Please read the abstract in the section 00front of this document / Dissertation (MSc (Ornamental Horticulture))--University of Pretoria, 2006. / Plant Production and Soil Science / unrestricted

Numerical simulation and remote sensing have indicated that the northern half of the Red Sea has a significant role in the thermohaline circulation within the basin. However, very few studies with in situ observation have been performed in a region where the formation of Red Sea Outflow Water (RSOW) and occasionally of Red Sea Deep Water (RSDW) take place during the winter in the northern Red Sea (NRS). This study provides new insights into the seasonal variability and the mechanisms that drive the thermohaline circulation of the north half Red Sea using high-resolution glider observations combined with reanalysis and satellite datasets. The study describes the water masses characteristics, the mesoscale activity, and the forcing mechanisms. In addition, we examine the biogeochemical responses to the physical drivers in the northern half of the Red Sea and how these processes alter the marine ecosystem. During winter, the mesoscale eddy activity and heat fluxes create the necessary conditions for the formation of RSOW in the NRS. The cyclonic circulation elevates relatively denser water in the surface, which is exposed to the atmosphere exchange. Thus, it leads to subduction of the surface layer forming of RSOW. The subducted water has been characterized by high oxygen as it has recently been ventilated. In addition, chlorophyll fluorescence has subducted along the isopycnals, contributing to exporting material below the sunlit layer. After the formation of RSOW, a period of strong anticyclonic circulation was observed In late February, which stirred and mixed the advected waters from the south in the northern region. It is accompanied by heat flux transition, and at the periphery of the observed Anticyclonic Eddy, an uplifting of the densest water to the surface occurred. The presence of the anticyclonic circulation enables the water advection from the south and extends the time of the surface water for atmospheric exposure. In April, the warmer intrusion of fresher waters from the south dominated the eastern part of the NRS, reestablishing the cyclonic circulation. To the best of our knowledge, this is the first in situ observation in the NRS that captured the seasonal progression of the transition of heat flux in wintertime and water advection that terminates the formation of RSOW. A continuous supply of northward warmer, lower salinity near the coast from the south is observed throughout the summertime period. Strong stratification with surface mixed layers no deeper than 25-30 meters due to the advection of lower salinity surface water and local heating. Another change that occurred during the summer period is that the source of low salinity inflow into the region transitioned from Gulf of Aden Surface Water (GASW) to Gulf of Aden Intermediate Water (GAIW)—assuming that the inflow of GAIW began with the onset of the Southwest Monsoonal winds in the south. The summertime heating and along basin evaporation set up the system for the wintertime cooling and additional evaporation that contributes to the formation of RSOW and RSDW. The mixed layer Price-Weller-Pinkel (PWP) model (Price et al., 1986) is implemented to quantify the influence of local heat fluxes compared with horizontal advection of the Gulf of Aden Water on the upper layer. Simulation of the mixed layer showed that advection was the major contributor to the seasonally integrated heat content and mixed layer simulation in summer. In contrast to winter, the timing of the mesoscale eddy activity, significant cooling, and advection add complexity to the region. The difference in the heat content was significant, and the PWP predicted an increasing mixed layer depth, while the observed mixed layer depth remained relatively constant. The differences between the calculated and simulated heat content were minimum during the absence of the mesoscale eddy and advection from the south. Overall, the quantification suggests a complex relationship between atmospheric forcing and advection on the heat content and the mixed layer depth.

In geometry we will consider n-dimensional generalizations of the Power of a Point Theorem and of Pascal's Hexagon Theorem. In generalizing the Power of a Point Theorem, we will consider collections of cones determined by the intersections of an (n-1)-sphere and a pair of hyperplanes. We will then use these constructions to produce an n-dimensional generalization of Pascal's Hexagon Theorem, a classical plane geometry result which states that "Given a hexagon inscribed in a conic section, the three pairs of continuations of opposite sides meet on a straight line." Our generalization of this theorem will consider a pair of n-simplices intersecting an (n-1)-sphere, and will conclude with the intersections of corresponding faces lying in a hyperplane. In graph theory we will explore the interaction between zero forcing and cut-sets. The color change rule which lies at the center of zero forcing says "Suppose that each of the vertices of a graph are colored either blue or white. If u is a blue vertex and v is its only white neighbor, then u can force v to change to blue." The concept of zero forcing was introduced by the AIM Minimum Rank - Special Graphs Work Group in 2007 as a way of determining bounds on the minimum rank of graphs. Later, Darren Row established results concerning the zero forcing numbers of graphs with a cut-vertex. We will extend his work by considering graphs with arbitrarily large cut-sets, and the collections of components they yield, to determine results for the zero forcing numbers of these graphs.

