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The template synthesis of rotaxanes and catenanes has allowed a detailed study of their intrinsically novel and interesting properties. A key strategy has been the deployment of transition metal ions with their well-defined coordination geometries allowing high-yielding and facile preparation of interlocked architectures. Knowledge of how to exploit the coordination sphere of metal ions and the design of ligands for the creation of intermediates that are pre-disposed to undergo ‘stoppering’ or ‘clipping’ has been a crucial requirement for this approach. This Thesis is in three parts describing the use of three dimensional, two dimensional and one dimensional coordination geometries in the synthesis of interlocked architectures. Firstly, the octahedral coordination geometry of cobalt(III) was utilized to organize dianionic pyridine-2,6-dicarboxamido ligands in a mutually orthogonal arrangement such that ring closing metathesis macrocyclizations gave access to interlocked or entwined products. A ‘figure-of-eight’ complex was obtained from a double macrocyclizations, whereas a catenate was accessed through a single macrocyclization. The topology of the isomers was proved by X-ray crystallography. An analogous [2]rotaxane was synthesized and the interlocked nature of the rotaxane demonstrated by 1H NMR spectroscopy and mass spectrometry. Secondly, an “active” metal template strategy, in which the metal ion plays a dual role – acting to both organize ligands and catalyze mechanical bond formation – allowed rotaxanes be constructed using the square planar coordination geometry and Lewis acidic nature of a palladium(II) complex. The interlocked nature of the rotaxane was proved by X-ray crystallography, demonstrating that a nitrile group present in the thread acted as a “station” for the Pd(II)-macrocycle. This observation led to the construction of a two “station” degenerate molecular shuttle in which the dynamics of translocation were controlled by reagent addition and observed by 1H NMR techniques. Lastly, the linear coordination geometry of gold(I) was successfully used as a template for construction of rotaxanes and catenanes via a ‘clipping’ strategy. The linear coordination geometry and the interlocked nature of the gold(I)-catenate was proved by X-ray crystallography, the rotaxane architecture was proved by 1H NMR spectroscopy and mass spectrometry. Chapters Two, Three and Four are in the form of articles that have been published in peer-reviewed journals, and are reproduced, in their published format, in the Appendix. No attempt has been made to rewrite the published work; as a consequence the numbering of compounds, whilst consistent within each Chapter, is not consistent throughout this Thesis. Another consequence is that the many failed synthetic routes have been left out. I hope the reader will forgive these omissions as well as the slight repetition that occurs in the introduction and bibliography of each chapter. Additionally, preceding each Chapter is a brief synopsis that places the work in context and acknowledges the contributions of my fellow researchers.

We show that the maximum size of a geometry of rank n excluding the (q + 2)-point line, the 3-wheel W_3, and the 3-whirl W^3 as minor is (n - 1)q + 1, and geometries of maximum size are parallel connections of (q + 1)-point lines. We show that the maximum size of a geometry of rank n excluding the 5-point line, the 4-wheel W_4, and the 4-whirl W^4 as minors is 6n - 5, for n ≥ 3. Examples of geometries having rank n and size 6n - 5 include parallel connections of the geometries V_19 and PG(2,3).

Over the past few decades, surface dielectric barrier discharge (SDBD) actuators have been studied extensively as aerodynamic flow control devices. There has been extensive research on producing SDBD plasmas through excitation by sinusoidal high voltage in low-speed flows, resulting in local acceleration of the flow through the electrohydrodynamic (EHD) effect. However, high-speed flow control using SDBD actuators has not been considered to the same extent. Control through thermal perturbations appears more promising than using EHD effects. SDBDs driven by nanosecond repetitively pulsed (NRP) discharges (NRP SDBDs) can produce rapid localized heating and have been used to produce better flow reattachment in high-speed flows. While surface actuators based on NRP DBDs appear promising for high-speed flow control, the physics underlying the plasma/flow coupling are not well understood and the actuators have yet to be fully characterized or optimized. In particular, methods for tailoring the plasma characteristics by varying the actuator’s electrical or geometrical characteristics have not been thoroughly explored.<div>In the current work, NRP SDBD actuators for control of high-speed flows are developed and characterized. As discussed previously, it is believed that the mechanism for high-speed flow control by these plasmas is thermal perturbations from rapid localized heating. Therefore, the goal is to design actuators that produce well-defined filamentary discharges which provide controlled local heating. The electrical parameters (pulse duration, PRF, and polarity) and electrode geometries are varied and the optimal configurations for producing such plasma filaments over a range of ambient pressures are identified. In particular, single and double sawtooth shaped electrodes are investigated since the enhanced electric field at the electrode tips may permit easier production of “strong” (i.e. higher temperature) filaments with well-defined spacing, even at low pressure. Time-resolved measurements of the gas temperature in the plasma will be obtained using optical emission spectroscopy (OES) to assess the thermal perturbations produced by the actuators. To the author’s knowledge, these will be the first such measurements of temperature perturbations induced by NRP SDBDs. The plasma structure and temperature measurements will be correlated with schlieren visualization of the shock waves and localized flow field induced by the discharges. Finally, the optimized actuators will be integrated into a high-speed flat plate boundary layer and preliminary assessment of the effect of the plasma on the boundary layer will be conducted.<br></div>

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1992. / Includes bibliographical references (leaves 185-195).

