In this thesis we take Einstein theory in dimension four seriously, and explore the special aspects of gravity in this number of dimension. Among the many surprising features in dimension four, one of them is the possibility of `Chiral formulations of gravity' - they are surprising as they typically do not rely on a metric. Another is the existence of the Twistor correspondence. The Chiral and Twistor formulations might seems different in nature. In the first part of this thesis we demonstrate that they are in fact closely related. In particular we give a new proof for Penrose's `non-linear graviton theorem' that relies on the geometry of SU(2)-connections only (rather than on metric). In the second part of this thesis we describe partial results towards encoding the full GR in the total space of some fibre bundle over space-time. We indeed show that gravity theory in three and four dimensions can be related to theories of a completely different nature in six and seven dimension respectively. This theories, first advertised by Hitchin, are diffeomorphism invariant theories of differential three-forms. Starting with seven dimensions, we are only partially succesfull: the resulting theory is some deformed version of gravity. We however found that solutions to a particular gravity theory in four dimension have a seven dimensional interpretation as G2 holonomy manifold. On the other hand by going from six to three dimension we do recover three dimensional gravity. As a bonus, we describe new diffeomorphism invariant functionnals for differential forms in six dimension and prove that two of them are topological.

The Small Telescopes at the Liverpool Telescope (STILT) is an almost decade old project to install a number of wide field optical instruments to the Liverpool Telescope, named Skycams, to monitor weather conditions and yield useful photometry on bright astronomical sources. The motivation behind this thesis is the development of algorithms and techniques which can automatically exploit the data generated during the first 1200 days of Skycam operation to catalogue variable sources in the La Palma sky. A previously developed pipeline reduces the Skycam images and produces photometric time-series data named light curves of millions of objects. 590,492 of these objects have 100 or more data points of sufficient quality to attempt a variability analysis. The large volume and relatively high noise of this data necessitated the use of Machine Learning and sophisticated optimisation techniques to successfully extract this information. The Skycam instruments have no control over the orientation and pointing of the Liverpool Telescope and therefore resample areas of the sky highly irregularly. The term used for this resampling in astronomy is ‘cadence’. The unusually irregular Skycam cadence places increased strain on the algorithms designed for the detection of periodicity in light curves. This thesis details the development of a period estimation method based on a novel implementation of a genetic algorithm combined with a generational clustering method. Named GRAPE (Genetic Routine for Astronomical Period Estimation), this algorithm deconstructs the space of possible periods for a light curve into regions in which the genetic population clusters. These regions are then fine-tuned using a k-means clustering algorithm to return a set of independent period candidates which are then analysed using a Vuong closeness test to discriminate between aliased and true periods. This thesis demonstrates the capability of GRAPE on a set of synthetic light curves built using traditional regular cadence sampling and Skycam style cadence for four different shapes of periodic light curve. The performance of GRAPE on these light curves is compared to a more traditional periodogram which returns a set of peaks and is then analysed using Vuong closeness tests. GRAPE obtains similar performance compared to the periodogram on all the light curve shapes but with less computational complexity allowing for more efficient light curve analysis. Automated classification of variable light curves has been explored over the last decade. Multiple features have been engineered to identify patterns in the light curves of different classes of variable star. Within the last few years deep learning has come to prominence as a method of automatically generating informative representations of the data for the solution of a desired problem, such as a classification task. A set of models using Random Forests, Support Vector Machines and Neural Networks were trained using a set of variable Skycam light curves of five classes. Using 16 features engineered from previous methods an Area under the Curve (AUC) of 0.8495 was obtained. Replacing these features with inputs from the pixel intensities from a 100 by 20 pixel image representation, produced an AUC of 0.6348, which improved to 0.7952 when provided with additional context to the dimensionality of the