Gravitational waves, predicted by the theory of General Relativity, are fluctuations in the curvature of space-time which arise from the asymmetric acceleration of mass. While gravitational waves have yet to be detected directly, measurements of the inspiral rate of a binary pulsar system have provided strong evidence for their existence and a world-wide effort to develop more sensitive detectors is ongoing. In addition to testing predictions of General Relativity, observation and analysis of gravitational waves from astrophysical sources will provide new insights into a wide range of phenomena including black holes, neutron stars and supernovae. Gravitational waves are quadruple in nature, and therefore produce fluctuating tidal strains on space. Long baseline gravitational wave detectors aim to measure this effect using laser interferometry to measure fluctuations in the relative separation of free masses, coated to form highly reflective mirrors and suspended as pendulums at the ends of perpindicular arms up to 4 km in length. There are currently several long baseline gravitational wave detectors in operation around the world, including the three LIGO detectors in the US, the UK/German GEO600 detector near Hannover and the French/Italian Virgo detector near Pisa. The strain expected from gravitational waves is very small, of order [~10-[superscript 22. The magnitude of the resultant displacement is such that the thermal motion of the mirrors and their suspensions forms an important limit to detector sensitivity. The level of thermal noise is related to the mechanical dissipation of the materials used in the test mass and the mirror coatings.

This thesis uses 32.88 1/fb of pp collision data gathered at the LHC by the ATLAS detector during 2016 at center of mass energy 13 TeV. The analysis employs kinematic fitting techniques by applying the KLFitter package on the signal-rich region using only the 6 jets selection mode (kB6). It construction variables providing good separation between signal and background in the search for ttH(H decay to b-barb) in the single-lepton final state (electron or muon). The scalar sum of transverse momenta is the variable of choice for the fit in signal-depleted regions. Using Boosted Decision Trees in the fit of signal-rich regions, a 95% CLs exclusion limit (significance) of 5.4 (4.25 \sigma) is obtained, with the corresponding ratio of the measured ttH signal cross-section to the Standard Model expectation of 3.69(+0.98,-0.88). This result indicates that there is an excess of events above the background expectation for the SM Higgs boson with mass of 125 GeV. The excess is even greater than the SM would predict (signal strength equal to 1). This excess over the SM prediction could be interpreted as a statistical fluctuation, and is not significant. More data would likely moderate this statistical aberration.

According to Einstein's theory of General Relativity, the acceleration of matter can cause ripples in the curvature of spacetime, given the name gravitational waves. Such ripples are negligible in magnitude for all but the most energetic astrophysical events, such as the coalescence of compact binary stars. In 2015, gravitational waves were first directly detected from a binary black hole (BBH) coalescence [19]. This was achieved using two independent laser interferometers which each measured the fluctuations caused by the gravitational waves as they passed by. Matched filtering and other data analysis techniques were then employed to identify the properties of the source and measure the likelihood that the detection is a false alarm. The efficacy of these matched filtering techniques is pivotal to not only detecting gravitational waves, but drawing as much information about their sources as possible. The methods for detecting a BBH involve the construction of a template bank; a group of synthesised waveforms which each represent a detectable series of gravitational waves that a BBH could produce. The characteristics of a BBH template are governed by the two masses and how they spin, the distance to the source, its orientation and its sky location. Current template banks do not include templates for sources where the spins are misaligned with the orbital momentum, which is the cause of precession in BBH. Thus, the algorithms are effective for detecting a non-precessing BBH, but much less sensitive towards precessing sources. Creating a template bank which includes all possible precessing waveforms is computationally infeasible and would induce enough statistical noise to negate any extra sensitivity gained. However, many precessing signals would be undetectable or indistinguishable from non-precessing signals. Including such signals in a bank would result in no gain in its sensitivity. This thesis attempts to locate areas of precessing parameter space where waveforms are distinguishable from non-precessing sources, and begins work on forming a function which maps observable precession through parameter space.

