The inner regions of discs around close binary systems are dominated by tidally truncated eccentric cavities. These are believed to play a key role in dictating where planets formed in these circumbinary discs halt their disc-driven migration. In this thesis we present work examining processes which could impact the evolution and structure of this region, and the planets which interact with it. First, we investigate the role of self-gravity and disc-mass on circumbinary discs and planets. The greatest impact of self-gravity was found in discs around highly eccentric binaries, and in discs with high masses. In these cases, self-gravity acts to compact the scale of the inner cavity region. For the highest disc masses, additional eccentric features arise in the outer disc. A range of scenarios examining planetary migration, accretion and disc dissipation find that if planets form and evolve in a high-mass environment, the disc structures formed by self-gravity can leave a fingerprint on the planetary architecture once the disc has dissipated. We also significantly modify the publicly available fargo-adsg hydrodynamical code, to include radiative effects such as disc irradiation by the binary stars, radiative transport and disc surface cooling. We present preliminary results of simulations of adiabatic circumbinary discs with these effects included, and consider also the migration of protoplanets within them. Fully radiative discs produce a smaller inner cavity than obtained in previous isothermal models - a promising result for the end point of planet migration in these discs. Whilst we have found significant alteration of the circumbinary enviroment by self-gravity and radiative effects, future simulations that capture the 3-D nature of these discs will be required to fully describe the observed architecture of the circumbinary systems.

Static Whirling Rods: Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This thesis shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady state equations of whirling rods are formulated in Lagrangian coordinates. Due to the non-linear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is a close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities”. This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived. Dynamic Rotating Annuli: In-plane modes of vibration of annular plates are investigated. Two different models of equations one from Bhuta and Jones and the other from Biezeno and Grammel that govern the rotational motions of annuli will be studied. Since Biezeno and Grammel’s model was originally derived in Eulrian coordinates, their model will be transformed to the Lagrangian coordinates for the purpose of comparison with Bhuta and Jones’ model. / The solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the annulus while it is in rotation. Exact and approximate solutions are obtained for the Bhuta and Jones’ model, where the approximate solutions on in-plane displacements and natural frequencies are acquired by ignoring the Coriolis effect. A proposed numerical scheme is implemented to solve the governing equations coupled with radial and circumferential displacements. Uniqueness of solutions will be mentioned although it will not be rigorously derived because it is out of the scope of this thesis. Approximate analytical results show that both radial and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing. The exact and numerical results on both models that take the Coriolis effect into account show that radial natural frequencies are increasing and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing.