An unsteady Reynolds Averaged Navier-Stokes (URANS) based turbulence model, the Spalart-Allmaras (SA) model, was used to investigate the flow pulsation phenomenon in compound rectangular channels for isothermal flows. The computational fluid dynamics (CFD) commercial package ANSYS CFX-11.0 was used for the simulations. The studied geometry was composed of two rectangular subchannels connected by a gap, on which experiments were conducted by Meyer and Rehme [34] and were used for the validation of the numerical results. Two case studies were selected to study the effect of the advection scheme. The results using the first order upwind advection scheme had clear symmetry and periodicity. The frequency of the flow pulsations was underpredicted by almost a factor of two. Due to the inevitable numerical diffusion of the first order upwind scheme, it was more appropriate to use a second order accurate in space advection scheme for comparison with the experiments. The span-wise velocity contours and the velocity vector plots at planes parallel to the bulk flow, together with the time traces of the velocity components at selected monitor points showed the expected cross-flow mixing between the subchannels through the gap. Although the SA model does not solve directly for the turbulence kinetic energy, a kinetic energy associated with the unsteady solutions of the momentum equations was evaluated and qualitatively compared with the experimental turbulence kinetic energy. The calculated kinetic energy followed the trends of the experimental turbulence kinetic energy at the gap area, predicting two peaks at the edges of the gap. The dynamics of the gap pulsations were quantitatively described through temporal auto-correlation and auto-power spectral density functions and the numerical predictions were in agreement with the experiments. Studies on the effect of the Reynolds number and the computational length of the domain were also carried out. The numerical results reproduced the relationship between the Reynolds number and the frequency of the auto-power spectral density functions. The impact of the channel length was tested by simulating a longer channel. It was found that the channel length did not significantly affect the predictions. Simulations were also performed using the (kappa) -(epsilon) model. While flow pulsations were predicted with this model, the frequency of the pulsation was in poor agreement with the experimentally measured value. / Thesis / Master of Applied Science (MASc)

This thesis explores the geometric principles underlying many of the known Trichotomy Theorems. The main aims are to unify the field construction in non-linear o-minimal structures and generalizations of Zariski Geometries as well as to pave the road for completely new results in this direction. In the first part of this thesis we introduce a new axiomatic framework in which all the relevant structures can be studied uniformly and show that these axioms are preserved under elementary extensions. A particular focus is placed on the study of a smoothness condition which generalizes the presmoothness condition for Zariski Geometries. We also modify Zilber's notion of universal specializations to obtain a suitable notion of infinitesimals. In addition, families of curves and the combinatorial geometry of one-dimensional structures are studied to prove a weak trichotomy theorem based on very weak one-basedness. It is then shown that under suitable additional conditions groups and group actions can be constructed in canonical ways. This construction is based on a notion of ``geometric calculus'' and can be seen in close analogy with ordinary differentiation. If all conditions are met, a definable distributive action of one one-dimensional type-definable group on another are obtained. The main result of this thesis is that both o-minimal structures and generalizations of Zariski Geometries fit into this geometric framework and that the latter always satisfy the conditions required in the group constructions. We also exhibit known methods that allow us to extract fields from this. In addition to unifying the treatment of o-minimal structures and Zariski Geometries, this also gives a direct proof of the Trichotomy Theorem for "type-definable" Zariski Geometries as used, for example, in Hrushovski's proof of the relative Mordell-Lang conjecture.

Transport properties of concentrated suspensions are of interest to many industries. Mineral slurries at higher solids concentrations have shown some rheologically interesting characteristics such as shear thickening, the increase of viscosity of a multi-phase mixture with increasing shear rate. The general literature on the rheology of suspensions records the presence of yield stresses, shear thinning and normal stress differences. Little is said specifically about shear thickening behaviour except for colloidal suspensions. The aim of this study is to examine the behaviour of coarse shear thickening suspensions and determine the causes of this phenomenon. The study intended to achieve the following objectives to; develop the appropriate techniques for rheometric studies of shear thickening suspensions; investigate the nature of particle-fluid interaction; develop a model of shear thickening behaviour as it occurs in non-colloidal suspensions and to develop a method of applying the rheology results to flows and flow geometries of practical relevance. The effects of wall slip dominate much of the literature of shear thickening materials. To investigate this aspect a significant portion of the experimental work examined the effect of shear thickening on torsional flow. The rheogram produced from parallel plate rheometry was reassessed as a non-controlled flow and a rheology model dependant analysis demonstrated that the effects of slip are considerably more problematic for shear thickening suspensions, particularly as wall slip is an increasing function of shear stress. As a consequence of the rheometric method described above it was observed that the rate of change of the first normal stress difference, N1, with shear rate changes as shear thickening commences for non-colloidal suspensions. N1 is initially negative and is increasingly negative at low shear rates. Additional rheometric analysis examined the transient effects in the behaviour of a non-colloidal shear thickening suspension. By employing large angle oscillating strain tests the strain required to initiate a shear thickening response was determined. Coherent back scattering of laser light experiments were able to show the change in orientation of the particles with respect to its rotation around the vorticity axis. After a viscosity minimum was reached the orientation became more random as particle rotation and lamina disruption occurred. This was considered to be the cause of the measured shear thickening. A model of shear thickening in concentrated, non-colloidal suspensions of non-spherical particles was developed. Based on hydrodynamic interaction in the Stokes flow regime, the flow of interstitial fluid subjected the adjacent particles to lubricating and Couette type forces, acting as a couple. When a series of force balances on a particle contained between two moving laminae are conducted as a time sequence, the particle orientation and motion can be observed. The model has qualitative agreement with several aspects of the experimentally observed behaviour of shear thickening suspensions, such as viscosity change with shear rate and concentration, and the first normal stress difference increasing with shear rate. Pipe line flow experiments were conducted on the model suspension. Particle settling produces unusual patterns in shear thickening suspensions, with an annulus of delayed settling near the wall.

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Gary L. Ebert, Dept. of Mathematical Sciences. Includes bibliographical references.

No abstract available. / Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 2002.