The extent of dynamical processes in the lower atmosphere of the Sun during solar flares is not fully understood. While it is widely accepted that the majority of the associated flare energy is deposited in the Sun's chromosphere, it is less clear how this energy is transported and how it influences the configuration of material flows. Current models of chromospheric evaporation and condensation assume an upwards expulsion of high-temperature plasma, with an accompanying downwards flow at cooler temperatures. In this thesis, the validity of these assumptions are tested using a combination of observations and modelling, with particular focus given to the Lyman lines of hydrogen.

Galaxy groups and clusters (GGCs) hold a privileged position within the cosmological hierarchy. As the most recent structures to have formed, their abundances, spatial distribution and individual properties bear the indelible imprint of the background cosmology, initial conditions and their formation history, making them valuable probes of both cosmology and astrophysics. It has, however, become increasingly clear over the past decade that making use of these probes for precision cluster cosmology requires detailed, realistic predictions for the observed properties of GGCs. Producing these necessitates the use of large cosmological hydrodynamical simulations with realistic ‘sub-grid’ prescriptions for baryonic physics. One mechanism in need of addressing is the effect of the cosmic background of massive neutrinos. As these remain relativistic to relatively late times, they will free-stream out of overdensities, altering the formation of large-scale structure (LSS). If this effect can be accurately modelled, it presents an independent method of constraining the value of the neutrino mass by means of LSS observations. This thesis makes use of the cosmo-OWLS and BAHAMAS cosmological hydrodynamical simulation suites to explore the separate and combined effects of baryon physics (particularly feedback from active galactic nuclei, AGN) and the free-streaming of massive neutrinos on large-scale structure. I focus on five diagnostics: i) the halo mass function; ii) halo mass density profiles; iii) the halo mass concentration relation; iv) the clustering of haloes; and v) the clustering of matter; and I explore the extent to which the effects of baryon physics and neutrino free-streaming can be treated independently. In comparing to the GAMA observations, I find that these data provide insufficient statistical power to constrain the value of the summed neutrino mass. This is primarily due to the intrinsic scatter in the stellar mass - halo mass relation, and the strong dependence of the sensitivity on precise mass binning. As a consequence, more precise estimations of the halo mass will be required in future work seeking to utilise this metric. Finally, I find that the clustering of simulated BAHAMAS groups is remarkably consistent with that of observed GAMA groups. This lends additional weight to the argument that BAHAMAS accurately reproduces the properties of the GGC population, and supports its use as a cosmological tool.

Jointing materials is an inevitable step in the fabrication of many high performance optical devices. Today there is an increasing demand, both from industry and academic research, for reliable techniques for jointing of optical components which can be performed simply and inexpensively, where the bonds possess high strength and precision with low mechanical loss. Several methods of bonding have been defined and employed over time. Currently, the most common techniques of bonding are optical contacting, diffusion, epoxy and glass frit. Each of these techniques has positive aspects which make them appropriate for a range of applications, but not ideal in cases where a thin optically transparent and mechanically strong joint between optical compounds is required. Hydroxide-catalysis bonding is an interesting candidate in such cases: it has already been demonstrated to have excellent performance with respect to mechanical stability, precision and strength in numerous applications, such as in space systems, optics and gravitational wave detectors. At present, there are not many papers that talk exhaustively about the optical properties of hydroxide-catalysis bonding. Most of the time, the published results are closely dependent on requirements imposed by the experiment that is being conducted. Since there are a lot of interesting potential applications and increasing industrial interest in usage of hydroxide-catalysis bonding, it is important to develop techniques to characterise the optical properties of these bonds. In this thesis, a non-destructive technique for measuring the optical properties of hydroxide-catalysis bonding is reported. More specifically, the bond refractive index and thickness are determined from reflectivity measurements. By applying this method, it will be possible to understand how the optical properties and chemistry of a hydroxide-catalysis bond vary when different bonding solutions and substrate materials are used and, consequently, to tailor better the bonds to various utilisations of interest. Sodium silicate solution at different concentrations with water and potassium hydroxide solution are used to bond fused silica and sapphire substrates. Curing at room temperature and at 100 °C for eight hours is chosen to study the influence of temperature on the properties of a hydroxide-catalysis bond. It was found that the bond optical reflectivities are less than 1% for fused silica samples and less than 10% for sapphire samples and they decrease over time. Bond refractive indices start from a value close to the refractive index of water and approach the refractive index of fused silica as the cure proceeds. Bond thicknesses cured at room temperature decrease over time plateauing at a more or less constant value, different for each case studied (about a few hundred nanometres), whereas bond thicknesses cured at high temperature seem to increase over time (less than about 400 nanometres).

