Thesis (MSc)--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: The dielectric-barrier discharge (DBD) is a source of non-equilibrium plasma that has seen widespread industrial application in recent years. A high-voltage arbitrary-waveform generator has been designed, built and characterised for the purpose of investigating the influence that the applied voltage waveform has on the operation of a DBD. The developed arbitrary-waveform generator is based on the principle of Fourier synthesis. Up to twenty Fourier components are generated by means of a digital circuit board, and then separately amplified by Class-AB amplifiers. Twenty step-up transformers are subsequently used to transform the Fourier components to higher voltages; the summation of the Fourier components are realised by the series connection of the transformer secondary sides. It was found that the digital generation of the Fourier components is very accurate and provides for the easy configuration of arbitrary waveforms. Furthermore, the amplification of the Fourier components by the Class-AB amplifiers introduces very little distortion. The principle of adding the Fourier components via the step-up transformers has been demonstrated; however, the large distributed capacitances of the transformers adversely affect the operation of the Class-AB amplifiers, leading to the introduction of distortion into the generated waveform. Furthermore, it was found that care had to be taken to limit the introduction of EMI through the system’s large ground plane. / AFRIKAANSE OPSOMMING: Die di¨elektriese versperringsontlading (DVO) is ’n bron van nie-ekwilibrium plasma wat in die afgelope jare wye toepassing in die nywerheid gevind het. ’n Arbitrˆere-golfvorm hoogspanningskragbron is ontwerp, gebou en gekarakteriseer, met die doel om die invloed wat die aangewende spanningsgolfvorm het op die werking van die DVO, te ondersoek. Die ontwikkelde arbitrˆere golfvormgenerator is gebaseer op die beginsels van Fourier samestelling. Tot twintig Fourier komponente word digitaal gegenereer, en dan afsonderlik versterk deur Klas-AB versterkers. Twintig transformators word dan gebruik om die Fourier komponente na ho¨er spannings te transformeer. Die sommasie van die Fourier komponente geskied deur die serieskakeling van die transformators se sekondˆere windings. Daar is bevind dat die digitale generasie van die Fourier komponente baie akkuraat is, en dat die arbitrˆere golfvorms maklik verstel kan word. Verder versterk die Klas-AB versterkers die Fourier komponente sonder enige noemenswaardige vervorming. Die gebruik van die transformators om die Fourier komponente saam te voeg, is gedemonstreer. Die groot verspreide kapasitansies van die transformators be¨ınvloed egter die funksioneering van die Klas-AB versterkers, wat lei tot ’n vervorming van die uittree. Daar is ook bevind dat die toetrede van EM versteurings deur die grondvlak van die sisteem problematies kan wees.

Abstract not available

Techn. Univ., Habil.-Schr.--Braunschweig, 2006.

Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods and the model are done to ensure the accuracy of the results. Finally an additional model that is closed to mass flow is introduced along with preliminary results. / vi, 55 leaves : ill. ; 29 cm.

xviii, 213 p. / A print copy of this title is available through the UO Libraries under the call number: SCIENCE QC476.5 .F67 2006 / We investigate models describing two classes of microresonators: those having the shape of a dome, and those having an oval (deformed circle or sphere) shape. We examine the effects of dielectric interfaces in these structures. For the dome cavity, we derive efficient numerical methods for finding exact electromagnetic resonances. In the dome consisting of a concave conductor and a planar, dielectric Bragg mirror, we discover a phenomenon which we call paraxial mode mixing (PMM) or classical spin-orbit coupling. PMM is the sensitive selection of the true electromagnetic modes. The true modes are generally mixtures of pairs of vectorial Laguerre-Gauss modes. While each member of an LG pair possesses definite orbital angular momentum and spin (polarization), the mixed modes do not, and exhibit rich, non-uniform polarization patterns. The mixing is governed by an orthogonal transformation specified by the mixing angle (MA). The differences in reflection phases of a Bragg mirror at electric s and p polarization can be characterized in the paraxial regime by a wavelength-dependent quantity εs - εp. The MA is primarily determined by this quantity and varies with an apparent arctangent dependence, concomitant with an anticrossing of the maximally mixed modes. The MA is zero order in quantities that are small in the paraxial limit, suggesting an effective two-state degenerate perturbation theory. No known effective Hamiltonian and/or electromagnetic perturbation theory exists for this singular, vectorial, mixed boundary problem. We develop a preliminary formulation which partially reproduces the quantitative mixing behavior. Observation of PMM will require both small cavities and highly reflective mirrors. Uses include optical tweezers and classical and quantum information. For oval dielectric resonators, we develop reduced models for describing whispering gallery modes by utilizing sequential tunneling, the Goos-H¨anchen (GH) effect, and the generalized Born-Oppenheimer (adiabatic) approximation (BOA). While the GH effect is found to be incompatible with sequential tunneling, the BOA method is found to be a useful connection between ray optics and the exact wave solution. The GH effect is also shown to nicely explain a new class of stable V-shaped dome cavity modes. / Adviser: Dr. Jens Noeckel.

