensional diffusive transport equation. Results calculated the average lab diffusion coefficient to be 2. 7 x 10 - 5cm 2. sec -1 which is twice that determined by Wang et al, 1952 but still reasonable. Short cores (50 cm) from lake Ontario had observed tritium concentrations with depth that reflected a variable diffusive profile. The increases and decreases in tritium with depth could be correlated between cores. Monthly tritium emission data was obtained and correlations between peaks in the tritium profile and emissions were observed. Monthly variations in release emissions corresponded to approximately a one centimeter slice of core. An average calculated diffusion coefficient of theses cores was 1. 0 x 10 -5 cm 2. sec -1 which compares to Wang's coefficient of 1. 39 x 10 -5 cm 2. sec -1. This implies that tritium is moving through the sediment column at a rate equal to diffusion. The results were obtained for smoothed values. It was not possible to model the perturbations of the data with a one dimensional model. The dynamics of the system imply that tritium could be used as a biomonitor for reactor emissions, mixing time and current direction scenarios and that a better understanding of this process could be gained by future coring studies and a new hypothesis.

This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime. The problem is split into five further sub-cases based on the alignment of the Maxwell and Weyl principal spinors of the underlying spacetime. Two of these sub-cases are considered, one of which is proved to be incompatible with Huygens' principle, while for the other, it is shown that Huygens' principle implies that the two principal null congruences of the Weyl tensor are geodesic and shear-free. Furthermore, an unpublished result of McLenaghan regarding symmetric spacetimes of Petrov type D is independently verified. This result suggests the possible existence of counter-examples of the Carminati-McLenaghan conjecture.

In any research program we begin with a hypothesis and when our expected results do not concur with the observed results we must try and understand the dynamics behind the changed process. In this study we were trying to understand the flux between regional groundwater systems, surface waters and sedimentation processes in order to predict the fate of contaminants entering one of the larger bodies of water in the world- Lake Ontario. This lake has increased levels of tritium due to anthropogenic inputs. Our first approach to the problem was to look at tritium fluxes within the system . Hydrological balances were constructed and a series of sediment cores were taken longitudinally and laterally across the lake. The second approach was to quantify the sediment accumulation rate (SAR) within the depositional basins and zones of erosion in order to improve the linkage between erosion control (sedimentation) and the water quality program. In the last chapter the movement of tritium, by molecular diffusion, through the clayey-silts of Lake Ontario is quantified in terms of an effective diffusion coefficient. In these sediments effective diffusion equals molecular diffusion. In a laboratory experiment four cores of lake sediment were spiked with tritium . The resulting concentration gradient changes in the sediment porewaters after six weeks could be modeled by an analytical one- dimensional diffusive transport equation. Results calculated the average lab diffusion coefficient to be 2. 7 x 10 - 5cm 2. sec -1 which is twice that determined by Wang et al, 1952 but still reasonable. Short cores (50 cm) from lake Ontario had observed tritium concentrations with depth that reflected a variable diffusive profile. The increases and decreases in tritium with depth could be correlated between cores. Monthly tritium emission data was obtained and correlations between peaks in the tritium profile and emissions were observed. Monthly variations in release emissions corresponded to approximately a one centimeter slice of core. An average calculated diffusion coefficient of theses cores was 1. 0 x 10 -5 cm 2. sec -1 which compares to Wang's coefficient of 1. 39 x 10 -5 cm 2. sec -1. This implies that tritium is moving through the sediment column at a rate equal to diffusion. The results were obtained for smoothed values. It was not possible to model the perturbations of the data with a one dimensional model. The dynamics of the system imply that tritium could be used as a biomonitor for reactor emissions, mixing time and current direction scenarios and that a better understanding of this process could be gained by future coring studies and a new hypothesis.

Ultra-wideband (UWB) radio techniques have long promised good contrast and high resolution for imaging human tissue and tumours; however, to date, this promise has not entirely been realised. In recent years, microwave imaging has been recognised as a promising non-ionising and non-invasive alternative screening technology, gaining its applicability to breast cancer by the significant contrast in the dielectric properties at microwave frequencies of normal and malignant tissues. This thesis deals with the development of two novel imaging methods based on UWB microwave signals. First, the mode-matching (MM) Bessel-functions-based algorithm, which enables the identification of the presence and location of significant scatterers inside cylindrically-shaped objects is introduced. Next, with the aim of investigating more general 3D problems, the Huygens principle (HP) based procedure is presented. Using HP to forward propagate the waves removes the need to apply matrix generation/inversion. Moreover, HP method provides better performance when compared to conventional time-domain approaches; specifically, the signal to clutter ratio reaches 8 dB, which matches the best figures that have been published. In addition to their simplicity, the two proposed methodologies permit the capture of a minimum dielectric contrast of 1:2, the extent to which different tissues, or differing conditions of tissues, can be discriminated in the final image. Moreover, UWB allows all the information in the frequency domain to be utilised, by combining information gathered from the individual frequencies to construct a consistent image with a resolution of approximately one quarter of the shortest wavelength in the dielectric medium. The power levels used and the specific absorption rates are well within safety limits, while the bandwidths satisfy the UWB definition of being at least 20% of the centre frequencies. It follows that the methodologies permit the detection and location of significant scatterers inside a volume. Validation of the techniques through both simulations and measurements have been performed and presented, illustrating the effectiveness of the methods.