image. Despite the inferior performance, the importance of the different pixels produced relations in the trained models demonstrating that they had produced features based on well-understood patterns in the different classes of light curve. Using features produced by Richards et al. and Kim & Bailer-Jones et al., a set of features to train machine learning classification models was constructed. In addition to this set of features, a semi-supervised set of novel features was designed to describe the shape of light curves phased around the GRAPE candidate period. This thesis investigates the performance of the PolyFit algorithm of Prsa et al., a technique to fit four piecewise polynomials with discontinuous knots capable of connecting across the phase boundary at phases of zero and one. This method was designed to fit eclipsing binary phased light curves however were also described to be fully capable on other variable star types. The optimisation method used by PolyFit is replaced by a novel genetic algorithm optimisation routine to fit the model to Skycam data with substantial improvement in performance. The PolyFit model is applied to the candidate period and twice this period for every classified light curve. This interpolation produces novel features which describe similar statistics to the previously developed methods but which appear significantly more resilient to the Skycam noise and are often preferred by the trained models. In addition, Principal Component Analysis (PCA) is used to investigate a set of 6897 variable light curves and discover that the first ten principal components are sufficient to describe 95\% of the variance of the fitted models. This trained PCA model is retained and used to generate twenty novel shape features. Whilst these features are not dominant in their importance to the learned models, they have above average importance and help distinguish some objects in the light curve classification task. The second principal component in particular is an important feature in the discrimination of short period pulsating and eclipsing variables as it appears to be an automatically learned robust skewness measure. The method described in this thesis produces 112 features of the Skycam light curves, 38 variability indices which are quickly obtainable and 74 which require the computation of a candidate period using GRAPE. A number of machine learning classifiers are investigated to produce high-performance models for the detection and classification of variable light curves from the Skycam dataset. A Random Forest classifier uses a training set of 859 light curves of 12 object classes to produce a classifier with a multi-class F1 score of 0.533. It would be computationally infeasible to produce all the features for every Skycam light curve, therefore an automated pipeline has been developed which combines a Skycam trend removal pipeline, GRAPE and our machine learned classifiers. It initialises with a set of Skycam light curves from objects cross-matched from the American Association of Variable Star Observers (AAVSO) Variable Star Index (VSI), one of the most comprehensive catalogues of variable stars available. The learned models classify the full 112 features generated for these cross-matched light curves and confident matches are selected to produce a training set for a binary variability detection model. This model utilises only the 38 variability indices to identify variable light curves rapidly without the use of GRAPE. This variability model, trained using a random forest classifier, obtains an F1 score of 0.702. Applying this model to the 590,492 Skycam light curves yields 103,790 variable candidates of which 51,129 candidates have been classified and are available for further analysis.

In this thesis we investigate several aspects of galaxy evolution. We begin by giving a brief introduction to the subject of galaxy evolution in the context of the Universe as we know it today. We discuss infrared surveys of galaxies as a tool for studying galaxy evolution. Initially, we are interested in the large scale environment of galaxies and identify clusters of galaxies at high redshift. We compare the mass and star-formation properties of galaxies in the cluster and field environments. To take this further we look to the AKARI all- sky survey and assess the potential of this survey for future studies. We calculate the completeness and reliability of the survey. Such wide surveys also allow for the possibility of studying rare and extreme phenomena. Such phenomena can push theories of galaxy evolution to their extremes and constrain these theories. We present the discovery of four such objects in the SWIRE survey. Finally, since environment plays a large role in the evolution of galaxies we extend this investigation to smaller scales. We investigate the progenitors of Type Ia Supernovae from a study of their host galaxies, which have implications for their use as standardisable candles.

