Magnetotactic bacteria (MTB) possess organelles called magnetosomes which contain magnetite (Fe_3O_4) or greigite (Fe_3S_4) nanocrystals. These particles generate a magnetic moment allowing the use of external magnetic fields to control the cell orientation. MTB use this magnetic moment to reach environments with optimal oxygen concentration, a process called magnetotaxis. There are many possible technological applications for MTB, for example, they have been used as nanorobots to push beads and they can be used to remove heavy metals and radionuclides from waste water. In order to fully understand the motion of these micron-size organisms, which takes place at very low Reynolds number where friction dominates over inertia, we set out to measure their drag coefficients. As a starting point, we used a well-studied species of MTB with a corkscrew shape, Magnetospirillum magneticum AMB-1. Simulations were done to find the best external magnetic field strength at which to observe their diffusion. We then imaged non-motile cells placed in these preferred uniform magnetic fields and used automated image analysis to determine the position and orientation of the cells in each frame. This allowed calculating orientation correlation functions and mean-squared displacements, from which rotational and translational diffusion coefficients were obtained for each individual cell. We observed that the four principal drag coefficients of these cells greatly vary as a function of cell length as predicted for cylindrical or elliptical objects with comparable radius. However, we also detecting a coupling between the rotation around and translation along the long axis of the cell only observed for chiral objects. We were able for the first time to experimentally fully characterize the friction matrix for a micron-size elongated chiral object. Continuing our work on MTB, to study live cells for long periods of time, we looked to confine them in PDMS nanowells, but found that MTB were not growing well in this environment. We then turned to a device, which incorporated a PDMS microchannel to provide continuous nutrients and a gel membrane to enable cellular growth into a 2D monolayer. Hopefully, this experimental setup combined with time-lapse microscopy can in the future be used to observe cell growth and cell division, and further to determine whether the magnetosome of the mother is passed on equally between daughter cells. / Thesis / Master of Applied Science (MASc)

The problem of the study was related to the asymptotic and relative efficiencies of the conventional biserial correlation coefficients and the two modified biserial correlation coefficients proposed by Brogden (1) and Lord-Clemans (2; 15). These were determined under some selected cutting points (p), and various sizes of samples (n) randomly drawn from the; simulated bivariate populations of four different shapes—normal, lognormal, double exponential, and the contaminated normal, and of various degrees in population parameter (p).

Solving for energy losses in pipe junctions has been a focus of study for many years. Although pipe junctions and fittings are at times considered "minor losses" in relation to other energy losses in a pipe network, there are cases where disregarding such losses in flow calculations will lead to errors. To facilitate these calculations, energy loss coefficients (K-factors) are commonly used to obtain energy losses for elbows, tees, crosses, valves, and other pipe fittings. When accurate K-factors are used, the flow rate and corresponding energy at any location in a pipe network can be calculated. K-factors are well defined for most pipe junctions and fittings; however, the literature documents no complete listings of K-factors for crosses. This study was commissioned to determine the K-factors for a wide range of flow combinations in a single pipe cross and the results provide information previously unavailable to compute energy losses associated with crosses. To obtain the loss coefficients, experimental data were collected in which the flow distribution in each of the four cross legs was varied to quantify the influence of velocity and flow distribution on head loss. For each data point the appropriate K-factors were calculated, resulting in over one thousand experimental K-factors that can be used in the design and analysis of piping systems containing crosses.

