In this thesis, methods for texture mapping voxel based terrain of arbitrary topology, are studied. Traditional methods for generating terrain often use 2D height maps which has its limitations in topology, but often can rely on fast and simple planar projection for texture mapping. To generate terrain of arbitrary topology and support features like caves, overhangs and vertical cliffs, the terrain representation needs to expand from two dimensions and surface rendering to three dimensions and volumetric rendering, and also needs other, more elaborate methods for texture mapping. The initial part of the thesis recounts \emph{Marching Cubes}, the main method used for volumetric rendering, and also some basics on texture mapping. A survey reviews different related work on the area and lists some of the features. Some initial tests, to achieve texture mapping on arbitrary terrain, are performed and are explained and evaluated. These tests focus on partition the terrain into submeshes of similar directional faces, using the initial voxel grid as a natural boundary, and project each submesh to a planar texture space called \emph{charts}. The texture of each chart is defined by the highest resolution of each submesh and all charts are stored in one \emph{texture atlas}. The charts then represent the texture used for all different resolutions of the submesh. The method results in gaps in the final texture due to mismatch occurring from the different mesh resolutions. To avoid the mismatch each chart is mapped to fixed shapes, namely triangles or quads. This solves the problem with gaps along chart boundaries but instead introduce heavy distortion in the texture due to stretching and resizing. Some tests have also been performed on editing the underlying scalar field directly by identifying and avoiding some unwanted cases, and creating a simpler mesh.

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The use of practically non-repeating spreading codes to generate sequence-based spread spectrum waveforms is a strong method to improve transmission security, by limiting an observers opportunity to cross-correlate snapshots of the signal into a coherent gain. Such time-varying codes, particularly when used to define multi-bit resolution arbitrary-phase waveforms, also present significant challenges to the intended receiver, which must synchronize correlator processing to match the code every time it changes. High-order phase shift keying (PSK) spread modulations do, however, provide an overall whiter spectral response than legacy direct sequence spread spectrum (DSSS) signals. Further, the unique ability to color the output signal spectrum offers new advantages to optimize transmission in a non-white frequency channel and to mitigate observed interference. In high data rate applications, the opportunity to inject a time-aligned co-channel underlay-based watermark for authentication at the receiver is an effective method to enhance physical layer (PHY) security for virtually any primary network waveform. This thesis presents a series of options to enhance the implementation of arbitrary-phase chaotic sequence-based spread spectrum waveforms, including techniques to significantly reduce fallthrough correlator hardware resources in low-power sensing devices for only minor performance loss, capabilities for programming chosen frequency domain spectra into the resulting spread spectrum signal, and design considerations for underlay watermark-based PHY-layer firewalls. A number of hardware validated prototypes were built on an Intel Arria 10 SoC FPGA to provide measurable results, achieving substantial computational resource gains and implementation flexibility. / Master of Science / This thesis presents a series of options for enhancing the implementation of arbitrary-phase spread spectrum waveforms, a highly-secure class of wireless technologies, in order to reduce design complexity with minimal loss, provide methods for real-time performance adaptations, and extend the traditional application space for increased security of communications in other networks. A number of enhanced hardware prototypes were implemented to provide measurable results, achieving substantial computational resource gains and design flexibility. Given the computational resources and power constraints of devices in the Internet of Things (IoT), the signal detection loss of 2.10 dB for reducing the hardware logic utilization of the brute force fallthrough correlator by more than 76% (and eliminating the need to dedicate computationally-expensive embedded multipliers) is a very reasonable trade. While the waveform is fundamentally designed for increased security, adapting to widespread and/or commercial use may allow some sacrifice of the signal’s ability to avoid interception/detection to improve performance in undesirable operating conditions. In a similar, yet reversed, case, injecting a watermarking signature at the physical layer (PHY) of less-secure wireless technologies for receiver-side authentication also proves to be beneficial.

