This dissertation reported an experimental answer to the long-standing question of how three-dimensionality appears in wall-bounded magnetohydrodynamic flows and presented also an experimental study on the transition to turbulence in a confined, mostly quasi two-dimensional flow. Accordingly, it was shown the analysis of a vortex array with susceptibility to three-dimensionality, enclosed in a cubic container and a mostly, quasi two-dimensional vortex pair confined by the walls of a shallow, cylindrical container. Both containers were hermetically filled by a liquid metal fluid and subject to a constant, homogeneous magnetic field. The flow forcing was made by injecting constant electric current from one wall that intersects magnetic field lines (Hartmann wall). Flow characteristics and the presence of three-dimensionality were monitored by measuring electric potentials on either Hartmann walls that confined the liquid metal. A form of three-dimensionality termed as weak appeared through differential rotation along the axis of individual vortices, while a strong form manifested itself in vortices that do not extend from one to the other Hartmann wall. In the cubic container, this resulted into an array of novel, spectacular flow structures that were both steady and strongly three-dimensional, and, yielded to a frequency-selective breakdown of quasi two-dimensionality in chaotic and turbulent flow regimes. The mostly quasi two-dimensional flow in the shallow, cylindrical container was shown to undergo a sequence of supercritical bifurcations to turbulence triggered by boundary layer separations from the circular wall. For very high forcing, the flow reached a turbulent regime where the dissipation increased drastically. This was related to a possible transition from a laminar to a turbulent Hartmann layer.

<p>In the telecommunications market, firms often give consumers the option of purchasing an individual plan or a family plan. An individual plan gives a certain allowance of usage (e.g., minutes, data) for a single consumer, whereas a family plan allows multiple consumers to share a specific level of usage. The theoretical challenge is to understand how the firm stands to benefit from allowing family plans. In this paper, we use a game-theoretic framework to explore the role of family plans. An obvious way that family plans can be profitable is if it draws in very low-valuation consumers whom the firm would choose not to serve in the absence of a family plan. Interestingly, we find that even when a family plan does not draw any new consumers into the market, a firm can still benefit from offering it. This finding occurs primarily because of the strategic impact of the family plan on the firm's entire product line. By allowing high- and low-valuation consumers to share joint allowance in the family plan, the firm is able to raise the price to extract more surplus from the individual high-valuation consumers by reducing the cannibalization problem. Furthermore, a family obtains a higher allowance compared to the purchase of several individual plans and therefore contributes more profits to the firm. We also observe different types of quantity discounts in the firm's product line. Finally, we identify conditions under which the firm offers a pay-as-you-go plan.</p> / Dissertation

Thesis (PhD)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The investigation of reservoir sedimentation has become an important and valuable research topic in engineering practice. Sediment deposition in reservoirs can affect ood levels, drainage for agriculture land, pumpstation and hydropower operation and navigation. An extensive review of the technical literature pertaining to suspended sediment transports as well as deposited sediment ushing from reservoirs has shown that most studies on sediment are still based on empirical formulas and experimental work, despite the availability of sophisticated computers. This is because sediment transport and particularly sediment deposition and erosion are complex processes, that involve the interaction of many physical factors which are not easily modelled numerically. In addition, most of the existing three-dimensional numerical models are not coupled hydrodynamic and sediment transport models. They first simulate the velocity field and water depth and then the concentration and bed change are calculated. Furthermore, they are not fully three-dimensional models for using layer-averaged approaches in conjunction with Saint-Venant equations. The key objective of the present research was to develop a coupled fully three-dimensional (3D) numerical model based on Navier-Stokes equations which includes both the sediment transport component and hydrodynamic parameters. In this regard, a physical model was set up in a laboratory ume in order to investigate the bottom outlet sediment ushing under pressure in a controlled environment. The proposed coupled fully 3D numerical model was used to simulate the experimental tests. Results from these simulations were in good agreement with the measurements. The geometric features of the scour hole (temporal and spatial hole development) upstream of the bottom outlet were reasonably well predicted compared to the experimental data. Furthermore, the velocity field upstream of the bottom outlet was in good agreement with measurements. The proposed numerical model can be considered reliable provided that the model is correctly set up to reflect the condition of a particular case study. Finally, the coupled fully 3D numerical model for turbulent suspended sediment transport in reservoirs was validated against a range of typical reservoir sediment transport and deposition laboratory flume cases. The proposed suspended sediment transport model successfully predicted both sediment deposition and entrainment processes and therefore, it can be used for turbulent suspended sediment transport assessments in reservoirs. / AFRIKAANSE OPSOMMING: Die ondersoek van damtoeslikking het 'n belangrike navorsing onderwerp in ingenieurswese praktyk geword. Sedimentdeponering in damme kan vloed vlakke, dreinering van landbo grond sowel as pompstasie en hidrokrag werking en navigasie benvloed. 'n Omvattende ontleding van die tegniese literatuur met betrekking tot gesuspendeerde sedimentvervoer asook die spoel van gedeponeerde sediment uit reservoirs het getoon dat die meeste studies oor sediment steeds op empiriese formules en eksperimentele werk gebaseer is, ten spyte van die beskikbaarheid van gesofistikeerde rekenaars. Dit is omdat sedimentvervoer en veral sedimentafsetting en -erosie komplekse prosesse is, wat die interaksie van baie fisiese faktore behels en nie moeiteloos numeries gemodelleer kan word nie. Daarbenewens, in die meeste van die bestaande drie -dimensionele numeriese modelle is die hidrodinamika en sedimentvervoer modelle nie gekoppel nie. Die numeriese modelle simuleer eerstens die snelheid veld en waterdiepte en dan word die sedimentkonsentrasie en bedverandering bereken. Verder is die bestaande modelle nie ten volle driedimensioneel nie, en gebruik laag-gemiddelde benadering in samewerking met Saint- Venant vergelykings. Die hoofdoelwit van die huidige navorsing was om 'n gekoppelde volle drie -dimensionele (3D) numeriese model gebaseer op Navier -Stokes-vergelykings wat beide die sediment vervoer komponent en hidrodinamiese parameters insluit, te ontwikkel. In hierdie verband is 'n fisiese model opgestel in 'n laboratorium kanaal om die bodem uitlaat spoel van sediment onder druk in 'n beheerde omgewing te ondersoek. Die voorgestelde gekoppelde 3D numeriese model is gebruik om die eksperimentele toetse na te boots. Resultate van hierdie simulasies het goed ooreengestem met die metings. Die geometriese eienskappe van die erosie gat (tyd en ruimtelike gatontwikkeling) stroomop van die bodemuitlaat was redelik goed voorspel vergeleke met die eksperimentele data. Verder is die snelheid veld stroomop van die bodem uitlaat ook goed voorspel. Die voorgestelde numeriese model kan beskou word as betroubaar met die wete dat die model korrek opgestel is om die toestand van 'n bepaalde gevallestudie te weerspiel. Ten slotte, is n gekoppelde 3D numeriese model vir turbulente gesuspendeerde sediment vervoer in reservoirs ontwikkel en getoets teen 'n reeks laboratorium kanaal eksperimente. Die voorgestelde gesuspendeerde sediment vervoer model voorspel suksesvol beide die sediment afsetting- en erosieprosesse en daarom kan dit gebruik word vir die simulasie van turbulente gesuspendeerde sediment vervoer in damme.