Observations of gravitationally microlensed quasars offer a unique opportunity to probe quasar structure on extremely small scales. In this thesis, we conduct extensive microlensing simulations and compare with observational data to constrain quasar accretion discs, and conduct preliminary probes of broad emission line region structure. This analysis is done using a new single-epoch imaging technique that requires very little telescope time, and yet produces results that are comparable to those obtained from long-term monitoring campaigns. / We begin by exploring the impact of variable smooth matter percentage and source size on microlensing simulations. Adding a smooth matter component affects minimum and saddle point images differently, broadening the magnification distribution for the saddle point image significantly. However, increasing the radius of the background source washes out this difference. The observation of suppressed saddle point images can therefore only be explained by microlensing with a smooth matter component if the background source is sufficiently small. We use these simulations, in combination with I-band imaging of the lensed quasar MG 0414+0534 to constrain the radius of the quasar source. This demonstrates the viability of a single-epoch imaging method for constraining quasar structure. / This technique is then expanded to single-epoch multi-band observations, in order to constrain the radial profile of quasar accretion discs as a function of observed wavelength. We present new Magellan observations of two gravitationally lensed quasars: MG 0414+0534 and SDSS J0924+0219. We also analyse two epochs of Q2237+0305 data obtained from the literature. Our results are compared with four fidicial accretion disc models. At the 95 per cent level, only SDSS J0924+0219 is inconsistent with any of the accretion disc models. When we combine the results from all three quasars -- a first step towards assembling a statistical sample -- we find that the two steepest accretion disc models are ruled out with 68 per cent confidence. / In addition, we are also able to use our microlensing simulations to constrain the smooth matter percentages in the lenses at the image positions. In both MG 0414+0534 and SDSS J0924+0219 we find smooth matter percentages that are inconsistent with zero. A smooth matter percentage of approximately 50 per cent is preferred in MG 0414+0534, and approximately 80 per cent in SDSS J0924+0219. Q2237+0305 is usually assumed to have a smooth matter percentage of zero at the image positions, as they lie in the bulge of the lensing galaxy. Though our measurement is consistent with a zero smooth matter percentage, there is a peak in the probability distribution at a value 20 per cent. This is perhaps a hint of additional intervening structures along the line of sight to the background quasar. / We test the sensitivity of our accretion disc constraints to a range of modelling parameters. These include errors in lens modelling, Bayesian prior probability selection, errors in observational data, and the microlens mass function. Constraints on the power-law index relating source radius to observed wavelength are found to be relatively unaffected by changes in the modelling parameters. Constraints on source radii are found to be more strongly affected. / Finally, the broad emission line region of Q2237+0305 is examined. Gemini IFU observations are presented clearly showing differential microlensing across the velocity profile of the CIII] emission line. To analyse this signature, we present three simple broad emission line region models: a biconical outflow, a Keplerian disc, and spherical infall. A method is developed to compare the shapes of simulated flux ratio spectra with the observed spectrum. We are unable to discriminate between the biconical outflow and Keplerian disc models when we average over all viewing angles and orientations. The spherical infall model, however, does not fit the observed data. We also find that for the non-spherically symmetric geometries, low inclination angles are essentially incompatible with the observations. This analysis offers hope that with sufficiently high signal-to-noise observations, differential microlensing signatures may allow us to constrain the geometry and kinematics of this poorly understood portion of quasar structure.

No description available.

This paper is a small remark on the analyticity of a limit of analytic sets in a particular case: when the sets are complex discs.

In this thesis, I discuss two studies concerned with modelling protoplanetary discs around stars from different ends of the stellar mass range. In Chapters 1 and 2, I give an introduction to the field of protoplanetary discs, both from an observational and a modelling point of view, and describe the radiative transfer methods I have employed. In Chapter 3, I present my work regarding the disc around the Herbig Ae star HD 163296. I show the results of applying a new modelling technique to this disc: I combine SED modelling with fits to the CO snowline location and C$^$O $J=2-1$ line profile from ALMA. I find that all of the modelling steps are crucial to break degeneracies in the disc parameter space. The use of all of these constraints favours a solution with a notably low gas-to-dust ratio ($g/d < 20$). The only models with a more interstellar medium (ISM)-like $g/d$ require C$^$O to be underabundant with respect to the ISM abundances and a significant depletion of sub-micron grains, which is not supported by scattered light observations. I propose that the technique can be applied to a range of discs and opens up the prospect of being able to measure disc dust and gas budgets without making assumptions about the $g/d$ ratio. In Chapter 4, I present my work on characterising the disc around the very low mass star V410 X-ray 1. Protoplanetary discs around such low mass stars offer some of the best prospects for forming Earth-sized planets in their habitable zones. The SED of V410 X-ray 1 is indicative of an optically thick and very truncated dust disc, with my modelling suggesting an outer radius of only 0.6 au. I investigate two scenarios that could lead to such a truncation, and find that the observed SED is compatible with both. The first scenario involves the truncation of both the dust and gas in the disc, perhaps due to a previous dynamical interaction or the presence of an undetected companion. The second scenario involves the fact that a radial location of 0.6 au is close to the expected location of the H$_2$O snowline in the disc. As such, a combination of efficient dust growth, radial migration, and subsequent fragmentation within the snowline leads to an optically thick inner dust disc and larger, optically thin outer dust disc. I find that a firm measurement of the CO $J=2-1$ line flux would distinguish between these two scenarios by enabling a measurement of the radial extent of gas in the disc. Many models I consider contain at least several Earth-masses of dust interior to 0.6 au, suggesting that V410 X-ray 1 could be a precursor to a system of tightly-packed inner planets, such as TRAPPIST-1. In Chapter 5, I summarise the work presented in this thesis, give an overview of future applications of the methods outlined in this dissertation, and an outlook on potential future projects.