The problem of developing a reliable technique for measuring instantaneous velocities at an arbitrary point in a magnetohydrodynamic (MHD) flow of mercury is the primary concern of the thesis. The solution to this problem is urgently needed in order that measurements may be taken in practical MHD devices and in order that the interesting theoretical work which has emerged in the past decade may be substantiated by experimental evidence. Much of the information on measurement techniques contained herein will be applicable to other liquid metal flows. The recent advances in the area of constant temperature hot-film anemometry have made this technique the best one for instantaneous measurements in low-temperature liquid metal systems. The thesis is divided into two parts. The study of thermoanemometry is described in chapter 2 and its application to some MHD experiments is described in chapter 3. Chapter 2 is divided into two main sections, §2.2 and §2.3, which discuss the theory of thermo-anemometry in mercury and demonstrate its application in calibration exercises. The hot-film sensors tested are the tiny (0.030mm diameter and 0.5mm length) quartz-insulated platinum film sensors which are now made available for work in electrically conducting fluids by Thermo-Systems Inc., St,Paul, Minnesota, U.S.A. An account of our attempts to construct somewhat similar sensors in the laboratory is given in Appendix B. In addition to discussing various calibration problems, such as MHD effects on free convective heat transfer from the hot-film and its dynamic response, chapter 2 develops, and demonstrates by experiment, new methods for the direct measurement of low turbulence intensi.ties in low Prandtl number fluids. The simple formulae presented are likely to be more accurate in the majority of cases than more sophisticated methods involving linearization of the anemometer voltage with respect to velocity because of their lack of sensitivity to signal drift. Chapter 3 discusses theoretical aspects in S3.2 and their experimental substantiation in §3.3 for two different types of MHD flow. The first of these is electrically driven flow in mercury between two circular, highly conducting electrodes Which are placed opposite one another in insulating planes with a magnetic field normal to their surfaces. The steady flow is examined theoretically by an asymptotic analysis and experimentally using Pitot tubes and electric potential probes. The experiments give some insight into the behaviour of these probes in MHD situations. This same flow is studied using a hot-film sensor with good results. This experiment points to the need for an extensive study of the MHD effects on hotfilm heat transfer and the associated MHD errors in measurements for various orientations of the sensor relative to the magnetic field. Hot-film techniques are then used to examine the instability and subsequent wave-like secondary flow (when the Hartmann number, M, is very high) in this same electrically driven flow. These phenomena are interesting but very difficult to understand. It is shown that the transverse magnetic field, if strong enough, can control the stability of, and secondary flow in, the electrically driven shear layprs through direct action on the most unstable three-dimensional disturbances even though most of the vorticity of these disturbances is parallel to the magnetic field. An attempt is made to discuss the physical mechanism involved. The second tyPe of MHD flow investigated is turbulent vorticity suppression behind a square-array wire grid in a transverse magnetic field. The exper-Iment,is of a preliminary nature but demonstrates some interesting phenomena which can be explained in order of magnitude terms. Both of the MHD flows studied demonstrete various aspects of the behaviour of the hot-film sensors as well as being interesting in themselves. The paper listed in the Table of Contents under Appendix A as "Malcolm (1968b)'may be read as an extended summary of the thesis.

New UV and EUV observations of off-limb and upper solar corona made by the UltraViolet Coronagraph Spectrometer (UVCS) and the Coronal Diagnostic Spectrometer (CDS) on SOHO (Solar and Heliospheric Observatory) are presented in this thesis. These data were used to establish the physical properties, such as temperature, density and element abundances, of different structures of the off-limb and upper corona. For this project, the UVCS team provided UV spectra of the extended solar corona, which included lines of primary interest for the characterization of this region and the solar wind. CDS data consisted of NIS (Normal Incidence Spectrometer) EUV spectra of the low corona. The data included several density-sensitive and temperature-sensitive lines which enabled diagnostic studies to be made. Absolute element abundances were derived from UVCS data; relative element abundances were derived from CDS data. The Differential Emission Measure (DEM) technique was used (for the first time on UVCS data) as the primary method for abundance study. Electron temperatures along the line of sight were derived applying the line ratio and the DEM techniques to both CDS and UVCS data. From