A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock and existing numerical solutions to the GEM challenge magnetic reconnection problem. The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to maintaining small gauge errors based on error propagation is suggested.Comment: 40 pages, 18 figures

3-Body Problems, Hidden Constants, Trojans and WIMPs

This work includes two new results - principally two new constants of motion for the linearised restricted 3-body problem (e.g. for the Trojan asteroids) and an important isosceles triangle generalisation of Lagrange's equilateral triangle solution of the restricted case leading to hidden constants for Hildans as well as Trojans. Both of these results are classical, but we also have included new results on Newtonian quantum gravity emanating from the asymptotics relevant for WIMPish particles, explaining the origin of systems like that of the Trojans. The latter result uses a generalisation of our semi-classical mechanics for Schr\"odinger equations involving vector as well as scalar potentials, presented here for the first time, thereby providing an acid test of our ideas in predicting the quantum curvature and torsion of WIMPish trajectories for our astronomical elliptic states. The combined effect is to give a new celestial mechanics for WIMPs in gravitational systems as well as new results for classical problems. As we shall explain, we believe these results could help to see how spiral galaxies evolve into elliptical ones. A simple classical consequence of our isosceles triangle result gives a Keplerian type $4^{\textrm{th}}$ Law for 3-body problems. This is confined to the Appendix.Comment: 43 pages, no figure

Neurological conditions : an exploration of positive consequences

It appears that over time, individuals appraise challenging health situations differently; they take a variety of meanings from them and report differing outcomes for similar events (Scherer, Shorr, & Johnstone, 2001). This variability has been attributed to differences in coping processes employed by individuals. Chapter 1 is a critical review of the evidence for Positive Growth in Multiple Sclerosis (MS PG). Whilst MS PG is not reported by all individuals with the condition, evidence suggests that it is particularly evident in areas of psychosocial functioning and health benefits. Implications for future research and clinical practice are also discussed. The wide reaching implications which invariably arise as a result of neurological conditions affect people’s families as well as individuals, this can lead to re-appraisal of circumstances in family member’s themselves. Chapter 2 examines the implications a partner’s stroke has on a spouse’s own health and their desire to remain healthy. 8 females were interviewed using semi-structured interviews. Within this chapter a grounded theory model is proposed which describes barriers and facilitators to an individual’s health following their partner’s stroke. Within the results section the 3 main categories and 11 sub-categories are illustrated by participant quotes. Clinical implications, methodological limitations and directions for future research are outlined. The final chapter, a reflective account, introduces and reflects upon the research process using therapeutic letters. This chapter also explores the dual purpose of therapeutic letters and includes two letters; one to the research participants and one to the principal researcher. The usefulness of each letter is assessed in terms of the functions identified for therapeutic letters. Finally the author reflects and decides upon whether to send the letter to participants

The composite-tendency Robert–Asselin–Williams (RAW) filter in semi-implicit integrations

The time discretization in weather and climate models introduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leapfrog integrations from first-order to fifth-order. This improvement is achieved by replacing the Robert--Asselin filter with the RAW filter and using a linear combination of the unfiltered and filtered states to compute the tendency term. The purpose of the present paper is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model, and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leapfrog scheme is suitable for use in semi-implicit integrations

Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere

We present a significantly-improved data-driven global weather forecasting framework using a deep convolutional neural network (CNN) to forecast several basic atmospheric variables on a global grid. New developments in this framework include an offline volume-conservative mapping to a cubed-sphere grid, improvements to the CNN architecture, and the minimization of the loss function over multiple steps in a prediction sequence. The cubed-sphere remapping minimizes the distortion on the cube faces on which convolution operations are performed and provides natural boundary conditions for padding in the CNN. Our improved model produces weather forecasts that are indefinitely stable and produce realistic weather patterns at lead times of several weeks and longer. For short- to medium-range forecasting, our model significantly outperforms persistence, climatology, and a coarse-resolution dynamical numerical weather prediction (NWP) model. Unsurprisingly, our forecasts are worse than those from a high-resolution state-of-the-art operational NWP system. Our data-driven model is able to learn to forecast complex surface temperature patterns from few input atmospheric state variables. On annual time scales, our model produces a realistic seasonal cycle driven solely by the prescribed variation in top-of-atmosphere solar forcing. Although it is currently less accurate than operational weather forecasting models, our data-driven CNN executes much faster than those models, suggesting that machine learning could prove to be a valuable tool for large-ensemble forecasting.Comment: Manuscript submitted to Journal of Advances in Modeling Earth System