The work presented within this thesis details the experimental investigation of the surface waves supported on metasurfaces. Particular attention has been given to the reflection of these surface waves from planar discontinuities associated with these metasurfaces. Various experimental techniques have been developed throughout this work to characterise surface wave supporting metasurfaces. These include a new technique for measuring the dispersion of surface waves supported on metasurfaces, characterisation of the near-field associated with the surface waves, a device for launching planar phase front surface waves and finally a technique for measuring the surface wave reflection coefficient. The dispersion of surface waves on a square array of square cross-section metal pillars has been fully characterised and compared to FEM modelling. The results show that a family of surface waves may be supported by pillar or crossed slit structures rather than just holes even though there is now no lowest cut-off frequency. A family of TM surface modes have been shown to exist with dispersions which asymptote to frequencies defined by the pillar heights (slit depth) and the refractive index of the material filling the slits. Primarily this work focussed on the surface wave properties associated with a square array of square metal patches on a dielectric coated ground plane and a Sievenpiper `mushroom' metasurface. The amplitude reflection coefficient of these surface waves has been studied for three distinct systems: Firstly for surface waves incident upon the termination of a these metasurfaces to free space, secondly for surface waves incident upon the interface between a dielectric coated and uncoated metasurface and thirdly for surface waves incident on the boundary between two metaurfaces. The reflection coefficient of surface waves incident upon the termination of the metasurface to free space is found to increase significantly with the confinement of the surface mode. This confinement, and therefore the form of the reflection coefficient, is significantly different for the two metasurfaces considered due to their dispersions. This increase in the reflection coefficient is caused by both the momentum mismatch of the surface wave compared to the freely propagating modes and the different field distributions of the two modes. The reflection coefficient of surface waves incident upon the boundary between a coated and uncoated metasurface has been experimentally characterised for the metal patch array and Sievenpiper `mushroom' metasurfaces. It is shown that the addition of a thin, significantly subwavelength, dielectric overlayer onto the metasurface vastly perturbs the surface wave dispersion. The reflection coefficient of the surface waves is found to depend on the dispersion of the mode supported on the coated and uncoated metasurface and the overlayer thickness. Most noticeably the thickness of the overlayer, by comparison to the surface wave decay length, has a significant effect on scattering to free space associated with the surface wave reflection. The final system considered was designed to investigate the impedance approximation, often used to describe metasurfaces, and found it to be an incomplete description of the surface waves supported on the metasurfaces used within this study. In the impedance approximation the two surfaces considered are said to be `impedance matched` at certain frequencies. It is demonstrated that the failure of the impedance approximation to accurately describe this system is due to the behaviour of the electric field within the metasurfaces. These are not analytically described in the impedance approximation and are required for an accurate description of the surface waves supported on these metasurfaces.

