This thesis examines the electrical transport properties of a series of n-type GaAs/(AIGa)As double barrier resonant tunnelling devices with well widths between 50 angstrem and 2400 angstrem . The current-voltage characteristics show peak-to-valley ratios as high as 25:1 and as many as seventy resonances, with clear evidence of quantum interference effects at room temperature. The application of a high magnetic field parallel to the current flow produces magnetooscillations in the transport properties which allow the sheet charge density in the accumulation layer to be determined. The energy level in the well over a wide range of bias is obtained from analysis of thermal activation of resonant tunnelling. The contributions of elastic scattering and LO phonon emission to the valley current are investigated spectroscopically with a magnetic field and two phonon modes of the (AIGa)As barrier are observed. The buildup of space charge in the quantum well at resonance leads to intrinsic bistability in the current and differential capacitance of an asymmetric structure. Magnetoquantum oscillations due to a degenerate electron gas in the well are used to measure this charge buildup and demonstrate that the tunnelling process is truly sequential. The bistability is dramatically enhanced at high magnetic fields when the lowest energy Landau level of the well can accommodate a high electron density. In a strongly asymmetric sample, a new kind of bistability is observed where the off-resonant current exceeds the resonant current due to enhancement of charge buildup by intersubband scattering. The modulation of the scattering rate by a magnetic field produces periodic oscillations in the width of the bistability. In a magnetic field applied perpendicular to the current, the resonances are broadened as a consequence of the conservation of canonical momentum. The transition from electric to magnetic quantisation in wide wells is investigated and tunnelling into interfacial Landau levels is observed. The angular dependence of the resonances is used to probe conduction band anisotropy. In a tilted field, a completely new type of magneto-oscillations is observed.

In this thesis, we investigate analytically and numerically the existence and stability of discrete solitons governed by discrete nonlinear Schrödinger (DNLS) equations with two types of nonlinearity, i.e., cubic and saturable nonlinearities. In the cubic-type model we consider stationary discrete solitons under the effect of parametric driving and combined parametric driving and damping, while in the saturable-type model we examine travelling lattice solitons. First, we study fundamental bright and dark discrete solitons in the driven cubic DNLS equation. Analytical calculations of the solitons and their stability are carried out for small coupling constant through a perturbation expansion. We observe that the driving can not only destabilise onsite bright and dark solitons, but also stabilise intersite bright and dark solitons. In addition, we also discuss a particular application of our DNLS model in describing microdevices and nanodevices with integrated electrical and mechanical functionality. By following the idea of the work above, we then consider the cubic DNLS equation with the inclusion of parametric driving and damping. We show that this model admits a number of types of onsite and intersite bright discrete solitons of which some experience saddle-node and pitchfork bifurcations. Most interestingly, we also observe that some solutions undergo Hopf bifurcations from which periodic solitons (limit cycles) emerge. By using the numerical continuation software Matcont, we perform the continuation of the limit cycles and determine the stability of the periodic solitons. Finally, we investigate travelling discrete solitons in the saturable DNLS equation. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton-Raphson method to find traveling solitons with non-oscillatory tails, i.e., embedded solitons. A variational approximation (VA) is also applied to examine analytically the travelling solitons and their stability, as well as to predict the location of the embedded solitons.

Quantum dynamics and tunnelling of methyl rotors has been studied using field-cycling nuclear magnetic resonance (NMR) spectrometer, in a variety of samples. The characteristic frequency of the tunnelling motion of methyl groups has been investigated using both low-field dipole-dipole driven experiments and tunnel resonance level-crossing experiments. The classical hopping and quantum tunnelling of methyl groups have been studied by making temperature-dependent and field-dependent measurements of the spin-lattice relaxation time T1. The spectral density functions of the dipolar interaction, mediated by the rotation of methyl groups, have been directly plotted, and the correlation times characteristic of the rotational motion have been determined. Electron spin resonance (ESR) tunnel resonance spectra have been studied in samples with unpaired electrons by making resonant contact between the methyl tunnelling reservoir and the electron spins. The phenomenon of dynamic proton polarisation (DNP) has also been investigated in these samples. Experiments demonstrating the cooling of methyl tunnelling reservoir and the diffusion of energy amongst tunnelling reservoirs are presented. In low-field dipole-dipole driven experiments, in order to avoid the tunnelling transition saturation problem, the sideband stirring radiofrequency (rf) irradiation technique has been utilised and the low-field NMR spectra have been observed with enhanced sideband peaks. The rf irradiation time-dependence of the low-field spectra has been investigated. The experimental data is supported by numerical simulations, using appropriate theoretical models.