Stars of all ages and evolutionary stages are seen to be surrounded by discs of matieral. during the formation of a stellar system the stars are orbited by a massive protoplanetary disc composed of interstellar gas and dust, in which planet formation occurs. Betewwen 1 and 10 Myr the protoplanetary disc disperses, leaving behind the newly formed system of planets and smaller bodies. The remaining material which has not formed into planets is referred to as a debris disc. Even though the interstellar dust grains from the protoplanetary disc have long been removed from the system, debris discs can contain large quantities of dust due to collisions between larger bodies and cometary activity. such dust can be detected by its thermal emission. This thesis focuses on observational studies at far-infrared and sub-millimetre wavelengths of debris discs and the late stages of protoplanetary disc evolution. An overview of surveys for debris discs performed to date is presented, highlighting the limitations and statistical biases. the motivation, design and sample selection for two large surveys for debris discs around nearby stars, with the Hershel space observatory and the SCUBA-2 sub-millimetre camera on the James Clerk Maxwell Telescope, are described. The combination of a uniform obstevational strategy, longer wavelengths than previous surveys, and a large, clearly chosen sample - unbiased by stellar properties - will allow robust statistical conclusions of how the incidence and properties of debris discs depend on system parameters such as stellar mass, age, metallicity, binarity and the presence of planets. As a precursor to the Hershel and SCUBA-2 surveys, a volume-limited ample of 130 A type star systems was surveyed using observations at 24 and 70 μm, which were required to determine the presence of emission from dust, were predicted by fitting model flux distributions to optical and near-infrared photometry. Debris discs were detected around 46 systems, 12 of which including the system with the largest dust mass - are new discoveries. This survey adds to the results of previous studies which show that debris disc incidence is not correleated with host star metallicity despite the wll known giant planet - metallicity correlation, This is in accordance with what is predicted from the core accretion theory of planet formation. The most signigicant result from this survey is that, contrary to results reported in a previous work, debris discs are oberall less common around binary stars. Further investigation shows that systems with separations of ~3-150 AU are especially deficient of debris, while closer binaries and the primaries of wider binaries show debris detection rates consisten with those for single stars. A sample of circumstellar discs around 29 young stellar systems with ages of 5-30 Myr were observed with the LABOCA sub-millimetre instrument on the APEX telescope at 870μm, to provide disc masses or mass upper limits in support of a large Hershel programme. These targets included the η Chamaeleontis cluster and four bright Herbig Ae/Be stars which have not previously been observed at this wavelength. All but the Herbig Ae/Be stars were not detected, and 3σ dust mass upper limits of ~ 0.1-3 M are determined, with corresponding total disc masses of ~0.03-1Mjup. These mass limits indicate that there is insufficient remaining material in these discs to form gas giant planets, and add to the prevailing view that protoplanetary discs typically disperse within 10 Myr and that gas giant planet formation must be completed before this time. A search for cold dust emimission from two of the Solar System's nearest neighbours - α Centauri AB and ε Indi - was also performed with LABOCA. In both cases no debris disc emission was detected. A bright resolved feature was detected near α Centauri AB, nowever, follow-up observations at a second epoch, two years after the initial observations, showed that the feature is not co-moving with the stars. It is argued that the feature is most likely a pre-stellar core. The stars α Centauri A and B are detected, which is one of only very few detections of main sequence stellar photospheres at sub-millimetre wavelengths.

