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.

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.

Colloidal nanoparticles exhibit unusual individual and collective behaviour, often associated with interesting electrical, optical or electromagnetic properties. Thiol-passivated colloidal gold nanoparticles possess in addition a self-organising property, which, when the particles are deposited on a substrate, yields a plethora of fascinating patterns. The conditions of formation of these patterns are investigated, in order to understand the principles of - and gain control over - non-equilibrium self-organisation following drop evaporation. The work presented in this thesis relies mostly on experimental observations, although the results are supported by numerical simulations carried out in the group and based on modified versions of the model developed by Rabani et al. in 2003 [1]. A novel deposition method is introduced, which provides controllable conditions for the occurrence of a wide variety of patterns, including close-packed monolayers of nanoparticles. Pattern and surface characterisation is achieved by combined microscopy techniques - atomic force microscopy (AFM) and real-time contrast-enhanced optical microscopy. The influence on pattern formation of the nanoparticle-solvent-substrate interactions is studied by altering the physical properties of all three components (substrate, solvent and nanoparticles). The experimental set-up allows a meniscus-driven evaporation of the solvent of the nanoparticle solution and enables monitoring of drying front instabilities during the dewetting process. The effects of these instabilities on pattern formation are investigated and highlight a strong contribution of free excess ligands. We have focused on two specific types of patterns which emerge in these experiments : fingering structures and nanoparticle rings. The former are reminiscent of patterns that form in a number of other systems, a process usually called "viscous fingering". A thorough investigation reveals that the mechanism of formation of such patterns involves the combination of specific experimental conditions and at least two different dewetting processes, with different time and length scales. A "pseudo-3D" Monte Carlo model recreates such conditions and yields simulated results which are in good qualitative and quantitative agreement with experimental results. On the other hand, nanoparticle rings, although they are a recurrent type of pattern observed in nanoparticle assemblies [2, 3], form according to a mechanism which is not yet fully understood. We show however that wetting properties play a central role in ring formation and growth. As in the case of fingering structures, a narrow range of parameters has been determined, via an exhaustive experimental investigation, which favours the occurrence of nanoparticle rings. For all the nanoparticle assemblies studied in this thesis (close-packed monolayers, fingering structures and nanoparticle rings), the deduction of pattern formation mechanisms from experimental observation (and simulations) relies on the very high degree of reproducibility that it is possible to attain using the combination of a meniscus-driven evaporation, a very fine tuning of experimental conditions and nanoparticle-solvent-substrate interactions, and a systematic cross-characterisation by complementary imaging techniques.

We investigate the dynamics of the geometric transitions associated to compactified spacetimes. By including the effects of gravity we are able to follow the evolution of collapsing cycles as they attempt to undergo a topology changing transition. We perform investigations where we add a perturbation to the momentum of a static solution and observe the consequences this has on the spacetime, looking for evidence of black hole formation or collapsing cycles which could lead to singular geometry. First we look into two possible four dimensional spacelike solutions to the Einstein equations called instantons. These both have a two-sphere at the origin, these are called bolt singularities. We introduce an initial perturbation to reduce the two-sphere to a point. Rather than achieving this singular geometry we find that either a horizon forms, shielding a curvature singularity, or the cycle re-expands after an initial contraction phase. For the case where a horizon forms we identify the final state with a known analytic black-hole solution. In seven dimensions we simulate the gravitational dynamics of the conifold geometries (resolved and deformed) involved in the description of certain compact spacetimes. As the cycles of the conifold collapse towards a singular geometry we inevitably find that a horizon develops, shielding the external spacetime. The structure of the black hole is examined and we find a candidate for the final state of the collapse. In ten dimensions we investigate the time evolution due to gravitational dynamics of a spacetime which is commonly used in brane-cosmology and string compactifications called the Klebanov-Strassler geometry. Here black holes are sometimes formed but more commonly the cycles are seen to re-expand after reaching a minimum value, showing the stability of the solution against perturbations which would change its size.

In this thesis, experimental evidence of sustained phonon oscillations, from an electrically pumped vertical-cavity SASER device, working in the THz frequency domain is presented. Experimental investigation of injection seeding of phonons at a particular frequency, by optical excitation, is also presented. The experimental evidence of phonon oscillation through SASER action consists of a non-linear increase in the initial rising edge of the ballistically propagating LA phonons signal and an increased directionality of emission, once threshold gain is exceeded. The build-up of phonon oscillation fitted well with the theoretical model, also discussed in this thesis, enabling other attributes of the SASER device such as the gain coefficient, maximum acoustic power and device efficiency to be obtained. The cavity was investigated by means of pump-probe reflectivity measurements. Good quantitative agreement is obtained for the cavity mode frequencies, compared to the calculated reflectance of the cavity modes. Good quantitative agreement of the phonon scattering losses, within the cavity, was also obtained, when compared with theoretical predictions. Also provided is experimental evidence of injection seeding in the SASER devices under different conditions. The SASER device yields analogous characteristics to a seeded laser in that it acts as a phonon amplifier, due to SASER action, for the injected modes. The results contribute not only towards understanding the fundamental principles of achieving SASER oscillations but also towards the possibility of achieving a practical SASER device in the future.