MSc (Chemistry) / Department of Chemistry

In this thesis, I study the group theoretic structure of the Schrodinger equations of simple systems by making use of a new systematic method. Group theoretic analysis of Schrodinger equations have been made previously by numerous physicists. The groups found may be classified as: a) geometrical groups; b) dynamical degeneracy groups; c) dynamical groups The geometrical group arises simply from the spatial symmetry of the system. Although the geometrical groups are very useful, they are not very interesting from the physical viewpoint. On the other hand, the study of the dynamical degeneracy groups and the dynamical group is very attractive because it reflects the dynamic of the system. Extensive studies have previously been made by other authors on systems which exhibit nontrivial degeneracy (accidental degeneracy). It turns out that all the states which belong to the same energy level provide a basis for a unitary irreducible representation of some compact group, and the group itself is generated by a set of constants of the motion. These groups are called “dynamical degeneracy groups”. Detailed discussion on degeneracy groups will be found in the paper by McIntosh alluded to above.

This dissertation consists of two parts, connected by the overarching theme of the dynamics of structured waves with internal degrees of freedom. Part I concerns light, whose internal degree of freedom is polarisation. We investigate the helicity, or handedness of light, which is a good quantum number for massless fields in general and light in particular. In free space it is always possible to describe the light field in a basis left- and right handed helicity modes which are solutions of Maxwell's equations, regardless what spatial structure is chosen. This is useful for bases of highly inhomogeneous waves, such as Bessel waves, for which the spin cannot be unambiguously defined. In chapter 1 we study the conservation of helicity and the preservation of its underlying symmetry, electric-magnetic duality symmetry when light travels through inhomogeneous and/or anisotropic media. We will discuss some of the unique properties of duality symmetric media and reformulate Maxwell's equations in such a way that the decoupling of different helicities for duality symmetric media becomes apparent. The feasibility of constructing duality symmetric media is discussed at the end of the chapter. In chapter 2 we consider superpositions of plane electromagnetic waves in free space. Such superpositions typically interfere. We present superpositions of up to six plane waves which defy this expectation by having a perfectly homogeneous mean square of the electric field. Because most matter interacts much stronger with the electric than with the magnetic field, these superpositions can be considered noninterfering. Our superpositions show complex patterns in their helicity densities, of which we will show many examples. We study the effects on our helicity patterns of imperfections that may occur in a realistic experiment: deviations from the optimal amplitudes, phases and polarisations of the superposed waves, small misalignments and partially coherent light. Our superpositions can be used to write chiral patterns in light sensitive liquid crystals. Conversely, these liquid crystals can be used for an `optical helicity camera' which records spatial variations in helicity. In the final paragraph of chapter 2 we discuss some mathematical questions concerning noninterfering superpositions. Part II concerns electrons, whose internal degree of freedom is spin. In chapter 3 we will present analytical solutions of the Dirac equation for an electron vortex beam in a homogeneous magnetic field. Including spin from the beginning reveals that spin polarised electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exist vortex beam solutions with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. Chapter 4 treats the interaction between electron vortex states in a homogeneous magnetic field and light, where we expand and quantise the radiation field in a basis of Bessel modes with definite helicity. Our results apply for magnetic field strength beyond the critical field strength at which the spin contributes as much to the electron's energy as its rest mass. We are able to compute spin flip rates for low lying states, finding a much higher degree of equilibrium spin polarisation than approximations for high lying electron states suggested.

A study on the behaviour of wave-packets and random disturbances, introduced by the vibrating-ribbon technique in a Blasius boundary layer, is presented. The experiments were conducted in the VPI & SU low turbulence wind tunnel. The flat plate model was constructed from an aluminum-paper honeycomb laminate and an aluminum leading edge with an elliptical profile. A theoretical model was developed to verify the random and step-function-form motion of the vibrating ribbon. In the case of random disturbance introduction it was found that the random disturbances behave like infinite number, single-frequency waves and measurements of their growth made possible to verify regions of the neutral-stability curve. In the case of wave-packet creation it was found that the wave packets behave like a structure that consists of waves of certain frequencies that grow or decay not necessarily according to the stability curve but in that way as to maintain the wave-packet structure. Their growth as they move downstream and their quick destruction into turbulence was compared to previously published data. / Master of Science

A new wave-kinetic numerical method for the propagation of optical waves in weakly inhomogeneous media is discussed, and it is applied to several canonical problems: the propagation of beam and plane waves through a weak 3-D ( or 2-D ) Gaussian eddy. The numerical results are also compared to those from a Monte-Carlo simulation and the first Born approximation. Within the validity of the Liouville approximation, the Wigner distribution function ( WDF ) is conserved along the conventional ray trajectories, and, thus, by discretizing the input WDF with Gaussian beamlets, we can represent the output WDF as a sum of Gaussians, from which irradiance can be obtained by analytical integration of each Gaussian with respect to wavevector. Although each Gaussian beamlet propagates along a geometrical optics ray trajectory, it can correctly describe diffraction effects, and the propagation of optical waves through caustics or ray crossings. The numerical results agree well with either the Monte-Carlo method or the first Born approximation in regions where one or both of these are expected to be valid. / M.S.