The study of dynamics and performance of flying discs is motivated by how variations in their design features influence the aerodynamic characteristics and flight performance, particularly range. Reviews in the literature focus on the development of fundamental research in flying discs and on the performance of sports projectiles. Theoretical background on disc dynamics, range and sensitivity are given. This work investigates disc aerodynamics by performing wind tunnel experiments to measure aerodynamic loads on a set of generic parametric discs and a set of commercial golf discs. The parametric discs isolate various geometrical features such as thicknesses, cavities, leading edge curvatures and cambers to study the influence of these parameters on aerodynamic characteristics. The commercial golf discs consist of three different categories known as putter, mid-range and driver: these discs are used for short, medium and long flight range, respectively. To study the performance, aerodynamic data of the golf discs are used as inputs in numerical simulations to predict their flight trajectories and range. Effects of launch attitude on range are assessed to study the optimal initial launch conditions to achieve maximum range. Further, the simulation provides a direct approach to analyse range sensitivity on launch parameters. Results from the experiments show a number of significant findings on disc geometry. First, a cavity is fundamentally important for a disc to have satisfactory flying qualities: the presence of the cavity produces a significant aft shift in the aerodynamic position to minimize the pitching moment about the centre of the disc. Hence, the disc will have a minimal tendency to roll about the flight axis. Second, the thickness of a disc has a significant effect on its profile drag: increasing the thickness increases the profile drag. Third, a disc with a positive camber produces a relatively higher lift-to-drag ratio (CL/CD) compared to one with no camber. Fourth, the effect of tapering a flat leading or trailing edge of a disc leads to a reduction in its lift (within the angles of attack tested in the study) with a significant reduction in its drag. Fifth, it is shown that peak lift-to-drag ratio of a free flying disc is not necessarily a good indicator of performance because the angle of attack (and hence, lift-to-drag ratio) varies widely through a typical flight. Furthermore, a disc with a significant pitching moment will roll significantly about the flight path direction, further reducing the achievable range for a given lift or drag characteristic. Finally, a novel method to quantify disc sensitivity with respect to changes in launch conditions has been developed. The simulations show that the range sensitivity of each disc with respect to launch pitch angle varies significantly, with discs design for long range being much more sensitive (and therefore harder to throw accurately) than discs designed for short range.

