This thesis treats several topics in the study of extra-dimensional models of the world, concerning Heterotic M-Theory and the dynamics of branes. We describe a reduction to five dimensions, over a Calabi-Yau manifold, of an improved version of Heterotic M-Theory, which is valid to all orders in the gravitational coupling. This provides a starting point for considering the consequences of the improved theory for the very fruitful phenomenology of the original. We investigate the singularities formed by the collision of gravitating branes in scalar field theory. By considering the asymptotic structure of the spacetime, the properties of the horizons formed and the growth of the curvature we argue that the singularity is not a black brane, as one might have expected, but rather a big crunch. Finally, we construct a restricted class of multi-galileon theories as braneworld models with codimension greater than one, developing in the process some of the formalism needed for the general construction.

The work described in this thesis involves an investigation of the implementation and application of simultaneous EEG and fMRI. The two techniques arc complementary, with EEG providing excellent temporal resolution and fMRI having good spatial resolution. Combined EEG/fMRI thus forms a powerful tool for neuroscience studies. In initial work, methods for improving the removal of the gradient and pulse artefacts, which are induced in EEG traces recorded during concurrent MRI, have been developed. Subsequently, the effects of the EEG hardware on MR images were investigated. This involved acquiring a series of scans to identify the sources of B0- and B1 inhomogeneities and the extent to which these affect EPI data. The adverse effects on data quality of combining EEG and fMRI increase with field strength. Consequently, EEG-fMRI at 7T is particularly challenging, although a number of advantages make its implementation desirable. Safety tests were performed which showed the presence of the EEG system caused a negligible increase in RF heating effects during scanning at 7T. After elimination of a number of noise sources, the first simultaneous EEG-fMRI experiments at 7T using commercially available equipment were performed. Concurrent EEG/fMRI at 3T was then used to investigate the correlation between the BOLD (blood oxygenation level dependent) response measured during visual stimulation and both the preceding alpha power and the strength of the driven, electrical response. In considering the correlation of the range of variation of the alpha power and BOLD response, a trend emerged which allowed tentative conclusions to be drawn. Variation of the BOLD and driven response with the frequency of visual stimulation relative to a subject's individual alpha frequency (IAF) was also investigated. A significant increase in the driven response, accompanied by a decrease in the BOLD response was observed in visual cortex when it was driven at the IAF.

In recent years the number of applications using NMR spectroscopy of hyperpolarised noble gases has expanded rapidly. The signal enhancement hyperpolarisation provides has led to its implementation in studies as diverse as materials science and biological imaging. 129Xe in particular, with its easily deformed electron cloud, is proving to be a uniquely sensitive probe for nanoporous structures. At present hyperpolarises gas production is limited to optical pumping (SEOP). In this study we investigate another approach, the brute force technique. At very low temperatures and high magnetic fields the Boltzmann distribution of spins for magnetic nuclei is heavily biased in a single direction. At temperatures below 10 mK and in magnetic fields of 15 T, 129Xe polarisations exceeding 40% are attainable. The utilisation of the brute force technique is hindered by the extraordinarily long relaxation time need for this polarisation to occur. In this study, we give details of our investigations of two relaxation catalysts, oxygen and helium-3. It is shown that paramagnetic molecular oxygen causes rapid relaxation of solid xenon at temperatures as low as 500 mK. We report on the enhanced relaxation, by liquid 3He of xenon films adsorbed on to silica gel and exfoliated graphite substrates. The investigation of this mechanism is extended to other magnetic nuclei and improved rates of relaxation are observed in 13C and 1 H. Details are also given, of how this mechanism of relaxation can be halted by the addition of superfluid 4He. Unique observations in the 129Xe NMR spectra are reported, providing a unique opportunity to study the coupling between individual layers of 129Xe atoms. Finally, a novel mechanism of cooling, by the filtering of energetic atoms through a porous ceramic membrane, is investigated.