the CDS data, electron densities along the line of sight were derived using the line ratio technique. For the UVCS data, the density was inferred using the 0 VI radiative and collisional components of the line. One equatorial and two mid-latitude streamers were observed with the two instruments, in the low corona and at about 1.6 R®. Electron density and temperature profiles with the solar distance were derived. They appeared to satisfy the hydrostatic equilibrium condition. The equatorial streamer appeared to be cooler than the mid-latitude one. Moreover, while the former tended to isothermal values already in the low corona, the latter was multithermal at the base and isothermal at 1.6 R®. The derived composition at 1.6 R®. showed a depletion with respect to the photospheric values for almost all the elements. The Fe/O ratio found here was consistent with values found in the solar wind. Moreover, a depletion in element composition with increasing solar distance was also found. While observing off-limb in the south polar coronal hole, CDS observations of a macrospicule were obtained. For the first time the background emission was isolated from that of the macrospicule itself, and a diagnostic study of both regions was made. The ambient coronal hole appeared to have a density of = 2 x 108 cm -3 that was about half the density found in the streamer base studied in this thesis. Multithermal components were found at the coronal hole base. The macrospicule spectrum indicated chromospheric and transition region temperatures, and fluctuations in density along the feature were registered. In particular, the data showed the presence of an outward-moving cloud of cool material. Its time evolution and velocity were studied. The maximum (initial) outflow velocity was about 80km s-1 , consistent with the outflow velocity measured in interplume regions. An off-limb hot loop system was observed with CDS at mid-latitude. Its top and base were selected for diagnostic studies. Some newly observed hot lines were identified. The loop system appeared to be composed of multi-thermal plasma. The highest temperature registered was log T=6.4 at the top of the loop. A depletion of element abundances which mainly involves the plasma at the top of the loop was found. A coronal hole bounded by a loop system was observed with CDS. Electron density appeared up to a factor two higher in the boundary than in the coronal hole, and the loop system appeared multi-thermal. The ambient coronal hole temperature appeared to be enhanced by the proximity of this loop arcade. Abundances were derived in both regions, and the coronal hole boundary showed slight depletions relative to photospheric values. New coordinated observations with CDS and UVCS were made during one of the SOlO-Ulysses quadratures. Preliminary results regarding temperatures and densities of the core and boundary regions of streamers were obtained from UVCS data.

This thesis is about an investigation into the formation of spheroidal type galaxies. The investigation began with modelling studies of early-type galaxies and spiral bulges (SBs). From galaxy formation modelling studies led by experiments with a sample galaxy, some results were obtained; nonsolar abundance ratios in Elliptical galaxies (Es) achieved better fits between model and data than solar abundance ratios. For both early-type and late-type galaxies, best fits with non-solar abundance ratios were more constrained than in the solar abundance ratio case. A strong link between star formation histories and the supernova Ia rate for the early and late-type galaxies was shown. The model code itself was tested by way of pseudo galaxy experiments, and shown to reliably reproduce model parameters. In the topic area of galaxy formation, regions of spectra particularly sensitive to a galaxy's age and metallicity were measured as equivalent widths and then calibrated to the common scale of the Lick Indices. The Lick Indices were used in deriving all key results throughout the thesis. The modelled sample of galaxies from Proctor & Sansom (2002) lacked data on low velocity dispersion (a) galaxies for line strengths versus kinematics correlations. In regards to low a galaxies, Low Luminosity Es (LLE5) were considered to be likely candidates. Long-slit spectra of a sample of 12 LLEs, taken at the European Southern Observatory New Technology Telescope, were sub-selected for their low velocity dispersions. The spectra of 10 of these LLEs were successfully reduced. Line strengths and kinematics were measured. The Lick Indices of these LLEs were correlated with velocity dispersion (a), alongside the previously modelled companion data set. Ages and metallicities of the LLEs were estimated. From these results, the LLEs were found to have significant correlations of line strength versus a with SBs. However, the LLEs do not appear to be younger than SBs, but younger than Es. The LLEs seem to consist of a low metallicity group (possibly misclassified dwarf spheroidal galaxies) and a high metallicity group. Future possible work that may uncover which models of galaxy formation for high and low metallicity LLEs these results support is suggested.