Glass transition, physical aging and dielectric relaxation in ultra-thin polymer films (< 100 nm) were investigated using complementary techniques (ellipsometry and dielectric spectroscopy). PtBMA films of different thicknesses were prepared and the thickness dependence of the glass transition temperature (Tg(h)) was investigated with ellipsometry. The uncapped films thinner than 40nm showed signicant depression of Tg and this was explained using the enhanced molecular mobility near the free surfaces. Several sets of PtBMA film samples were then prepared and capped by Al layers; the coating procedure is different for each set. The Tg(h) in PtBMA films with evaporated Al capping layers was essentially the same as that of the uncapped PtBMA films, and this suggests evaporated Al capping layers can not remove the free surface effect. Another set of samples was capped with Al layers using a novel '2(h=2)' sample preparation procedure, and was expected to have no free surface effect. These samples exhibit no apparent thickness dependence. These results suggest that the effect of free surfaces are responsible for the altered dynamics in thin polymer films. However great care has to be taken in attempt to remove the free surface effects caused by solid capping layers. The frequency dependence of the thickness dependence of α relaxation temperature (Tα(h)) in ultra-thin PVAc films was measured using dielectric spectroscopy. Films thinner than 80nm exhibit smaller Tα's than the bulk values at a measurement frequency lower than 10Hz, but there is no signicant thickness dependence of Tα at measurement frequencies higher than 10Hz. The results demonstrated that the Tα(h) has an intrinsic dependence on measurement frequency. We also measured the cooling rate dependence of the Tg(h) using the same samples, and compared Tg(h) with Tα(h) for different cooling rates/measurement frequencies. The results help to address the existing controversial reports about the apparent discrepancies observed between measurements that are performed using different techniques. Dielectric spectroscopy in the temperature domain ε"(T) was measured on thin(<486nm) PVAc films. The data were plotted against ln τ and the parameters describing the widening and distortion of the α relaxation peaks are constant for all measurement frequencies. The observed symmetry of the α relaxation peaks in ε"((T)were related to the constant shape parameters of the asymmetric α relaxation peaks in ε"(ln τ). An explanation is given to the observed widening of the α relaxation peaks with increasing measurement frequency in ε"(T). At a lower measurement frequency (<1Hz), the data obtained from thinner PVAc films showed wider α relaxation peaks (in ε"(T)) than the data obtained from thicker films, and at a higher frequency (>1Hz) this thickness dependence doesn't exist. This was explained using the existence of the liquid-like surface layer with enhanced molecular mobility, and using the measurement frequency effects. PS films of different thickness were prepared and physical aging process in these samples was investigated using ellipsometry. On each sample the measurements were performed at different aging temperatures, and a trend of a decreasing aging rate with decreasing aging temperature is found for all samples. In ultra-thin PS films (<100nm thick) a maximum aging rate at ~17K below Tg film is observed, and these observations were explained using the competition of the two factors that affect the aging, that is, the distance to the equilibrium and the fraction of the free volume. A comparison between the thickness dependence of aging rate and the thickness dependence of Tg suggests that the aging rate serves as a more sensitive probe in the study of polymer molecular dynamics than Tg does.

The main mm of this study was to investigate the prophetic calling of the Church and the role of the state in the moral renewal of the South African community. The method of research followed in this study was to study primary and secondary sources, as well as appropriate biblical teachings and theological principles relevant to this study and to systematize the information therein. The gist of the study was to outline the profile and manifestation of moral decay in South African community and, to define the role of the Church and state towards moral regeneration. What transpired was that due to the profile of moral decay within the South African context, the Church and state should play a critical and positive role towards the renewal of morality in South Africa. In conclusion, the fact that the Church and the state each have a particular role to play as driving agents for moral regeneration of South African was confirmed. It is also important to stress the fact that the State cannot be value free or neutral. The word of God speaks of human governments in two-fold way: in a normative way, and in a descriptive way; telling us what they ought to do and be and what they actually turn out to do and be. Both these elements in God's word are reflected in of the Reformed Confession. Therefore, the modern-day concept of a neutral or secular state can be questioned. / Thesis (M.A. (Ethics))--North-West University, Potchefstroom Campus, 2008.

In this thesis I review the definition of topological quantum field theories through state sums on triangulated manifolds. I describe the construction of state sum invariants of 3-manifolds from a graphical calculus and show how to evaluate the invariants as boundary amplitudes. I review how to define such a graphical calculus through SU(2) representation theory. I then review various geometricity results for the representation theory of SU(2), Spin(4) and SL(2,C), and define coherent boundary manifolds for state sums based on these representations. I derive the asymptotic geometry of the SU(2) based Ponzano-Regge invariant in three dimensions, and the SU(2) based Ooguri models amplitude in four dimensions. As a corollary to the latter results I derive the asymptotic behaviour of various recently proposed spin foam models motivated from the Plebanski formulation of general relativity. Finally the asymptotic geometry of the SL(2,C) based model is derived.