Dynamic Nuclear Polarisation (DNP) was suggested for the first time by Albert Overhauser in early 1950s. In DNP experiments the polarisation from electrons can be transferred to nuclei by irradiation of the electron resonance line. There are several possible mechanisms for polarisation transfer that involve DNP in solid state depending on the width of the electron line in respect to the nuclear Larmor frequency. In this thesis, the efficiency of TEMPO radical (2,2,6,6 tetramethilpiperidine, 1 oxyl) for DNP is demonstrated in combination with nuclear polarisation transfer techniques for dissolution experiments. New cryo-probes were developed for DNP and cross polarisation (CP) for operation temperatures as low as 1.5 K. Two of them were designed for dissolution experiments. Some published sequences of nuclear polarisation transfer were tested at low temperatures and compared. Novel sequences were implemented for efficient CP in organic samples doped with TEMPO to allow for a consecutive dissolution experiment. The combination of DNP with new CP sequences at low temperatures, achieved at least twice the 13C polarisation obtained with DNP and in a substantially shorter time (between 5 to 10 minutes) in samples doped with TEMPO. The polarisation levels obtained in samples of [13C-1] labelled Na acetate in a few minutes was comparable to the polarisation obtained with trityl radicals in a few hours. In addition, another strategy was investigated by using brute force polarisation as a mechanism for achieving large levels of nuclear spin order. The problem presented by this method is the long relaxation time required to obtain the thermal equilibrium polarisation. By doping with lanthanides samples of [13C-1] labelled Na acetate in 1:1 glycerol-water, it was possible to obtain thermal equilibrium for a 13C spin system in less than one hour.

The microstructure of the lung is complex, containing many branching airways and alveolar sacs for optimal gas exchange. Lung diseases such as cystic fibrosis (CF), asthma, and emphysema lead to a destruction of this microstructure. As such, there is a growing interest in the early identification and assessment of lung disease using non invasive imaging techniques. Pulmonary function tests such as spirometry and plethysmography are currently used for this purpose but can only provide quantitative lung function measurements rather than direct measurements of lung physiology and disease. Computed tomography (CT) has also been used but due to risk of cell damage and mutation from the ionising radiation, long term monitoring of the lungs is severely constrained. Recently, new methods based on magnetic resonance imaging (MRI) have been developed to provide diagnostic imaging of the lung. Conventional MRI is not very well suited for lung imaging due to the very low proton density of the pulmonary airspaces. This problem can be overcome by making the patient inspire noble gases such as 3He whose polarisations have been vastly increased through optical pumping. Therefore 3He MRI permits a non-invasive determination of lung function. The high diffusion coefficient of 3He can be exploited to probe the microstructure of the lung. By measuring how fast 3He diffuses within the lung, the size of the lung microstructure can be assessed. Normally, the airspace walls impede the diffusion of the gas but for diseased lungs where microstructure has been destroyed, diffusion is less restricted and a higher apparent diffusion coefficient (ADC) is observed. The research conducted for this thesis focused on the measurement of ADC using three different MRI pulse sequences with each sequence being designed to assess the peripheral airspaces over different length scales. These sequences were then implemented on three different subject study groups.

Dynamic nuclear polarisation is a technique that allows one to increase the signal-to-noise ratio in an NMR experiment substantially, by transferring the inherently larger electron polarisation to the nuclei. Quantum mechanical models of this effect have thus far been limited to the description of only a few nuclei. This is due to the exponential scaling of the matrices involved in the description of the system. In this thesis methods of reducing the state space needed to accurately describe the simulation of solid effect DNP were explored and tested. Krylov Bogoliubov averaging has been used to remove high frequency oscillations from the system Hamiltonian and confine the trajectory of the dynamics to the zero quantum coherence subspace. Truncation of the basis spanning the Liouville space to low spin correlation orders has been tested and a condition for a minimum truncation level was found. A strategy based on a projection method, which allows one to describe the spin polarisation transient with multi-exponential functions, is introduced. This results in a linear scaling of the propagator with the number of spins. The influence of the parameters involved in the solid effect on the dynamics of the polarisation build up is discussed. The second part of this thesis is concerned with a novel approach to detecting fast molecular dynamics with the use of multiple RF receive and transmit coils. A proof of principle probe with two decoupled RF coils is presented, as well as a field map based shimming strategy and fast 2D data acquired with the probe. Lastly a probe with six RF coils, based on the design of the dual coil probe, will be presented, and initial data shown. The potential for using this probe in hyper-polarisation experiments for protein binding and folding studies will be discussed.