Solar flares release an enormous amount of energy (up to 10^32 erg) which is transported through the Sun`s atmosphere until it is deposited in the chromosphere, resulting in a broadband enhancements to the solar radiative output. The bulk of the flare radiative output originates from the chromosphere. Despite the importance of the chromosphere we do not yet have a comprehensive understanding of the radiation produced there following flare energy deposition, and the diagnostic potential of radiation from this layer of the atmosphere has not been fully exploited. Additionally, there is evidence that the standard model of flare energy transport via non-thermal electron beams might not be the complete scenario. Chromospheric radiation will be crucial in discriminating between the standard model and alternative energy transport mechanisms. Through near-UV spectroscopy, optical imaging, and radiation hydrodynamic modelling using both the electron beam model and energy transport via Alfven waves, the chromospheric response to flare energy input was investigated. One of the first detailed analyses of the response of the Mg II h & k spectral lines to flare energy input is presented. These are strong, optically thick, lines formed in multiple locations of the chromosphere. In addition to showing a strong intensity enhancement, the lines were redshifted, showed a blue wing asymmetry in the most intense sources, and were substantially broadened. The lines were also single peaked during the flare, in contrast to their double peaked, centrally-reversed structure in the non-flaring Sun. Despite this, the analysis suggested they remained optically thick during the flare. Using snapshots from radiation hydrodynamic flare simulations in combination with a radiation transfer code capable of modelling partial redistribution effects, the Mg II h & k line formation properties during flares were analysed. These simulations showed the same qualitative behaviour as observations, but instead of being single peaked they contained a shallow central reversal. Additionally the lines were too narrow, suggesting the lower chromosphere was too cool in the simulations. Line core Doppler shifts were well-correlated with atmospheric velocity. The lines were formed lower than in the quiet Sun, with source functions (and therefore emergent intensities) that were more strongly coupled to the Planck function during the flare - that is, they reflected the local conditions to a greater degree. While the lines did indeed remain optically thick during the flare, some optically thin contributions resulted in asymmetries. However, the strongest blue wing asymmetries were the result of a stationary component to the line profile when the line core was redshifted. Optical continuum enhancements are amongst the strongest emission during solar flares, though are relatively rare to observe. Understanding the emission mechanism responsible is important for models of flare energy transport, but there remains debate as to the dominant mechanism. This emission may originate from the heated photosphere, or from an overionised region of the chromosphere. Imaging in three optical passbands during a strong flare was used to analyse the temperature enhancement and luminosity of optical sources were under the assumption of two simple models. This was in an effort to determine the most likely emission mechanism. The models were a photospheric (blackbody) model and a chromospheric model with enhanced recombination radiation. Observations were most consistent with the photospheric origin, although some evidence that both mechanisms play a role is discussed. Additionally, initial analysis of observations of a flare in which both the optical continuum and near-UV continuum were observed is presented. Finally, a radiation hydrodynamic numerical model was adapted to include flare energy transport via the dissipation of Alfven waves. Some representative simulations surveying the parameter space are discussed. Additionally, a detailed comparison is presented between a simulation using the standard model of energy transport via non-thermal electron beams, and a simulation using Alfv\'en wave dissipation. Both the hydrodynamic response is compared, as well as the radiative response of the Ca II 8542 and Mg II k-line. It was found that Alfven waves are able to sufficiently heat the chromosphere during flares, making them a viable candidate for energy transport, and that there is the potential for discriminating between energy transport models using observations of chromospheric radiation.