This thesis examines techniques that provide a method of computer visualisation of bushfire spread. Existing techniques studied include, Kourtz & O???Regan, Green???s Contact, Heat Accumulation, Percolation modelling and Huygens??? Principle by Anderson et.al., French, Roberts, Richards. Many of these techniques are extended as part of a comprehensive study into how they perform in a two dimensional reference frame (ie over flat terrain only). New techniques are defined for Percolation Modelling and Huygens??? Principle. Each technique is examined in a series of test cases which include computer simulations with no wind, constant wind, variable wind, variable vegetation (including patchy fuel and two fuels) and where fuel burns out. These test cases provide: (a) an incremental approach to understanding the operation of each technique; (b) a basis for comparison; and (c) verification of correctness of the technique in two dimensions. Several of the techniques are shown, by these test cases, to be equivalent. For instance, the Kourtz & O???Regan technique using a square template is equivalent to the Contact Technique, Site percolation is similar to the Heat Accumulation technique and Template percolation is similar to the Contact Technique. Overall the Huygens??? Principle techniques provide the most accurate simulations of bushfire spread.

Localisation, which is a mechanism for discovering the spatial relationship between objects, is an area that has received considerable research and development in recent times. A common name given to localisation operations based on the absolute reference frame of Earth is Geolocation. One important example of geolocation research is E-911, where wireless carriers in the United States must provide the location of 911 callers. The operation of E-911 can be based on either a network configuration, or the Global Positioning System (GPS). With the importance of localisation being acknowledged, a review concerning the vulnerability of the Global Navigation Satellite System (GNSS) is provided as background and motivation for this research. With the current vulnerability of GNSS, this dissertation presents the results of a research program undertaken with the objective of developing an electromagnetic localisation technique that can determine the relative position of GPS Radio Frequency Interference (RFI) sources. Intended for operation in a hostile environment, blind and passive localisation methodologies must be incorporated into the developed model. In performing localisation research, a background of current techniques is provided in addition to a review of current electromagnetic propagation models. From the review of propagation models, the Parabolic Equation Model (PEM) was chosen for investigation concerning localisation. The selection of PEM is due to model properties that are required for blind/passive localisation. The localisation system developed in this research program is based on the integration of inverse diffraction propagation (IDP) within the parabolic equation model. The title chosen for the localisation method is Inverse Diffraction Parabolic Equation Localisation System (IDPELS). This thesis presents the simulation and field trial results of IDPELS. Under simulation, the terrain or obstacle profiles were not based on any geodetic datum. Any estimate provided by IDPELS under simulation is therefore a "Localisation" solution. In the field trials however, IDPELS operation is referred to as "Geolocation" as geodetic datum's where used to determine the receiver's position. Under simulation analysis, IDPELS operation was considered to provide good promise as it could simultaneously perform localisation on multiple transmission sources. In each investigated simulation scenario, a display of signals amplitude (dB units) is displayed over the entire region. By determining the field convergence regions, a localisation estimate of IDPELS is provided. By defining the convergence regions as areas having the greatest signal amplitude values (i.e. ≥ 99%), elliptical areas as low as 3.2m² were considered to indicate an excellent localisation capability. With the theoretical validity of IDPELS operation in electromagnetics having been established under simulation, further investigation into the practical feasibility of the IDPELS was performed. The field trials positioned a continuous-wave (CW) transmission source at a known location. By measuring signal phasors along a straight section of road, the geodetic spatial-phase profile was used as the input signal for IDPELS. Road sections used were cross-wise to the transmitter's boresight. Many data sets were recorded, each being made over a sixty second time period. Different regions and ranges where used to continuously measure the spatial-phase profile of the signal with fixed antennas in a moving vehicle. Such a measurement process introduced an analogy with Synthetic Aperture Radar (SAR) processes. In quantitating the accuracy of the IDPELS geolocation estimate in field trials, the linear error of range and cross-range components was analysed. A free-space PEM model was chosen for development of IDPELS and hence, data sets demonstrating properties of a free-space environment were able to be considered suitable for testing of the geolocation method. Data sets demonstrating free-space propagation characteristics were measured at the base of the Mt Lofty ranges in South Australia, where the range and cross-range error are respectively 3.14m, and 0.15m. Such low error values clearly demonstrate the practical feasibility of IDPELS geolocation. With the practical feasibility of IDPELS having been established in this research program, a novel contribution to electromagnetic geolocation methodologies is provided. An important characteristic of any geolocation technique concerns its robustness to operate in a wide variety of possible environments. With continued development of IDPELS, the robustness of this passive/blind geolocation technique can be enhanced. Further assistance with geolocation of multiple transmission sources is also indicated to be available by IDPELS, as shown in the simulation analysis.

This thesis examines techniques that provide a method of computer visualisation of bushfire spread. Existing techniques studied include, Kourtz & O???Regan, Green???s Contact, Heat Accumulation, Percolation modelling and Huygens??? Principle by Anderson et.al., French, Roberts, Richards. Many of these techniques are extended as part of a comprehensive study into how they perform in a two dimensional reference frame (ie over flat terrain only). New techniques are defined for Percolation Modelling and Huygens??? Principle. Each technique is examined in a series of test cases which include computer simulations with no wind, constant wind, variable wind, variable vegetation (including patchy fuel and two fuels) and where fuel burns out. These test cases provide: (a) an incremental approach to understanding the operation of each technique; (b) a basis for comparison; and (c) verification of correctness of the technique in two dimensions. Several of the techniques are shown, by these test cases, to be equivalent. For instance, the Kourtz & O???Regan technique using a square template is equivalent to the Contact Technique, Site percolation is similar to the Heat Accumulation technique and Template percolation is similar to the Contact Technique. Overall the Huygens??? Principle techniques provide the most accurate simulations of bushfire spread.