In this thesis we study the neutron transport (Boltzmann transport equation) which is used to model the movement of neutrons inside a nuclear reactor. More specifically we consider the mono-energetic, time independent neutron transport equation. The neutron transport equation has predominantly been solved numerically by employing low order discretisation methods, particularly in the case of the angular domain. We proceed by surveying the advantages and disadvantages of common numerical methods developed for the numerical solution of the neutron transport equation before explaining our choice of using a discontinuous Galerkin (DG) discretisation for both the spatial and angular domain. The bulk of the thesis describes an arbitrary order in both angle and space solver for the neutron transport equation. We discuss some implementation issues, including the use of an ordered solver to facilitate the solution of the linear systems resulting from the discretisation. The resulting solver is benchmarked using both source and critical eigenvalue computations. In the pseudo three--dimensional case we employ our solver for the computation of the critical eigenvalue for three industrial benchmark problems. We then employ the Dual Weighted Residual (DWR) approach to adaptivity to derive and implement error indicators for both two--dimensional and pseudo three--dimensional neutron transport source problems. Finally, we present some preliminary results on the use of a DWR indicator for the eigenvalue problem.

Scanning probe microscopy (SPM) allows us to directly measure the interactions between a probe and a sample at the atomic scale. Techniques such as non-contact atomic force microscopy (NC-AFM), allows us to to characterize the forces present on a surface, resolve the atomic structure of molecules or examine their chemical properties, while scanning tunneling microscopy (STM) allows their electronic properties to be characterized. As the interactions take place at the atomic scale, the atomistic state of the probe apex plays a crucial role. In AFM, it is the atomic scale forces between the outermost atoms of the probe and surface that are dominant, while for STM the density of states (DOS) that contribute to tunneling are crucial. Therefore, understanding and controlling the tip termination is crucial to derive meaningful interpretations from experimental data. In this thesis, the role of the tip termination is examined for various surfaces and situations. We find that determining the "right" tip state depends critically on the experiment and several general strategies for shaping the tip apex into a preferred state are therefore outlined. H:Si(100) surfaces were used as a substrate for lithographic patterning using STM. We have successfully implemented an automated extraction routine for performing large scale patterning with high fidelity and single atom specificity. Our ultimate goal is to combine the extraction routine with SPM image recognition software to allow analysis and manipulation of atomic scale features without human intervention. To perform manipulations reliably, the tip influence on "what we see" (tip imaging states), or specifically on what the recognition software can identify, needs to be considered. We find, counter-intuitively, that atomic scale manipulation with the highest fidelity occurs when silicon dimers are observed as rows as opposed to when atomic resolution imaging occurs. The tip state influence on measuring surface diffusion of PTCDA on Ag(110) surfaces, was also investigated. We find that the adsorption kinetics of diffusing molecules can only be detected for specific tip imaging states. To allow examination with no-human intervention, the tip state needs to be carefully considered, and a combination of analytical and spectroscopic tools needs to be implemented in conjunction with the experiment. Additionally, characterization of the tip apex was investigated at the tunnel junction between a STM tip and a metal surface using field emission measurements. Our results suggest that field emission measurements performed at the tunnel junction are sensitive to changes in the nanoscopic/mesoscopic tip apex structure, thus opening up the possibility of automating the process of characterization the tip apex.

A search for the electroweak production of charginos and neutralinos decaying into final states involving three electrons or muons is presented. The analysis is based on 36.1 fb^-1 of √s = 13TeV proton–proton collisions recorded by the ATLAS detector at the Large Hadron Collider. Scenarios considered are based on simplified models with the associated production of the next-to-lightest neutralino and the lightest chargino, followed by their decays into final states with leptons and the lightest neutralino via either sleptons or Standard Model gauge bosons. No significant deviations from Standard Model expectations are observed and stringent limits at 95% confidence level are placed on the masses of relevant supersymmetric particles. For a massless lightest neutralino, masses up to 1.13TeV are excluded for the associated production of the next-to-lightest neutralino and the lightest chargino, assuming slepton mediated decays, whereas for gauge-boson-mediated decays, masses up to 380 GeV are excluded.

Phase transitions and critical phenomena are of central importance in quantum field theory and statistical physics. We investigate the low energy properties of O(N) symmetric scalar field theories using functional renormalisation group methods for all N. This modern formulation of Wilson's renormalisation group allows a continuous interpolation between short and long distance physics without resorting to a weak coupling expansion. To leading order in the derivative expansion, we study the phase transition and the approach to convexity in the deep infrared limit. In the limit of infinite N, the fluctuations of the Goldstone modes dominate allowing for a complete analytical discussion of the effective potential. For finite N, the radial fluctuations become important and we resort to systematic series expansions. In both cases a systematic and thorough analysis of the diverse fixed point solutions is carried out. This leads to a comprehensive picture of the scaling potential for a large number of universality classes. We also study the dependence of our results on the regularisation scheme. Finally, we establish that the infrared completion of the effective potential in the broken phase is driven by a fixed point that leads to the flattening of the non-convex part of the potential.