This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". To give the reader some inkling of what we mean by "shape of space", consider the fact that the shape of a triangle is given solely by its three internal angles; its position and size in ambient space are irrelevant for this ultimately intrinsic description. Analogously, the shape of a 3 dimensional space is given by a metric up to coordinate and conformal changes. Considerations of a relational nature strongly support the development of such dynamical theories of shape. The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1 form (ADM). What is special about this theory is that it does not possess foliation invariance, as does ADM. It replaces that "symmetry" by another: local conformal invariance. In so doing it more accurately reflects a theory of the "shape of space", giving us reason to call it shape dynamics. (SD). Being a very recent development, the consequences of this radical change of perspective on gravity are still largely unexplored. In the first part we will try to present some of the highlights of results so far, and indicate what we can and cannot do with shape dynamics. Because this is a young, rapidly moving field, we have necessarily left out some interesting new results which are not yet in print and were developed alongside the writing of the thesis. The second part of the thesis will develop a gauge theory for "shape of space"--theories. To be more precise, if one admits that the physically relevant bservables are given by shape, our descriptions of Nature carry a lot of redundancy, namely absolute local size and absolute spatial position. This redundancy is related to the action of the infinite-dimensional conformal and diffeomorphism groups on the geometry of space. We will show that the action of these groups can be put into a language of infinite-dimensional gauge theory, taking place in the configuration space of 3+1 gravity. In this context gauge connections acquire new and interesting meanings, and can be used as "relational tools".

Two important areas of physics are spontaneous pattern formation and droplet motion on surfaces. These two areas can be brought together since the texture of a surface can influence its wetting properties. Therefore by controlling the factors that determine the length scales of the patterns during spontaneous pattern formation, it is possible to design surfaces with very specific wetting properties. This was used to create surfaces that could direct the motion of sessile water droplets. Patterned surfaces with micro-wrinkled surface structures were prepared by thermally evaporating thin Aluminium (50−500nm thick) (Al) layers on to thick pre-strained layers of a silicone elastomer and subsequently releasing the strain. This resulted in the formation of sinusoidal periodic surface wrinkles with characteristic wavelengths in the 3 − 45μm range and amplitudes as large as 3.6μm. The Al thickness dependence of the wrinkle wavelengths and amplitudes were determined for different values of the applied pre-strain and compared to a selection of wrinkle formation theories. Samples with spatial gradients in wrinkle wavelength were also produced by applying mechanical strain gradients to the silicone elastomer layers prior to deposition of the Al capping layers. Sessile water droplets that were placed on these surfaces were found to have contact angles that were dependent upon their position. When vibrated close to their resonant frequency, these water droplets were observed to move from regions of short wrinkle wavelength to regions of large wrinkle wavelength. These samples are therefore viable candidates for the production of low cost gradient energy surfaces.

Kinetically constrained models (KCMs) are able to account for many of the slow dynamical properties of glass forming systems such as dynamic heterogeneity and Stokes-Einstein breakdown using simple models with simple dynamical rules. In this thesis we study several KCMs and extend them to include fast degrees of freedom. We show how the method of Monte Carlo with absorbing Markov chains can be applied to a particular class of KCMs, the facilitated spin models, to create an efficient numerical algorithm that can speed up simulations by several orders of magnitude. Another branch of KCMs, the constrained lattice gases, are studied and new results for a version on an FCC lattice in three dimensions are presented. This model is necessary when fast dynamics are studied and dimension plays an important role. To establish how fast degrees of freedom can be introduced without changing the character of the underlying KCMs we introduce coupled Ising spins to several existing models. We find that these models can reproduce much of the fast behaviour seen in the beta-relaxation of real supercooled liquids without changing the slow behaviour that is already well described by KCMs. Lastly, by considering harmonic interactions between particles we study the relation between short-time vibrational modes and long-time relaxational dynamics in two constrained lattice gas models. We find an excess in the vibrational density of states similar to the "Boson peak" of glasses and we find a correlation between the location of these low (high) frequency vibrational modes and regions of high (low) propensity for motion in agreement with recent results from atomistic simulations.

The molecular shape of any nonlinear molecule can be strongly influenced by the coupling between electrons and vibrations (vibronic coupling) via the Jahn-Teller (JT) interaction within the molecule. This influence appears as a distortion of the symmetrical shape of the original molecule. In such molecules, the adiabatic potential energy surface (APES) possesses either a trough of minimum-energy points or several isoenergetic minima ('wells') depending on the nature of the interactions present. In the case when coupling is infinite, the wells are very deep and the system will be locked into one of these distorted states. The vibronic states associated with these wells are good eigenstates of the system in this limiting static case. However, real molecules have finite coupling, so the system can migrate from one well to another in a process that is often referred to as the dynamic JT effect. If the wells are deep, then the motion must involve quantum mechanical tunnelling. Generally, the motion between wells gives the illusion that the molecule has rotated and this type of motion is referred to as pseudorotation. The eigenstates of the general system can then be approximated by symmetry-adapted states (SAS) which are a linear combination of the states associated with the wells. In this thesis, we focus on studying the dynamical nature of the JT effect through investigating the pseudorotation mechanism in different systems using a simple method employing the time-evolution operator. This allows us to obtain analytical expressions for the probabilities that a system that starts off localised in one initial well, may become localised in another well at some later time. These expressions are plotted versus time to show the pseudorotation regime and a comparison between different cases of pseudorotation in different molecules is made. Determination of the rates of pseudorotation leads to a better knowledge of the strength and nature of the vibronic coupling in the system and is a quantity that is, in principle, experimentally measurable. Also, more information about the tunnelling splitting between the SASs can be gained from this study.