In this thesis we explore low energy extensions of Einstein's theory of General Relativity (GR). Initially our motivation will be the cosmological constant problem where large radiative corrections due to quantum field theories minimally coupled to the dynamical metric in GR leads to unacceptably large space-time curvatures. We will discuss the cosmological constant problem in detail, paying special attention to how it affects the global structure of a space-time whose dynamics are dictated by GR. With this in mind we will present and discuss recently proposed global modifications of GR which in the semi-classical limit sequester the radiatively unstable loop corrections to the cosmological constant from the space-time curvature. This is achieved by supplementing the local dynamics of GR with highly non-trivial global constraints, and we demonstrate how this can be achieved in a theory which is manifestly local. In this theory we will also consider the effects of an early universe phase transition on the late time dynamics. Away from global modifications of GR we will also consider local modifications which necessarily involve the propagation of new degrees of freedom. We outline the possible screening mechanisms which, since no new gravitational degrees of freedom have been observed in local environments, are an important feature of any local modification of GR. For one of these mechanisms, namely, the Vainshtein mechanism, we will consider the regime of validity of theories which make use of the Vainshtein mechanism and assess suggestions that one can trust these theories beyond the scale we would naively expect them to become strongly coupled. Following this we will move onto the chameleon mechanism, another example of a screening mechanism, and present a high energy extension motivated by the breakdown in the original chameleon theory in the early universe. The interactions of the resulting DBI chameleon theory will be motivated by our discussion of the Vainshtein mechanism.

The Earth’s surface bears the scars of 4.5 billion years of bombardment by asteroids, despite most having been erased by tectonic activity and erosion. Asteroids predominantly orbit the Sun in the asteroid belt between Mars and Jupiter, but a large number occupy orbits close to the Earth’s. These bodies are termed Near Earth Objects (NEOs) and they present a very real impact threat to the Earth. In 1998 NASA inaugurated the ‘Spaceguard Survey’ to catalogue 90% of NEOs greater than 1 km in diameter. The smaller bodies, meanwhile, remain undetected and far more numerous. In order to understand the NEO hazard, the consequences resulting from an asteroid impact require modelling. While the atmospheric entry of asteroids is a critical part of the impact process, it is the surface impact which is most important, both onto land and into the oceans. It is the impact generated effects (IGEs) that are hazardous to human populations on the Earth and the infrastructure they occupy. By modelling these IGEs and the consequences they present for humans and infrastructure, an understanding of the global vulnerability to the hazard is developed. ‘NEOimpactor’ is the software solution built to investigate the global vulnerability to NEO impacts. By combining existing mathematical models which describe the impact and effects, a unified impact simulator tool has been developed with the capacity to model the real consequences of any terrestrial impact. By comparing the consequences of multiple impact events, a complete vulnerability assessment of the global NEO hazard is derived. The result maps are designed for ease of dissemination to explain the impact risk to a non-specialist audience. The system has identified China, US, India, Japan and Brazil as facing the greatest overall risk, as well as indicating the various factors influencing vulnerability. The results can be used for informing the international decision making processes regarding the NEO hazard and potential mitigation strategies.

Optical measurements of small-scale auroral structures are here combined with spectrographic data in order to study the relationship between auroral morphology and the energy characteristics of the precipitating population. It is shown that rayed auroral structures are associated with precipitating electrons with a broad range in energy, including a significant population at energies of around 100 eV. In comparison, observations of fast-moving auroral arc elements are shown to result from precipitation energy distributions peaking at several keV with a very small low-energy component. This spectrographic information feeds directly into the study of naturally enhanced ion-acoustic lines, or NEIALs, which have been observed by incoherent-scatter radars at high-latitudes. It has been proposed that these radar enhancements result from natural plasma instability, causing the generation of ion-acoustic waves through the decay of unstable Langmuir waves, themselves driven by low-energy electron streams. Using multi-spectral imaging in combination with radar observations, a direct link is shown between ion-acoustic wave enhancements and precipitating electrons at 100 eV energies. Wave enhancements at the radar wavevector which are three orders of magnitude above the thermal level, are successfully modelled using the Langmuir decay interpretation for the time of observation. Electron populations with a broad energy range are thought to result from Alfv´enic acceleration mechanisms, which play an important role in the generation of smallscale auroral structure. With the recent advancements in multi-spectral imaging, it is now possible to resolve auroral filaments of a few hundred meters width. An interferometric imaging capability is under development for the EISCAT Svalbard Radar system, in order to resolve scattering wave structures on similar spatial scales within the radar beam. A technique is demonstrated by which to calibrate the position of coherent echoes detected by the interferometer. This will be of great use in clarifying the role of precipitating electron beams in turbulent plasma processes on small scales.