Far-infrared observations have detected dusty star-forming galaxies, a subset of galaxies which is extremely dust-extincted from the ultraviolet down to near-infrared colours. Recent studies show that this population of sources contributes significantly to the history of star formation, especially out to very high redshift. Recent surveys with the Herschel Space Observatory have uncovered around half a million of these sources, with the largest of these surveys, the H-ATLAS, covering 616 square degrees. One of the most exciting discoveries is the lensing nature of the brightest of these sources, where the gravitational potential of a foreground galaxy lenses and amplifies the signal. The applications of gravitational lensing range from studying individual sources down to unprecidented resolution at high redshift in sub-mm wavelengths with ALMA, to cosmological studies by analysing the distribution of groups of lenses. In this thesis, I explore the effect of applying a more inclusive selection criterion for lensed sources, and study the properties of the sources that are selected. Whereas the first attempts at finding lensed sources use a strict S500μm > 100 mJy flux density cut, the sample I study is selected with a flux cut at 80 mJy: The Herschel Bright Sources (HerBS) sample. A photometric redshift cut of zphot > 2 is also taken, as most lensing takes place out at higher redshift. This redshift is calculated by fitting a spectral template to the 250, 350 and 500 μm observations from the Herschel SPIRE instrument. I push down the selection flux in order to select more lensed sources from the sub-mm surveys, whilst potentially including several unlensed sources. These unlensed sources could be among the most intrinsically luminous and star-forming objects in the Universe. Only less than five of such objects are known to exist, while our HerBS sample could contain up to 35 of these sources, which could teach us about the upper-limits of star-formation and their contribution to forming the most massive galaxies in the Universe. I use 850 μm SCUBA-2 observations on the James Clerk Maxwell Telescope (JCMT) to remove blazar interlopers, which results in 209 sources in the HerBS sample, after removing 14 blazar sources. At the time I wrote the paper upon which Chapter 2 is based, 24 sources had a spectroscopic redshift. I use this sub-sample to fit a two-temperature modified blackbody, and find a cold-body temperature of 21.3 K, a warm-body temperature of 45.8 K, a mass ratio of 26.7 and a dustemissivity index of 1.8. These values do not challenge the current knowledge of sub-mm galaxies, but the quality of the fit suggests a large diversity among the galaxies in the sub-sample, and that they are poorly fitted by a single template. This diversity is also found by the spectroscopic observations with the IRAM 30m-telescope observations on eight of the highest-redshift (zphot > 4) sources of the HerBS sample. We found five spectroscopic redshifts, with one of the sources at the highest known HerBS redshift at zspec = 4.8. The spectrum fitted in Chapter 2 shows a poor agreement with the photometric data points. The spatial resolution of the SPIRE instrument on Herschel is not fine enough to resolve the structure of these high-redshift sources. Worse still, the beam width is so large, ranging from 18 to 36 arcseconds, that it is unsure whether we observe a single galaxy, or perhaps observe multiple galaxies together. The beam width of the SCUBA-2 instrument at 850 μm is only 13 arcseconds. In the case the sample would be dominated by blended sources, one would expect to resolve several of the sources into their individual components. This is not seen in any of the continuum images, although the blended sources might be blended on scales smaller than 13 arcseconds. The IRAM-observations of two sources have detected multiple, contradicting spectral lines, suggesting we might be observing multiple sources, instead of a single source, that are aligned along the line-of sight. Unfortunately, only single spectral lines have been observed per source, and we are awaiting more observations verifying the blending nature of these sources, which are still expected to lie at high redshift. The hypothesis that our sample consists for a significant portion out of blended sources is in contradiction with multi-wavelength observations. When I look at the positions of these sources at different wavelengths, I find that most sources have a counterpart in these multi-wavelength observations, also when chance-encounters are considered. Considering the high redshift nature of our sources, together with the possibility of lensing, these counterpart sources are most likely foreground, lensing galaxies. I compare the positions of the HerBS sources to both the Sloan Digital Sky Survey (SDSS), which covers 121 out of the 209 sources, and the VISTA Kilo-Degree Infrared Galaxy (VIKING) survey, which covers 98 HerBS sources. For the SDSS counterparts, I use the H-ATLAS catalogue of counterpart sources, which was done by using a statistical estimator. This statistical estimator assumes a certain angular