This study focuses on developing novel modeling techniques for fiber-reinforced composites with polymer and ceramic matrix based on Peridynamic approach. To capture the anisotropic material behaviors of composites under quasi-static and dynamic loading conditions, a new peridynamic model for composite laminate and a modified peridynamic approach for non-uniform discretization are proposed in this study. In order to achieve the numerical implementation of the proposed model and approach, a mixed implicit-explicit solver based on GPU parallel computing is developed as well. The new peridynamic model for composite laminates does not have any limitation in fiber orientation, material properties and stacking sequence. It can capture the expected orthotropic material properties and coupling behaviors in laminates with symmetric and asymmetric layups. Unlike the previous models, the new model enables the evaluation of stress and strain fields in each ply of the laminate. Therefore, it permits the use of existing stress- or strain-based failure criteria for damage prediction. The computation of strain energy stored at material points allows the energy-based failure criteria required for delamination propagation and fatigue crack growth. The capability of this approach is verified against benchmark solutions, and validated by comparison with the available experimental results for three laminate layups with an open hole under tension and compression. The modified peridynamic approach for non-uniform discretization enables computational efficiency and removes the effect of geometric truncations in the simulation. This approach is a modification to the original peridynamic theory by splitting the strain energy associated with an interaction between two material points according to the volumetric ratio arising from the presence of non-uniform discretization and variable horizon. It also removes the requirement for correction of peridynamic material parameters due to surface effects. The accuracy of this approach is verified against the benchmark solutions, and demonstrated by considering cracking in nuclear fuel pellet subjected to a thermal load with non-uniform discretizations. Unlike the previous peridynamic simulations which primarily employs explicit algorithm, this study introduces implicit algorithm to achieve peridynamic simulation under quasi-static loading condition. The Preconditioned Conjugate Gradient (PCG) and Generalized Minimal Residual (GMRES) algorithms are implemented with GPU parallel computing technology. Circulant preconditioner provides significant acceleration in the convergence of peridynamic analyses. To predict damage evolution, the simulation is continued with standard explicit algorithms. The validity and performance of this mixed implicit-explicit solver is established and demonstrated with benchmark tests.

Design of antenna arrays for present day requirements has to take into account both mechanical and electrical aspects. Mechanical aspects demand the antennas to have low profile, non-protruding structures, structures compatible to aerodynamic require­ments and so on. Electrical aspects may introduce several constraints either due to. technical reasons or due to readability conditions in practice. Thus, arrays of modern requirements may not fall into the category of linear or planar arrays. Further, due to the nearby environment, the elements will generate complicated individual patterns. These issues necessitate the analysis and synthesis of antenna arrays which are arbi­trary as far as the orientation, position or the element pattern are concerned. Such arrays which may be called arbitrary arrays are being investigated in this thesis. These investigations have been discussed as different aspects as indicated below: Radiation Characteristics of Arbitrary Arrays Radiation fields of an arbitrarily oriented dipole are obtained. Such fields are plotted for typical cases. Further, methods for transforming the electromagnetic fields are discussed. Having obtained the field due to an arbitrary element, the fields due to an arbitrary array are obtained. Factors controlling the radiation fields, like, the curvature in the array and element pattern are investigated. Radiation patterns of circular and cylindrical arrays are plotted. Synthesis of a Side Lobe Topography Requirements of a narrow beam pattern generated by an antenna array are identified. A problem of synthesizing such a pattern using an arbitrary array is formulated. The envelope of the side lobe region which may be called, the side lobe topography (sit), is included in the computation of the covariance matrix. This problem which has been formulated as a problem of minimizing a quadratic function subjected to a system of linear constraints is solved by the method of Lagrangian multipliers. An iterative procedure is used to satisfy all the requirements of the pattern synthesis. The procedure has been validated by synthesizing linear arrays and is used to synthesize circular and parabolic arrays. Patterns with tapered sit, Taylor-like sit have been synthesized. Asymmetric patterns are also synthesized. Role of sit is brought out. Shaped Beam Synthesis Synthesis of shaped broad beams is discussed. Amplitude constraints are formulated. Phase distribution is linked with the phase centre. Quadratic problems thus formu­lated are solved by the Lagrangian method of undetermined multipliers. An iterative procedure is made use of to synthesize flat topped beams as well as cosecant squared-patterns using linear arrays as well as circular arrays. Reasonable excitation dynamic has been obtained. Optimum phase centres obtained by trial and error are made use of. Effects of the Frequency and Excitation on the Synthesized Patterns In general, synthesized patterns can be sensitive towards any specific parameter either excitation or to frequency or any such parameter. Several methods can be used to observe these issues. In this thesis, these effects are also studied. Using a specific array configuration, to synthesize a specified radiation pattern, frequency is changed by 10% from the design frequency and the pattern is computed. Similarly, excitation phase distribution is rounded to the nearest available phase distribution using a digital phase shifter (say 8 bit) and the resulting pattern is computed. Further, excitation dynamic is also controlled by boosting the amplitudes of the array elements which are less than the permissible (i.e. the maximum excitation/allowed dynamic). Effects of these variations are also recorded. It appears that reasonable patterns can be obtained, in spite of significant variations in these parameters in most of the cases. Reconfigurable Arbitrary Arrays It would be very useful if a single array configuration can be used for different ap- plications. This may be either for the different phases of a single application or for different applications that may be required at different times. Attempts are made to synthesize a variety of patterns from a single array. Such arrays which may be called as reconfigurable arrays can be of much use. Obviously, the excitations are different for different patterns. Both narrow beams, as well as shaped broad beams, with different side lobe topographies have been synthesized using a single array.

