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.

The charge transfer dynamics between adsorbate molecules and surfaces are important for a variety of different technologies but especially for dye-sensitized solar cells. The main aim of this thesis was to study charge transfer between organic molecules and surfaces, especially relating to the situation observed in dye sensitized solar cells. This broad aim can be split into two distinct research objectives. One of these was to study the charge transfer between a Au (111) surface and a variety of different molecules using synchrotron-based photoemission spectroscopy. Resonant photoemission spectra of a C60 monolayer on Au (111) showed distinctive superspectator features which were not observed for the multilayer or clean gold spectra. These features were determined to be resultant from spectator decay involving electrons transferred from the gold substrate to the adsorbed molecule, either in the ground state or during the timescale of the core-hole lifetime. These features were also found for monolayers of bi-isonicotinic, isonicotinic, nicotinic and picolinic acid on gold, but not for the dye molecule, N3, on gold. This suggests that, although charge transfer occurs between the surface and the ligand molecules that constitute N3, no charge transfer occurs between the N3 dye molecule and the gold. The other objective was to determine whether the core-hole clock technique, previously only used in photoemission spectroscopy, could be adapted for resonant inelastic x-ray scattering. For this, bi-isonicotinic acid on TiO2 was studied because this system had already been explored using photoemission spectroscopy. The charge transfer times were measured using the relative decrease in the elastic peaks for the LUMO and LUMO+1 photon energies of the multilayer and monolayer. This gave a similar result to the photoemission studies providing more confidence for using this adaptation in situations where photoemission would be impossible, such as buried interfaces.

In the solid state the rotation of a methyl group is hindered by a potential barrier and at low temperature the rotational motion is characterised by quantum tunnelling. The Pauli Exclusion Principle imposes constraints on the allowable eigenstates of the methyl rotor and leads to a combination of spatial and spin variables. The characteristics of these quantum tunnelling states, labelled A and E, are explored experimentally and methods are investigated for creating prescribed non-equilibrium states. We will investigate and explore the tunnelling polarization associated with the A and E tunnelling-magnetic levels by means of field-cycling NMR. Secondary rf irradiation is used to drive A-E and E-A transitions associated with NMR tunnelling sidebands. This polarization is then transferred to the 1H Zeeman system at a field-dependent level-crossing where the methyl tunnelling frequency equals one or two times the 1H Larmor frequency. The level-crossing contact is a necessary step since the tunnel temperature cannot be measured directly with a pulse. A new pulse sequence is described and the resulting spectra are analogous to the solid effect and dynamic nuclear polarization. Therefore we assign the phrase ‘dynamic tunnelling polarization’ to describe the experiments. Two samples are studied in depth, methyl ethyl ketone and acetophenone which have tunnel frequencies of 495 and 1435 kHz respectively. The experiments investigate the phenomena as a function of a variety of physical parameters in order to determine the fundamental physics.

Surface Plasmons provide a relatively high axial sensitivity and thus are generally used in a thin surface film sensing and imaging. Objective lens based surface plasmon microscopy enables measurement of local refractive index on a far finer scale than the conventional prism based systems. However, researchers find that a trade-off between the lateral resolution and the axial sensitivity exists in the conventional intensity based surface plasmon microscopy. In order to optimize the trade-off, interferometric surface plasmon microscopy was exploited. An interferometric or confocal system gives the so-called V(z) curve, the output response as a function of defocus, when the sample is scanned axially, which gives a measure of the surface plasmon propagation velocity. Considering the complexity of the two arm interferometric system, in this thesis, I show how a confocal system provides a more flexible and more stable alternative. This confocal system, however, places greater demands on the dynamic range of the system. Firstly, the sharp edge of the pupil on the back focal plane of the objective can generate similar effect with the surface plasmon (SPs) ripples; Secondly, the SPs ripples that convey much of the information are much smaller compared to the in focus response which means the confocal system suffers from low signal to noise ratio (SNR). In order to overcome the limitations, I proposed pupil function engineering which was to use a spatial light modulator to modulate the illumination beam profile by using the designed pupil functions with smooth edges. The results show that the sharp edge effect of confocal setup can be greatly reduced and the SNR is improved. Based on this system, I demonstrated that images obtained from the setup are comparable with the two arm interferometric SPR microscope and other wide-field non-SPR microscope. Secondly, I demonstrate the technique of V(α). A phase Spatial Light Modulator (SLM) was applied to replace the previous amplitude SLM. I show how a phase spatial light modulator (i) performs the necessary pupil function apodization (ii) imposes an angular varying phase shift that effectively changes sample defocus without any mechanical movement and (iii) changes the relative phase of the surface plasmons and reference beam to provide signal enhancement not possible with previous configurations using ASLM. Later, I extend the interferometer concept in the confocal system to produce an ‘embedded’ phase shifting interferometer in chapter 6, where I can control the phase between the reference and surface plasmon beams with a spatial light modulator. I demonstrate that this approach facilitates extraction of the amplitude and phase of the surface plasmons to measure of the phase velocity and the attenuation of the surface plasmons with greatly improved signal to noise compared to previous measurement approaches[1]. I also show that reliable results are obtained over smaller axial scan ranges giving potentially superior lateral resolution. In the end of the thesis, future work will be discussed. Firstly, I will propose another technique called ‘artificial’ plasmon. Secondly, I will recommend constructing another system and develop the ideas discussed so the system can work in aqueous environment.