distribution between the sources in the Herschel position, and the opticalor near-infrared observations. I expect the majority of my sources to be lensed, and therefore I adjust the original angular distribution by including the effect of gravitational lensing. The adjustment is based on 15 ALMA observations of lensed, bright H-ATLAS sources. The revised analysis finds 41 counterparts, instead of the 31 that were found by the initial analysis. This catalogue is not available for VIKING counterparts, and therefore I had to do the entire analysis for the VIKING counterparts, starting from the VIKING fields. I use the sextractor package to extract the potential counterparts, and then derive the necessary estimators for the statistical method. I find a significantly different angular distribution, even than the one derived from the 15 ALMA observations of lensed H-ATLAS sources. The angular distribution extends to much larger angular scales, potentially suggesting a stronger contribution to galaxy-cluster lensing, which produces larger angular offsets due to the larger masses and different mass profiles associated with galaxy clusters. In total, I find 60 counterparts with a reliability greater than 80% to the 98 HerBS sources covered by VIKING. Possibly, not all counterparts could be positively identified, as the analysis showed 88% of sources has a source within 10 arcseconds when taking chance encounters into account. This is mostly due to ambiguity between several nearby sources, which causes a low reliability of the counterpart identification, but it does allow us to state that an counterpart could be present. A cosmological model suggest that 76% of our sources are gravitationally lensed. This model assumes a certain distribution of halo masses, and lensing magnification based on mass density profiles. The validity of these models has been shown with the 15 ALMA observations of lensed H-ATLAS sources, and also agree with the SMA observations from Bussmann et al. (2013). The IRAM observations provide me with both line luminosities and line velocity widths. Larger galaxies are expected to be brighter, and have larger line velocity widths. The five sources with confirmed redshift (and therefore line luminosity) have a luminosity-to-velocity width ratio agreeing with a magnification of around 10, when compared to unlensed, and known lensed sources. I show that the SDSS is not deep enough to observe all the foreground galaxies, while the VIKING observations agree with the results from the simulation, with 60 sources actually cross-compared, and 88% of sources have a source nearby, when accounting for random chance.

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Solar tornado-like prominences have been observed for over 90 years, but their true nature has recently been one of the most hotly debated aspects of prominence research. They have been linked to prominence eruptions, so understanding their stability and the plasma motions seen could provide a link between these dynamic features and the Sun-Earth space weather, which is important to fully understand in modern-day society. This thesis aims to answer some of the open questions on solar ‘tornadoes’, specifically on the plasma behaviour at different temperatures and the magnetic field structure of these apparently-rotating phenomena. Using a range of spectral diagnostic techniques and data from space-based and ground-based instruments, a more complete picture of solar tornadoes is built here. Optically thin emission at coronal temperatures (∼ 1.5 MK) has previously been shown to give anti-symmetric Doppler velocity patterns in a tornado, indicative of rotation. Using the same data set, from 14 September 2013, it has been possible to show that the Doppler pattern is visible in all spectral lines formed above 1 MK, but at lower plasma temperatures the pattern is not present. Electron densities are calculated from density-sensitive line pairs, and it is found that the electron density is lower in the tornado than the surrounding corona. Non-thermal line widths are calculated, showing that there is some additional broadening at the tornado compared to the surrounding corona, which could be due to a turbulent magnetic field component or the presence of unresolved Kelvin-Helmholtz instabilities at the tornado-corona boundary. The temperature structure along an observed line of sight is calculated using the technique of Differential Emission Measure, and this indicates that tornadoes are part of the larger prominence structure that is seen in some wavebands. A dedicated coordinated observation was designed to study tornadoes at lower plasma temperatures (< 1 MK), and to investigate their unknown magnetic structure. An observation of two tornadoes from 15 July 2014 is presented, from which the Mg II h and k lines and the magnetic field are analysed in detail. The optically thick Mg II lines, formed at chromospheric temperatures, show no velocity patterns similar to those seen at higher temperatures. The Mg II lines show a mix of reversed and non-reversed profiles in the prominence. This is the first report of strong central