For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.

No / A proxy climate record from a raised bog in County Fermanagh, Northern Ireland, is presented. The record spans the interval between 2850 cal. yr BC and cal. yr AD 1000 and chronological control is achieved through the use of tephrochronology and 14C dating, including a wiggle-match on one section of the record. Palaeoclimatic inferences are based on a combination of a testate amoebae-derived water table reconstruction, peat humification and plant macrofossil analyses. This multiproxy approach enables proxy-specific effects to be identified. Major wet shifts are registered in the proxies at ca. 1510 cal. yr BC, 750 cal. yr BC and cal. yr AD 470. Smaller magnitude shifts to wetter conditions are also recorded at ca. 380 cal. yr BC, 150 cal. yr BC, cal. yr AD 180, and cal. yr AD 690. It is hypothesised that the wet shifts are not merely local events as they appear to be linked to wider climate deteriorations in northwest Europe. Harmonic analysis of the proxies illustrates statistically significant periodicities of 580, 423-373, 307 and 265 years that may be related to wider Holocene climate cycles. This paper illustrates how the timing of climate changes registered in peat profiles records can be precisely constrained using tephrochronology to examine possible climatic responses to solar forcing. Relying on interpolated chronologies with considerable dating uncertainty must be avoided if the climatic responses to forcing mechanisms are to be fully understood.

<p> The frequency pulling of the van dcr Pol nonlinear oscillator due to an external forcing signal is investigated. The nonlinearity is of the zero-memory symmetric-cut-off type following a cube law.</p> <p> An experimental oscillator was built, and curves of the frequency shift of the oscillator fundamental against the magnitude of the input forcing signal are shown, both for a sinusoidal input and for a narrow band noise input. An empirical result is derived.</p> <p> The case of the sinusoidal input is examined theoretically. The importance of harmonic and intermodulation frequencies in the oscillator output is shown, and relations giving the oscillator frequency shift are given for small forcing amplitudes and for large amplitudes when the oscillator is nearly synchronized.</p> / Thesis / Master of Engineering (MEngr)

Difference equations arise in many fields of mathematics, both as discrete analogs of continuous behavior (analysis, numerical approximations) and as independent models for discrete behavior (population dynamics, economics, biology, ecology, etc.). In recent years, many models - especially in mathematical biology - are based on higher order nonlinear difference equations. As a result, there has been much focus on the existence of periodic solutions of certain classes of these equations and the asymptotic behavior of these periodic solutions. In this dissertation, we study the existence and global attractivity of both periodic and quasiperiodic solutions of two different higher order nonlinear difference equations. Both equations arise in biological applications.

With the increased application of large eddy simulations and hybrid Reynolds-averaged Navier-Stokes techniques, the generation of realistic turbulence at inflow boundaries is crucial for the accuracy of numerical results. In this dissertation research, two novel turbulence inflow generation methods are derived and validated. The first method, the Triple Hill's Vortex Synthetic Eddy Method, is a new type of synthetic eddy method, where the fundamental eddy is constructed through a superposition of three orthogonal Hill's vortices. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergenceree anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on isotropic turbulence decay, turbulent channel flow, and a spatially developing turbulent mixing layer. The Triple Hill's Vortex Synthetic Eddy Method exhibited a quicker recovery of the desired turbulent flow conditions when compared with other current synthetic turbulence methods. The second method is the Control Forced Concurrent Precursor Method which combines an existing concurrent precursor method and a mean flow forcing method with a new extension of the controlled forcing method. Turbulent inflow boundary conditions are imposed through a region of body forces added as source terms to the momentum equations of the main simulation which transfer flow variables from the precursor simulation. Controlled forcing planes imposed in the precursor simulation, allow for specific Reynolds stress tensors and mean velocities to be imposed. A unique feature of the approach is that the proposed fluctuating flow controlled forcing method can be applied to multiple fluctuating velocity components and couple their calculation to amplify the existing fluctuations present in the precursor flow field so that prescribed anisotropic Reynolds stress tensors can be reproduced. The new method was tested on high and low Reynolds number turbulent boundary layer flows, where the proposed fluctuating flow controlled forcing method greatly accelerated the development of the turbulent boundary layers when compared with cases without controlled forcing and with only the original controlled forcing.

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