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Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model interactions involving economic agents and biological populations. In particular we will explore the stability properties of equilibria associated with inter-species and intergenerational population dynamics in biology and market price and agent composition dynamics in economics.

Mass-transport deposits (MTDs) are virtually ubiquitous on the modern seafloor and common in ancient slope successions. Their upper surfaces are often irregular due to surface topography, which may vary significantly in wavelength and geometry. Turbidity currents are highly sensitive to topography, resulting in the modification of their density and velocity profiles during topographic interaction, thus affecting their depositional architecture. It is therefore expected that supra-MTD turbidite systems are also affected so. Previous analysis of the upper surface of MTDs and conformable overlying turbidite systems suggests that the upper surface of MTDs support irregularities that vary in wavelength, from 10 m to greater than 1000 m, by which longer length-scales may compartmentalise turbidite systems. But such studies do not investigate in detail the mechanisms by which topography is generated and the effect of the three-dimensional form of topography on supra-MTD turbidite systems. This study therefore addresses these aspects by the application of spectral analysis methods, synthetic modelling of three-dimensional topography, and architectural and lithofacies relationships of turbidite systems with the upper surface of MTDs, illustrated using an ancient slope succession cropping out at Cerro Bola, Argentina, and a modern deepwater system of the Sabah slope, offshore Brunei. In this thesis, an analytical model is described that characterises the three-dimensional form of the upper surface of MTDs in to two types: isolated topographic highs (termed positive topography) and isolated topographic lows (termed negative topography), which describe topography with a low and high degree of confinement, respectively. The geometry of these 'types' of topography are illustrated to vary significantly depending on the variability in the confinement across the surface in question, the degree of anisotropy and the obliquity of the flow direction to its orientation, which are similarly quantified using the analytical model described. Such topographic variability and anisotropy are demonstrated to relate to horizontal variations in thickness of the underlying MTD, generated by various mechanisms, including: internal structure, basal shear surface topography and post-emplacement creep and compaction. Each mechanism may support a variety of wavelengths that typically vary in length-scale and are generated simultaneously upon syn- and post-MTD emplacement. As a consequence, a turbidity current may interact with multiple length-scales of topography that might be produced contemporaneously with deposition. Topographic interaction may therefore not occur over the same length-scale as topographic ponding and, thus, supra-MTD ponded turbidite systems may have vertical and horizontal facies transitions that occur over similar length and height scales to the underlying topography despite ponding over a longer wavelength. Due to the three-dimensional complexity and variability of MTD topography, facies and architectures of supra-MTD reservoirs cannot be generalised in two-dimensions or extrapolated with ease into the third-dimension from isolated exposures/data.

Mortality in eiders (Somateria mollissima) on the Ythan estuary, Aberdeenshire, and elsewhere, has been claimed to be associated with the spiny-headed worm, Profilicollis botulus. Eiders acquire the disease by eating crabs (Carcinus maenas) infected with the cystacanth stage of the parasite. A detailed quantitative study was undertaken to elucidate some of the factors which control the abundance of the parasite in its intermediate and definitive hosts. During 1979-81 the P. botulus burdens in eiders and crabs were regularly monitored. Eiders were either taken alive off the estuary, or off the nest, and sacrificed, or found dead on the shore line. Crabs were caught in traps at two sites on the estuary. Female P. botulus in eiders were assigned to one of five categories according to the state of development of the eggs contained within their pseudocoelom. To estimate the size range and numbers of crabs eaten by eiders, crab chelipeds, or parts of chelipeds, were recovered from eider faeces collected monthly from roost sites. Regression equations relating certain cheliped dimensions to crab carapace width were used to estimate the size range eaten. The numbers of chelipeds per unit weight of faeces, equivalent to the quantity excreted per eider per day, was used to estimate the numbers of crabs eaten. Daily P. botulus infection rates in eiders were calculated by combining the quantitative data on crab intake by eiders with the cystacanth burdens in the crabs. Captive eiders, reared from eggs, were used to determine the age, days post-infection, of the five categories of female parasites. These development times were combined with the burdens found in the eiders sampled from the estuary to produce a static life-table of the mortality of female P. botulus. From this, estimates of the parasite's establishment rate, mortality rate and lifespan were obtained.