reversal of the h and k lines in a prominence. Comparing to a grid of isothermal isobaric Mg II models reveals that the large central reversals seen in the 15 July 2014 prominence indicates high optical thicknesses and pressures in the prominence slab. The magnetic field in the tornadoes on July has been measured using spectropolarimetry of the He I D3 line, which gives the magnetic field strength and orientation. Field strengths of up to 60 G are found in places, but the average field strength is around 20 − 30 G. The inclination of the magnetic field indicates that it is horizontal, parallel to the solar surface. These observations suggest that the tornado magnetic field is not twisted, but instead horizontal with plasma suspended in dips. An attempt has been made to find correlations between plasma parameters and the observed magnetic field parameters. No correlations are found, but this study has allowed a clearer, statistical investigation into the parameters available from this coordinated observation. These statistics are useful for comparing observations to models, in order to better understand the physical conditions that created the observed line profiles. Finally, this thesis contains an update to a radiative transfer prominence modelling code, PROM, to include calculations of the emergent intensities of Mg II lines. This step was taken to have the ability to freely explore models for larger ranges of model parameters than presented by previous authors, with the scope to investigate more complex (2D, 3D) multi-thread models. The output of the updated code is compared to the results of another Mg ii modelling code, finding good agreement in the recovered optical thickness, but integrated intensities are found to vary by 30−40% for some models. An extended grid of isothermal isobaric and PCTR models is then explored in order to understand the links between observable Mg II h and k line parameters and model parameters. A number of correlations are found, meaning that observed Mg II h and k lines can be used to identify physical parameters in a prominence. These models are compared to observations from 15 July 2014, finding that they can explain some of the observed line profiles, but more complex models are required to fully explain the observations.

This thesis is structured in two parts. In part 1 we summarise the necessary theoretical background and the numerical tools in order to conduct the research in part 2. In chapter 2 we summarise the 3 + 1 approach to numerical relativity, with a focus on the initial data formalism in the weighted transverse and conformal thin-sandwich decompositions. We then move on to discuss initial data for black hole simulations in chapter 3, where we focus on the moving puncture approach. We note that the standard gauge evolution equations force the initial numerical wormhole slices to evolve into trumpet slices, which suggests the construction of a priori trumpet initial data. We summarise the literature on trumpet research, with a focus on maximal Schwarzschild trumpet initial data in its analytical form. In chapter 4 we provide the necessary numerical tools and techniques, which we use in part 2 to solve the constraint equations numerically. We focus on finite difference methods in connection with the Thomas algorithm and successive over-relaxation to solve boundary value problems in one and two variables. Part 2 contains the novel research of this thesis. In chapter 5 we discuss Kerr in quasi-isotropic coordinates and point out that it represents a maximal trumpet foliation for extreme Kerr, however a wormhole foliation for slow Kerr. We lay out our approach to numerically derive maximal Kerr trumpet initial data. The approach is based on the proposition that two nontrivial impositions on the constraints suffice to construct the data numerically. We propose that these relations can be generalised from Schwarzschild and extreme Kerr to slow Kerr. The main motivation for this stems from the observation that the square of the extrinsic curvature for Bowen-York shows the same behaviour as for Kerr for small radii, and Bowen-York trumpets have been constructed successfully. Our main results are then presented in chapters 6 and 7 in which we test our approach for the special cases of zero and maximal spin, ie for Schwarzschild and extreme Kerr. We succeed with Schwarzschild and present the first ever purely numerical derivation of maximal Schwarzschild trumpet initial data in the weighted transverse decomposition – our first main result. Because of the complexity of the problem for extreme Kerr, we proceed in steps and start out by using more information of the analytical solution to treat the constraints separately. For instance, we provide the conformal metric to the Hamiltonian and momentum constraints, and solve them successfully for the trumpet solution – our second main result. Finally we elaborate on how to relax the assumptions. In particular, we introduce an additional equation which we can solve successfully for the function which describes the deviation of the conformal metric from being flat – our third main result.