The determination of limiting activity coefficients in liquid mixtures has become an important tool in chemical engineering. It has been investigated intensively during the past in order to find new alternatives and improved methods for its accurate detennination. The limiting activity coefficient is a fundamental thermodynamic quantity which measures the solution non-ideality and acts as a correction factor to deviations from Raoult's Law. This dissertation involves the determination of limiting activity coefficients using the inert gas stripping (IGS) technique only. It is considered to be the best method as it is a direct method involving exact concentrations of components in the mixtures encountered in industry. A comprehensive study of activity coefficients at infinite dilution for various systems, using the inert gas stripping (IGS) method has been undertaken. Various other methods and their suitability have also been discussed but preference is given to the superior quality of measurements obtained using the inert gas stripping technique. Extensive research has been conducted into the background and origination of the technique. Various improvements of the equilibrium cell designed by various authors for different types of systems have been outlined along with the various equations derived by the authors. The equipment was designed for use with the double-cell technique as well as the single-cell technique and in some cases both techniques were used. The techniques involve the use of a dilutor cell in which the highly diluted, volatile solute is stripped from a liquid solution using the inert gas nitrogen, introduced into the cell through capillaries and dispersed through the solution as small bubbles, at a constant flow rate. Analysis of the stripped solution is accomplished through the use of a gas chromatograph; the peak areas obtained from these analyses as well as the residence times and other system data such as temperature, pressure, mass and flow rate were used to compute the infinite dilution activity coefficient through the use of the various equations available in literature. The original equipment was designed for the use of the single cell technique by Soni (2004). Various modifications have been made to the equipment in order to measure limiting activity coefficients of more diverse systems with high accuracy. A major change to the equipment was the introduction of a second saturation cell of similar design to the dilutor cell. This enabled the determination of activity coefficients at infinite dilution of difficult systems i.e. systems where the solvent volatility is high and for higher order systems. The equipment was redesigned and built using ideas and improvements by previous researchers in the field and commissioned using test systems that have been classed as easy systems for this technique. The new equipment is now applicable to almost all systems, however good separation in the GC column could be a problem for complex systems. The determination of infinite dilution activity coefficients for one-component solute + onecomponent solvent systems and multi-component solvent systems were accomplished. The systems that were investigated consisted of a mixture of components of alkanes, alkenes, phenols and ketones, mostly in binary mixtures. Multi-component mixtures have also been investigated in the form of ternary systems involving a binary solvent mixture at varying concentrations, and a solute in order to show the diversity, uniqueness and efficiency of the IGS technique. Major variables affecting the system (the dilutor cell), namely the stripping gas flow rate and the dilutor cell temperature, were also investigated for all systems. Two test systems, cyclohexane in 1-methyl-2-pyrrolidone (NMP) and n-heptane in NMP were used to determine if the equipment is operating properly by comparing values obtained, to literature values where the inert gas stripping technique was used to determine the activity coefficients at infinite dilution. Another test system n-hexane in NMP was used to compare the two techniques, Le. the results of the single cell technique with the results of the double cell technique. The experimental results were thereafter compared to published literature values. Systems where the inert gas stripping technique has not been used to determine activity coefficients at infinite dilution were also investigated. These systems include 1-hexene in 0- cresol as well as the ternary systems '-hexene in various concentrations of NMP + o-cresol. A thorough literature survey has been completed and the relevant theory has been summarized. The validity of the equations proposed by Bao and Han (1995), Duhem and Vidal (1978), Leroi et a!. (1977), Hovorka and Dohnal (1997) and Krummen et al. (2000) for the determination of activity coefficients at infinite dilution were investigated. The experimental values obtained were consistent with literature values, with percentage errors of less than 1 % where the same equation was used to determine the limiting activity coefficient. Comparing limiting activity coefficients with the values obtained from other equations proposed by other authors mentioned above resulted in deviations no greater than 2.5 %, and where possible limiting activity coefficients were compared to values obtained from the single-cell technique. The theory section of this thesis covers all the various formulae (and where possible a summary of their derivation) used in the analysis of results. Some limiting activity coefficients for the systems involving n-heptane, n-hexane, n-hexene, cyclohexane, o-cresol and n-methyl-2-pyrrolidone under various experimental conditions have been reported making it readily available for use in other works. The effect of two major variables temperature and inert gas flow rate on the limiting activity coefficients with regard to all the systems studied have also been investigated and reported. This was also done in order to check that the data was reproducible. A sensitivity analysis was also performed in order to check the effect that certain measured variables would have on the limiting activity coefficient. These errors are estimated possible errors and may not exist at all, so not much consideration was given to this when reporting limiting activity coefficients for the various systems. The maximum error range for any given limiting activity coefficient as determined by the sensitivity analysis is ±11 %. The inert gas stripping technique is also extended to the determination of Hendry's constants. The actual values for the Hendry's constants were not determined but a comprehensive study of its determination was undertaken by Miyano et al. (2003) and summarized here. In addition the suitability and diversity of the inert gas stripping technique has been outlined, along with the advantages and disadvantages of the technique. The various designs of equilibrium cells have been outlined taking into account mass transfer considerations as proposed by Richon et al. (1980). The assumptions and limits of the method have also been outlined and must be taken into consideration when using the technique. A detailed description of the equipment setup and experimental procedure has been provided. The purpose, suitability, operation and applicability, of the various pieces of equipment used to make up the final equipment have been discussed in detail. Details for consideration when designing the equilibrium cells have also been provided. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2008.

