A Self-Consistent Marginally Stable State for Parallel Ion Cyclotron Waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, {\omega} (k), smoothly rises from the usual MHD behavior at small |k| to reach {\omega} = {\Omega}p as k \rightarrow \pm\infty. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple "box function", we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the v\bot direction. The threshold anisotropy for generation of ion cyclotron waves is also larger than that given by estimates which assume bi-Maxwellian proton distributions.Comment: in press in Physics of Plasma

Analysis of trends and causes of death in SLE patients over a 40-years period in a cohort of patients in the United Kingdom

BACKGROUND: Systemic Lupus Erythematosus (SLE) an autoimmune rheumatic disease with a complex pathogenesis, remains potentially life-threatening. SLE patients have increased morbidity and premature mortality compared to non-SLE patients. The five-year survival rate has improved from 90% in the 1980s. Lupus patients still have a mortality risk three times that of the general population. OBJECTIVES: To provide a detailed analysis of the causes of death, main characteristics and trends in the management of the deceased SLE patients from the lupus clinic at the University College London Hospital (UCLH); during the past four decades. METHODS: This was a non-interventional, retrospective study based on historical real-world data from paper and electronic records of patients followed up at UCLH. The analysis focused on data collected between 1st January 1978 and 31th December 2018. We collected the: causes of death, duration of disease, key laboratory and clinical parameters and the treatment received. We compared the results from the four decades to ascertain trends in the causes of mortality. All statistical analyses were performed using the Statistical Package for Social Sciences (SPSS), version 22.0. The 95% confidence intervals for the means of data were calculated. RESULTS: 111 SLE patients (15%), died during follow-up. Their median age was 51 years (interquartile range (IQR) = 38-63 years) and the median duration of disease, 15 years (IQR = 8.5-24 years). The main causes of death in the past 40 years were infection (31.7%), cancer (26.7%) and cardiovascular disease (CVD) (21.8%). 93.6% of these patients were immunosupressed. During the 40-year period, there were several therapeutic developments notably the introduction of mycophenolate mofetil (MMF) and rituximab; the latter initially only given to patients when more conventional inmunosupressants had failed, but more recently offered to patients at diagnosis. There was a statistically significant increase in the use of hydroxycloroquine (HCQ), MMF and rituximab. In contrast, the use of Azathioprine (AZA) and steroids, hardly changed over time. CONCLUSIONS: This retrospective review shows how epidemiological factors, causes of death and treatment of SLE patients have changed during the last 40 years in the UCLH cohort

Resonant Interactions Between Protons and Oblique Alfv\'en/Ion-Cyclotron Waves

Resonant interactions between ions and Alfv\'en/ion-cyclotron (A/IC) waves may play an important role in the heating and acceleration of the fast solar wind. Although such interactions have been studied extensively for "parallel" waves, whose wave vectors ${\bf k}$ are aligned with the background magnetic field ${\bf B}_0$, much less is known about interactions between ions and oblique A/IC waves, for which the angle $\theta$ between ${\bf k}$ and ${\bf B}_0$ is nonzero. In this paper, we present new numerical results on resonant cyclotron interactions between protons and oblique A/IC waves in collisionless low-beta plasmas such as the solar corona. We find that if some mechanism generates oblique high-frequency A/IC waves, then these waves initially modify the proton distribution function in such a way that it becomes unstable to parallel waves. Parallel waves are then amplified to the point that they dominate the wave energy at the large parallel wave numbers at which the waves resonate with the particles. Pitch-angle scattering by these waves then causes the plasma to evolve towards a state in which the proton distribution is constant along a particular set of nested "scattering surfaces" in velocity space, whose shapes have been calculated previously. As the distribution function approaches this state, the imaginary part of the frequency of parallel A/IC waves drops continuously towards zero, but oblique waves continue to undergo cyclotron damping while simultaneously causing protons to diffuse across these kinetic shells to higher energies. We conclude that oblique A/IC waves can be more effective at heating protons than parallel A/IC waves, because for oblique waves the plasma does not relax towards a state in which proton damping of oblique A/IC waves ceases

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit

A rigidity theorem for nonvacuum initial data

In this note we prove a theorem on non-vacuum initial data for general relativity. The result presents a ``rigidity phenomenon'' for the extrinsic curvature, caused by the non-positive scalar curvature. More precisely, we state that in the case of asymptotically flat non-vacuum initial data if the metric has everywhere non-positive scalar curvature then the extrinsic curvature cannot be compactly supported.Comment: This is an extended and published version: LaTex, 10 pages, no figure

TURBULENT HEATING OF THE DISTANT SOLAR WIND BY INTERSTELLAR PICKUP PROTONS IN A DECELERATING FLOW

Previous models of solar wind heating by interstellar pickup proton-driven turbulence have assumed that the wind speed is a constant in heliocentric radial position. However, the same pickup process, which is taken to provide the turbulent energy, must also decelerate the wind. In this paper, we extend our phenomenological turbulence model to include variable wind speed, and then incorporate the deceleration due to interstellar pickup protons into the model. We compare the model results with plasma and field data from Voyager 2, taking this opportunity to present an extended and improved data set of proton core temperature, magnetic field fluctuation intensity, and correlation length along the Voyager trajectory. A particular motivation for including the solar wind deceleration in this model is the expectation that a slower wind would reduce the resulting proton core temperature in the region beyond ~60 AU, where the previous model predictions were higher than the observed values. However, we find instead that the deceleration of the steady-state wind increases the energy input to the turbulence, causing even higher temperatures in that region. The increased heating is shown to result from the larger values of the ratio of Alfven speed to solar wind speed that develop in the decelerating wind.Jet Propulsion Laboratory (U.S.) (NASA contract 959203)United States. National Aeronautics and Space Administration (NASA grant NNX08A147G)United States. National Aeronautics and Space Administration (NASA Guest Investigator grant NNX07AH75G)United States. National Aeronautics and Space Administration (NASA Guest Investigator grant NNX08AJ19G

Fuchsian methods and spacetime singularities

Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian equations have been recalled, various ways in which these equations have been applied in general relativity are described. Possible future applications are indicated