Non-hydrostatic effects on mountain wave breaking in directional shear flows

Mountain waves excited by narrow 3D orography are investigated using idealized numerical simulations of atmospheric flows with directional wind shear. The stability of these waves is compared with the stability of hydrostatic mountain waves. The focus is on understanding how wave breaking is modified via gravity wave-critical level interaction, when non-hydrostatic (dispersive) effects arise. The influence of nonhydrostatic effects on wave breaking appears to be a function of the intensity of the background shear, increasing the stability of the flow (inhibiting wave breaking) for weak wind shear, but decreasing it instead (enhancing wave breaking) for stronger wind shear

Genetic and molecular studies of skeletal muscle channelopathies

This thesis investigates the genetic and molecular aspects of the skeletal muscle channelopathies, in particular periodic paralysis. A genetic study was conducted to identify causative mutations in a cohort of patients who did not have a genetic diagnosis following routine diagnostic screening. Through screening of the coding regions of SCN4A 9 mutations were identified, 6 of which were novel. Additionally, exome sequencing in a PMC family identified 10 variants in 7 genes, although only three genes of interest: RYR-1, AGRN and COL6A3. However, further work is needed to confirm the variants found. Two SCN4A mutations identified in this thesis were studied in vitro using twoelectrode voltage clamp and patch clamp in Xenopus laevis oocytes and HEK-293 cells, respectively. D1420G is associated with a Hypo PP phenotype and is located within the S3 segment of DIV. No Hypo PP mutation has been associated with this region of the channel. D1420G was found to produce a gating pore current which is activated by negative voltages. This is the first Hypo PP mutation outside of the S4 voltage sensor to produce a gating pore current and support the notion that D1420G is a pathogenic mutation. R222Q was identified in a patient showing a myotonic phenotype. R222Q affects the S4 R2 gating charge of DI. A known Hypokalemic Periodic Paralysis mutation, R222W, affects the same residue. Both R222 mutations were compared in order to determine how two mutations affecting the same residue can cause different phenotypes. R222Q was found to cause a 16 mV hyperpolarizing shift in the voltage dependence of channel activation, which is consistent with a myotonic phenotype, whilst R222W had no effect. Both mutations were found to produce a gating pore current. This is the first time a myotonia related mutation has been found to cause a gating pore current

Aggregation of chemotactic organisms in a differential flow

We study the effect of advection on the aggregation and pattern formation in chemotactic systems described by Keller-Segel type models. The evolution of small perturbations is studied analytically in the linear regime complemented by numerical simulations. We show that a uniform differential flow can significantly alter the spatial structure and dynamics of the chemotactic system. The flow leads to the formation of anisotropic aggregates that move following the direction of the flow, even when the chemotactic organisms are not directly advected by the flow. Sufficiently strong advection can stop the aggregation and coarsening process that is then restricted to the direction perpendicular to the flow

The Divine Clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

We consider the Bohr correspondence limit of the Schrodinger wave function for an atomic elliptic state. We analyse this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Kelperian orbit for eccentricities greater than 1/\sqrt{2} which do not occur classically.Comment: 42 pages, 18 figures, with typos corrected, updated abstract and updated section 6.

Asperitas – a newly identified cloud supplementary feature

Cloud images obtained through a crowd-sourced international observing network suggest a cloud variety that has hitherto not been explicitly classified. This cloud feature shows a roughened base, which, under some solar illumination conditions, provides a particularly dramatic appearance. The growing body of photographic observations have led the World Meteorological Organisation to consider adding ‘asperitas’ to the 2017 edition of the International Cloud Atlas as a new form of supplementary cloud feature. We compare reported sightings with available meteorological data to investigate the conditions that give rise to this newly recognised cloud description