published_or_final_version / abstract / Computer Science / Master / Master of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Obstetrics and Gynaecology / Doctoral / Doctor of Philosophy

In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices. The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.

This dissertation presents the results of an investigation into the performance characteristics of a unique hemispherical SPECT (single-photon emission computed tomography) imaging system capable of producing three-dimensional (3D) tomographic images of the human brain. The system is completely stationary and collects all necessary views of the patient simultaneously, with no system motion. The imager consists of twenty small (10cm x 10cm crystal area), digital gamma cameras arranged in a hemispherical pattern around the patient's head and a hemispherical lead aperture. The hemispherical aperture is positioned between the cameras and the head and contains a large number of pinholes; in this way each camera sees a number of overlapping pinhole projections of the radioactive distribution within the patient's brain. The initial investigation of the performance characteristics of a 3D SPECT system of this design were carried out using a computer simulation in which effects due to radiometry, finite pinhole size, finite detector resolution, photon noise, and object attenuation were included. We used a digital 3D brain phantom as the test object and an iterative search algorithm to perform the reconstructions. The simulations were used to compare the performance of a variety of system configurations. Based upon the results of the simulation study, we constructed a laboratory prototype of the 3D SPECT system, which we used to further characterize the expected performance of a clinical imaging system of the same design. Prior to collecting SPECT data we calibrated the imaging system, which required that we efficiently measure and store the spatially variant system response function. These calibration data were then included in the reconstructions of the SPECT phantoms that we imaged. A number of different SPECT phantoms were imaged to demonstrate the system performance. We measured a reconstructed spatial resolution of 4.8mm full-width at half-maximum and a full-system sensitivity of 36cps/μCi, where both values were measured for a point source in air located at the center of the field of view. We also describe an analysis that we performed to determine the equivalent, non-multiplexed system sensitivity; using this method, we found that the equivalent sensitivity was 79% of the measured value for the system configuration and the particular task that we investigated.

Eukaryotic protein kinases are one of the most important classes of human proteins, and a great deal of research has focused on the development of small molecule inhibitors as biological probes for the determination of their cellular function or as therapeutics for the treatment of disease, such as cancer. The need for new selective inhibitors and a better understanding of the selectivities of existing small molecules is readily apparent. Towards the goal of better understanding protein kinases and the molecules that inhibit them, I have developed a split-protein-based approach for the investigation of these kinase-small molecule interactions. Employing split-firefly luciferase as a reporter domain, we engineered a three-hybrid system capable of determining kinase inhibition through competitive interactions between an active site-directed ligand and a small molecule of interest. This method measures luciferase activity as a function of ligand binding, as opposed to the more traditional assays which quantify kinase activity directly, and alleviates the laborious process of protein purification. The model kinase PKA and the promiscuous ligand staurosporine were used in an initial test case to successfully validate the general design principles of our assay. The modular nature inherent to the assay's design enabled us to adapt it to roughly 300 additional protein kinases and two different ligands. We were able to establish a protocol for rapidly ascertaining the inhibition of a kinase by a library of 80 commercially available kinase inhibitors in a 96-well, high-throughput format. This protocol was then systematically applied to the AGC group of kinases to observe patterns of inhibition across similarly related kinases. We have further shown how these results might be correlated with the sequence identity between kinases to better anticipate inhibitor promiscuity. Finally, we were able to illustrate how a kinase-centric approach could be applied to correlate alterations to the kinase domain with changes in luminescence. This has use for the interrogation of different modes of inhibition as well as in identifying the specific determinants of inhibitor binding. In total, these efforts represent the optimization of a new, general platform for determining kinase inhibitor selectivity across the kinome, and it could potentially be applied universally to the interrogation of protein-ligand interactions.