This study determines the impact of ESTA on estate planning. The researcher indicates the extent to which ESTA alters the traditional property concept and analyses the practical implications of ESTA on estate planning. It appears, from the research that the traditional property concept has developed to include rights in property which are inferior to traditional ownership. The land reform process creates new rights which are afforded constitutional protection. These new rights create tension between land owners' perception of what their ownership entails, and the reality. The writer attempts to indicate that estate planning may minimize the possible disadvantages of ESTA. / Thesis (LL.M. (Estate Law))--North-West University, Potchefstroom Campus, 2006.

Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered.

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / In many signal processing and telemetry applications only a portion of the Discrete Fourier Transform (DFT) of a data sequence is of interest. This paper develops an algorithm which enables computation of the FFT only over the frequency values of interest, reducing the computational complexity. As will be shown, the algorithm is also very modular which lends to efficient parallel processing implementation. This paper will begin by developing the frequency selective FFT algorithm, and conclude with a comparative analysis of the computational complexity of the algorithm with respect to the traditional FFT.

This study determines the impact of ESTA on estate planning. The researcher indicates the extent to which ESTA alters the traditional property concept and analyses the practical implications of ESTA on estate planning. It appears, from the research that the traditional property concept has developed to include rights in property which are inferior to traditional ownership. The land reform process creates new rights which are afforded constitutional protection. These new rights create tension between land owners' perception of what their ownership entails, and the reality. The writer attempts to indicate that estate planning may minimize the possible disadvantages of ESTA. / Thesis (LL.M. (Estate Law))--North-West University, Potchefstroom Campus, 2006.

Naming refers to encountering a new word and subsequently being able to use it both expressively and receptively. Sometimes, this can happen in as little as a single experience. Several recent studies have explored factors that influence the acquisition of naming in adults. However, these studies used familiar stimuli for which the participants already had names. In these studies, preexisting stimulus-response relations with the stimuli could have impeded the acquisition of new names for some participants. In contrast, the present study used unfamiliar ("arbitrary") stimuli. In addition, an equivalence test was used to validate the findings because some theorists have claimed that naming is required for equivalence. The results revealed some advantages to teaching naming with arbitrary stimuli. Interestingly, a subset of participants had high scores on equivalence tests without having high scores on expressive tests. This indicates that, contrary to naming theory, naming may not be necessary for equivalence and match-to-sample tests may not be the best test of equivalence. These findings support the independence of the expressive and receptive repertoires both in the development of naming and equivalence.