Egg weight and fecundity of Clyde spring-spawning and autumn-spawning herrings, Clupea harengus L., in the nothern North Sea and North Minch in different years were analysed. For Clyde spring-spawning herring high variation in egg weight was found and it was attributed to more than one spawning group spawning in the area. Annual variation in fecundity between 1963-1984 was found. Fecundity in 1984 was found to be about 10% higher than previous years. For autumn-spawning herring, fish spawn in the North Minch produce about 1.18 times heavier eggs than those spawning in the northern North Sea. Regional annual variation in fecundity between 1971-1984 was found. In 1984 fecundity of samples collected from Shetland was 1.12 higher than those of North Minch. Fecundity indices for Shetland samples were found to be 1.23 to 1.77 higher in 1984 than 1971-1973. Annual variation between 1971-1973 was also found. It was concluded that fecundity is a potential contributor to population regulation not necessarily related to population density. Monthly analysis of energy content of soma and gonad was carried out for Clyde spring-spawning herring. Differences in the magnitude and timing of energy allocated to the gonad was found between sexes. Energy budget was prepared for each sex at ages 2 and 3. No deficient of energy during winter was apparent due to gonad maturation and metabolic activity. Routine metabolic rate was measured in a group of herring in a respirometer. Oxygen consumption was estimated to be 31.3, 93.3 and 278.6 mgO2 kg-1 h-1 at 5, 10 and 15oC respectively. Standard oxygen consumption was derived from oxygen consumption and theoretical swimming speed to be 20.4, 59.5 and 164.8 mgO2 kg-1h-1 at 5, 10 and 15oC.

Computer simulations provide a powerful tool for the investigation of liquid crystalline phases. In this thesis the ability of simulations to calculate accurately the values of material parameters of liquid crystal molecules is investigated. An all-atom force field for liquid crystal molecules is developed using first principles density functional theory calculations on small organic molecules, which encompass key structural features of a range of common liquid crystalline molecules. Molecular dynamics simulations of these 'fragment' molecules are carried out in the liquid phase to test the force field parameters by determining densities and heats of vapourisation. Good agreement is found between experimental values and those calculated from simulation. Equilibrium molecular dynamics (MD) calculations were then performed for the nematogen n-4-(trans-n-pentylcyclohexyl)benzonitrile (PCH5). These simulations were performed using a fully atomistic model for several temperatures. The MD trajectories were used to obtain densities, order parameters, and values for the rotational viscosity coefficient 71. Several methods of obtaining 71 were tested based on the director angular velocity correlation function, the director mean-squared displacement, and statistical mechanics methods based on the rotational diffusion model. Good agreement is obtained between experimental values of 71 and those found from simulation. Further MD simulations of PCH5 using a 216 molecule system and the force field derived in this thesis were carried out to calculate the flexoelectric coefficients e(_s) and e(_b) for PCH5. The temperature dependence of and was examined along with the separate contributions to e(_s)and e(_b)arising bom the electrostatic and van der Waals interactions. The calculated values of e(_s)and e(_b) are consistent with available experimental data. The van der Waals and electrostatic contributions are found to be of similar magnitude and opposite sign.