In this thesis, an assessment is made of the value of optical CMDs as a useful diagnostic of the accretion properties of young stars. An analysis has been made of the phenomena that we observe and their effect on the position of stars in the CMD. Limitations and potential biases have been identified and evaluated. Variability causes some luminosity spread at a given colour in optical CMDs. A detailed characterisation of variability has been performed which places strong constraints on the magnitudes and the timescales on which the variability is seen. On timescales 15 minutes, almost no variability is detected (at levels greater than ≈ 0.2%) in the i band for a sample of ≈ 700 disc-bearing young stellar objects (YSOs). This suggests that the variability predicted by some accretion shock models is either very weak or not present. On hours to days timescales the optical variability in most stars is well described by a simple power law. The amplitude of the variability, a ∝ f−k, where f is the frequency of the variability in days. Disc-bearing and discless YSOs exhibit median values of k of 0.85 ± 0.02 and 0.95 ± 0.03 respectively, the uncertainity being the error on the median. The power law is valid up to a certain timescale (tmax) at which point the variability amplitude does not increase any further. tmax is found to be 1.50 ± 0.07 days and 1.41 ± 0.10 days for disc-bearing and discless stars respectively. Disc-bearing stars show greater variability amplitudes than the discless stars. However, it is notable that the variability timescale and power spectrum exponent are remarkably similar. This implies that the amplitude of the variability is driven by the physics of the underlying process, but that the timescales are instead driven by geometric effects. For disc-bearing stars, the highest amplitude variables are the accreting stars, which often appear to vary in the CMD along lines that correspond to changes in accretion luminosity. Four disc-bearing stars (approximately 0.5% of the disc-bearing sample) in Cep OB3b show extreme variability on timescales of years. Three (possible EXor candidates), show long-timescale changes that have a dramatic effect on their CMD position. However their small numbers mean that the overall impact on the CMDs of young associations is small. Variability on timescales of the rotational period and shorter adds uncertainty to age estimates of individual stars that are calculated by comparison with PMS models. Having provided a detailed description of variability and its impact on the CMD, it is clear that there are further significant mechanisms that affect the positions of YSOs in the CMD. I show that the spread in luminosity seen in the Orion Nebula Cluster and NGC 2264 could not be explained by accretion at rates of M ̇ ≥ 5 × 10−4 M⊙ yr−1 occurring within the protostellar phase of YSO evolution. Thus it appears that CMDs are not a useful diagnostic for study of the accretion histories of YSOs. The wavelength dependence of the extinction by dust within the inner regions of YSO discs is shown to differ from that seen in the ISM. Typically the wavelength dependence of the extinction is given by RV ≈5-8, compared with the value of RV ≈3.1 typical of the ISM. The interpretation is that grain growth has occurred. The location of this material within the ‘snow line’ implies that grains have coalesced rather than simply gaining an ice mantle. This is evidence for the beginning of planet formation. The effect of the high value of RV on the CMD is to add additional uncertainty of 0.1 mag to photometric measurements that have been corrected for the effects of extinction. Accretion luminosity is shown to be the dominant signal in the luminosity spread seen in CMDs of young associations. Stars which exhibit excess flux in the U band or Hα are displaced in CMD space. The accretion vector is shown to be a significant blueward shift in colour accompa- nied by a modest brightening in the g, g − i CMD. Accretion results in a luminosity spread as stars are displaced blueward below the PMS locus. This effect is not seen in non-accreting disc-bearing stars. Examination of the underlying excess luminosity spectrum for 15 accreting stars shows that the colour of the emission excess is not consistent across the sample. Thus to quantify the effect of accretion luminosity on CMD positions for individual stars, moderate resolution spectra are required with a large range in wavelength. This accretion luminosity may systematically bias estimates of PMS ages. A simple mitigation is to exclude accreting stars from age analysis. U band and Hα flux excesses are shown to vary independently by ≈ 1 dex on timescales shorter than the rotation period of the star. The relation between U band flux excess and veiling at 7000Å also appears to be variable. This implies that single epoch measurements of these parameters will add an uncertainty of ≈ 1 dex on accretion rates derived from them. Accretion rates derived from either U or Hα excess should be calculated from a mean of several photometric measurements, separated by significant fractions of the rotation period of the star. In most stars, the veiling at 7000Å is shown not to be a good measure for the calculation of the accretion rate. Despite providing a detailed characterisation of phenomena that influence the positions of YSOs in the CMD, there exists some residual luminosity spread at a given Teff that cannot be explained by variability on any timescale, extinction uncertainties or accretion luminosity. This residual spread should provide an opportunity to study an as-yet uncharacterised aspect of young stars.

The circumnuclear disc (CND) orbiting the Galaxy's central black hole is a reservoir of material that can ultimately provide energy through accretion, or form stars in the presence of the black hole, as evidenced by the stellar cluster that is presently located at the CND's centre. In this paper, we report the results of a computational study of the dynamics of the CND. The results lead us to question two paradigms that are prevalent in previous research on the Galactic Centre. The first is that the disc's inner cavity is maintained by the interaction of the central stellar cluster's strong winds with the disc's inner rim, and secondly, that the presence of unstable clumps in the disc implies that the CND is a transient feature. Our simulations show that, in the absence of a magnetic field, the interaction of the wind with the inner disc rim actually leads to a filling of the inner cavity within a few orbital time-scales, contrary to previous expectations. However, including the effects of magnetic fields stabilizes the inner disc rim against rapid inward migration. Furthermore, this interaction causes instabilities that continuously create clumps that are individually unstable against tidal shearing. Thus the occurrence of such unstable clumps does not necessarily mean that the disc is itself a transient phenomenon. The next steps in this investigation are to explore the effect of the magnetorotational instability on the disc evolution and to test whether the results presented here persist for longer time-scales than those considered here.