The aim of this investigation was to develop and test a theory that allowed for the calculation of the activity coefficients at infinite dilutions (l' ~ 3) from G.L.C. measurements using moderately volatile solvents. The solvents chosen for study were straight chained (Cs to C7) and cyclic (Cs, C6 and benzene) liquid hydrocarbons using cis- and trans-decahydronaphthalene (decalin) as the stationary liquid phase (solvent). The systems were studied at two different temperatures, 283.15 K and 298.15 K. The solutes were n-pentane~ n-hexane, n-heptane, cyclopentane, cyclohexane and benzene. This method for the determination of activity coefficients has the advantage of being able to work at infinite dilution, whereas in other techniques, extrapolation to infinite dilution of finite-concentration data is necessary. In addition solutes are separated from impurities when chromatographed so that only very small quantities of moderately pure material need be· used. However the technique is also limited since the solute studied (injected reagent) needs to be volatile, while the solvent (liquid stationary phase) should be involatile. The solvents chosen in this experiment (cis- and transdecalin) are moderately volatile which introduces many limitations since the theory developed for the determination of activity coefficients at infinite dilution is restricted to involatile solvents. However a novel method for working with moderately volatile solvents is developed by relating the loss of solvent to its partial pressure and modifying the existing theory. In the past the use of precolumns and/or saturators, coarse packing, small pressure gradients, and internal standards were used when working with volatile solvents. However employing this new method excludes the use of precolumns, saturators, or internal standards, and allows any type of packing and pressure gradient to be used. The calculated activity coefficients are compared with literature values, where the wor~ers employed G.L.C. techniques, and with predicted values. The activity coefficients calculated at both temperatures are used in the calculation of excess partial molar enthalpies. These results are compared with values obtained from finite concentration data by other workers. / Thesis (M.Sc.)-University of Natal, Durban, 1992.

This investigation is designed to find the net rate of decrease in the component of velocity parallel to the original direction of motion of a proton moving through an electron gas exhibiting a non-spherical velocity distribution.

by Wing-keung Mak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 51-53). / by Wing-keung Mak. / Acknowledgments --- p.i / Abstract --- p.ii / Table of Content --- p.iii / Chapter Chapter One --- Introduction --- p.1 / Chapter Chapter Two --- Theory / Chapter 2.1 --- Theory of Two-wave Coupling --- p.3 / Chapter 2.2 --- Theory of Fanning --- p.8 / Chapter 2.3 --- Theory of Time Dependent Absorption Coefficients of Photorefractive Crystals --- p.10 / Chapter Chapter Three --- Photorefractive Fabry-Perot Etalon / Chapter 3.1 --- Theory and Numerical Computation --- p.12 / Chapter 3.2 --- Summary of Crystal Parameters --- p.15 / Chapter 3.3 --- Experimental Studies of Interference Patterns --- p.16 / Chapter 3.4 --- Intensity Dependence of Fabry-Perot Etalon Interference Patterns --- p.25 / Chapter 3.5 --- Fanning --- p.29 / Chapter 3.6 --- Bright Spots on Interference Patterns --- p.31 / Chapter Chapter Four --- Time Dependent Absorption Coefficients of Photorefractive Crystals / Chapter 4.1 --- Experiments Using Laser Light --- p.34 / Chapter 4.2 --- Experiments Using White Light --- p.44 / Chapter Chapter Five --- Conclusion and Future Outlook --- p.49 / References --- p.51

W1,p estimate for the solutions of elliptic equations whose coefficient matrix can have large jump along the boundary of subdomains is obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO seminorms. The domain and subdomains are Reifenberg flat domains and moreover, it has been shown that the estimates are uniform with respect to the distance between the subdomains.

Oblique weirs are those weirs placed at an angle with respect to the channel centerline. They can be used in canal applications where more discharge is needed, but there is limited freeboard. The discharge coefficients were determined for 54 different weirs by measuring total head for various flows over each weir. These weirs included sharp, half round and quarter-round-crested weirs. There were 18 weirs for each crest shape with three weir heights for each angle tested. The oblique angles tested were 10°, 15°, 25°, 45°, 60°, and 90° with respect to the channel centerline, with the nominal weir heights being 4, 8, and 12 inches. The half-round-crested weirs were the most efficient, followed by the quarter-round-crested weirs and the sharp-crested weirs were the least efficient. By decreasing the oblique angle, the weir length became longer and the weir would be more efficient than the normal weir.