There is a common requirement in the process, oil and gas turbine industries for high performance axial flow compressors operating over a wide range of mass flow rate and rotational speed at high efficiency. The trends have been for higher blade loadings (greater pressure rise per stage) and higher efficiency which are increasingly achieved through sophisticated Computational Fluid Dynamics designs. These trends, however, tend to mitigate against stable operating flow range (reduced surge margin), which can often lead to performance compromises. The objective of this work is to investigate the possibility of using alternative means to gain ow range by better use of variable geometry, which may permit design objectives to be better achieved. Variable geometry of the type envisaged is already often employed to overcome part-speed operating problems, but it proposed here that there may be additional benefits from their more intelligent control. The operation of axial compressors with a wide operating range is limited by instabilities, which cause a full breakdown of the flow, which is surge. These instabilities, which are caused by high incidence and subsequent stalling of stages occur due to different phenomena at part and full speed operation. The problem at part-speed is that the front stages are often heavily stalled and rear stages choked, whereas at high speeds, the front stages are operating close to choke and the rear stages tend to be stalling. Optimisation of the design to full load conditions can often provide part-speed problems and to achieve the acceptable performance, variable geometry over the front region of the compressor is sometimes used to modify the flow angles and avoid stage stall and subsequent surge. To-date, such variable settings follow some schedule established by analysis and experiment whereas this work presents a methodology of setting blade rows using an optimisation procedure and investigates the likelihood of performance benefits being obtained by a control technique which reacts° to these changing conditions. The construction of the numerical method presented in this thesis was done with an emphasis upon its intended contribution towards a eventual online control application. Therefore, a practical approach has been employed in the development of the compressor modelling techniques used in the work. Specifically, a highly empirical one-dimensional performance prediction code was constructed, employing successful correlations taken from the literature. This was coupled to a surge prediction method that has been shown in the past to function more than satisfactorily in a multistage environment. Finally, the predicted stage and overall performance (including the surge point) characteristics were passed to a optimisation program, which allowed these simulated conditions to be investigated. It is hoped that the work presented has illustrated the potential (from a aerodynamic performance point of view) of such a control technique to offer additional freedom in the operation of a multistage axial flow compressor. Moreover, the numerical modelling techniques have been developed enough to envisage (at least in part) their simple integration within a practical system. Clearly, some further investigations are required to take this work forward and the next logical step would be to improve the empirical rules with which the blade performance is predicted. A experimental programme would also be of great advantage, for example in the study of how the deviation angle for a given blade row varies over time (operating hours) in a real machine due to ageing and fouling. This would allow better estimates of the stage work during long term operation so that the optimiser could adapt to the slowly degrading performance of the blades. Finally, it is important to verify the simulated results with measured data, taken at the same optimal stator vane settings as given by the program. This must be carried out before it can be applied to a real application, although a limited study of this nature is presented in chapter 6.

Call number: LD2668 .T4 1952 C7 / Master of Science

The current research study is based on a model proposed by job design theorists, Fried, Grant, Levi, Hadani and Slowik (2007). This proposal is valuable in the organisational psychology research as it is the first to evaluate and incorporate career dynamics into the conceptualisation of the job design premise. As their argument, Fried et al. (2007) suggest that employees’ attitudinal reactions that result from the stimulation (or lack thereof) obtained from the design of their jobs is influenced by their career dynamics. More specifically, Fried et al. (2007) infer that career dynamics would moderate the relationship, whereby employees would be more likely to respond favourably to a lack of stimulation when they perceive themselves in the early stages of their careers; or when they perceive their jobs as enabling career advancement. The aim of this study is to quantitatively assess the hypotheses suggested by Fried et al. (2007); and therefore conduct an investigation that evaluates job design from a career dynamics perspective. Ninety five employees from sister accounting firms in Johannesburg and Cape Town formed the sample utilised in the study by volunteering to complete the self-report measures that were administered. The measures that are used in this study encompass the job diagnostic survey, an occupational tenure questionnaire, the expected utility of present job scale and the affective well-being scale. A biographic inventory was also administered in order to comprehend the demographic characteristics of the sample. The research hypotheses were evaluated using moderated multiple regression statistics. Insufficient evidence was found to conclude any moderating effects of career dynamics on the relationship between the stimulation derived from the job and the attitudinal reaction of affective well-being. Following the exploration of the research study and the interpretation of the findings, limitations of the study, directions for future research and practical implications are addressed.

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