On a vector-valued generalisation of viscosity solutions for general PDE systems

We propose a theory of non-differentiable solutions which applies to fully nonlinear PDE systems and extends the theory of viscosity solutions of Crandall-Ishii-Lions to the vectorial case. Our key ingredient is the discovery of a notion of extremum for maps which extends min-max and allows "nonlinear passage of derivatives" to test maps. This new PDE approach supports certain stability and convergence results, preserving some basic features of the scalar viscosity counterpart. In this first part of our two-part work we introduce and study the rudiments of this theory, leaving applications for the second part.Comment: 34 pages, 6 figure

N-body simulations of stars escaping from the Orion nebula

We study the dynamical interaction in which the two single runaway stars AE Aurigae and mu Columbae and the binary iota Orionis acquired their unusually high space velocity. The two single runaways move in almost opposite directions with a velocity greater than 100 km/s away from the Trapezium cluster. The star iota Ori is an eccentric (e=0.8) binary moving with a velocity of about 10 km/s at almost right angles with respect to the two single stars. The kinematic properties of the system suggest that a strong dynamical encounter occurred in the Trapezium cluster about 2.5 Myr ago. Curiously enough, the two binary components have similar spectral type but very different masses, indicating that their ages must be quite different. This observation leads to the hypothesis that an exchange interaction occurred in which an older star was swapped into the original iota Orionis binary. We test this hypothesis by a combination of numerical and theoretical techniques, using N-body simulations to constrain the dynamical encounter, binary evolution calculations to constrain the high orbital eccentricity of iota Orionis and stellar evolution calculations to constrain the age discrepancy of the two binary components. We find that an encounter between two low eccentricity (0.4<e<0.6) binaries with comparable binding energy, leading to an exchange and the ionization of the wider binary, provides a reasonable solution to this problem.Comment: 14 pages, 13 figures, 5 tables, accepted for publication in MNRA

Comparing the effects of sun exposure and vitamin D supplementation on vitamin D insufficiency, and immune and cardio-metabolic function: the Sun Exposure and Vitamin D Supplementation (SEDS) Study

BACKGROUND Adults living in the sunny Australian climate are at high risk of skin cancer, but vitamin D deficiency (defined here as a serum 25-hydroxyvitamin D (25(OH)D) concentration of less than 50 nmol/L) is also common. Vitamin D deficiency may be a risk factor for a range of diseases. However, the optimal strategies to achieve and maintain vitamin D adequacy (sun exposure, vitamin D supplementation or both), and whether sun exposure itself has benefits over and above initiating synthesis of vitamin D, remain unclear. The Sun Exposure and Vitamin D Supplementation (SEDS) Study aims to compare the effectiveness of sun exposure and vitamin D supplementation for the management of vitamin D insufficiency, and to test whether these management strategies differentially affect markers of immune and cardio-metabolic function. METHODS/DESIGN The SEDS Study is a multi-centre, randomised controlled trial of two different daily doses of vitamin D supplementation, and placebo, in conjunction with guidance on two different patterns of sun exposure. Participants recruited from across Australia are aged 18-64 years and have a recent vitamin D test result showing a serum 25(OH)D level of 40-60 nmol/L. DISCUSSION This paper discusses the rationale behind the study design, and considers the challenges but necessity of data collection within a non-institutionalised adult population, in order to address the study aims. We also discuss the challenges of participant recruitment and retention, ongoing engagement of referring medical practitioners and address issues of compliance and participant retention. TRIAL REGISTRATION Australia New Zealand Clinical Trials Registry: ACTRN12613000290796 Registered 14 March 2013

On the phase structure of five-dimensional SU(2) gauge theories with anisotropic couplings

The phase diagram of five-dimensional SU(2) gauge theories is explored using Monte Carlo simulations of the theory discretized on a Euclidean lattice using the Wilson plaquette action and periodic boundary conditions. We simulate anisotropic gauge couplings which correspond to different lattice spacings a_4 in the four dimensions and a_5 along the extra dimension. In particular we study the case where a_5>a_4. We identify a line of first order phase transitions which separate the confined from the deconfined phase. We perform simulations in large volume at the bulk phase transition staying in the confined vacuum. The static potential measured in the hyperplanes orthogonal to the extra dimension hint at dimensional reduction. We also locate and analyze second order phase transitions related to breaking of the center along one direction.Comment: 28 pages, 22 figures, 4 tables; few explanations and references added; version accepted for publication in Nucl. Phys.

A Quintessential Axion

The model independent axion of string theory has a decay constant of order of the Planck scale. We explore the properties of this quintessence candidate (quintaxion) in the scheme of hidden sector supergravity breakdown. In models allowing for a reasonable $\mu$ term, the hidden sector dynamics may lead to an almost flat potential responsible for the vacuum energy of $(0.003 {\rm eV})^4$. A solution to the strong CP-problem is provided by an additional hidden sector pseudoscalar (QCD axion) with properties that make it an acceptable candidate for cold dark matter of the universe.Comment: 11 pages, Revtex, 1 figur

Fixed points of quantum gravity in extra dimensions

We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low-scale gravity and compact extra dimensions.Comment: Wording sharpened, refs added, to appear in PL

The Antarctic ozone hole during 2015 and 2016

We reviewed the 2015 and 2016 Antarctic ozone holes, making use of a variety of ground-based and spacebased measurements of ozone and ultraviolet radiation, supplemented by meteorological reanalyses. The ozone hole of 2015 was one of the most severe on record with respect to maximum area and integrated deficit and was notably longlasting, with many values above previous extremes in October, November and December. In contrast, all assessed metrics for the 2016 ozone hole were at or below their median values for the 37 ozone holes since 1979 for which adequate satellite observations exist. The 2015 ozone hole was influenced both by very cold conditions and enhanced ozone depletion caused by stratospheric aerosol resulting from the April 2015 volcanic eruption of Calbuco (Chile)

The Antarctic ozone hole during 2014

We review the 2014 Antarctic ozone hole, making use of a variety of ground-based and space-based measurements of ozone and ultra-violet radiation, supplemented by meteorological reanalyses. Although the polar vortex was relatively stable in 2014 and persisted some weeks longer into November than was the case in 2012 or 2013, the vortex temperature was close to the long-term mean in September and October with modest warming events occurring in both months, preventing severe depletion from taking place. Of the seven metrics reported here, all were close to their respective median values of the 1979–2014 record, being ranked between 16th and 21st of the 35 years for which adequate satellite observations exist

On the interaction of microquasar jets with stellar winds

Strong interactions between jets and stellar winds at binary system spatial scales could occur in high-mass microquasars. We study here, mainly from a dynamical but also a radiative point of view, the collision between a dense stellar wind and a mildly relativistic hydrodynamical jet of supersonic nature.}{We have performed numerical 2-dimensional simulations of jets, with cylindrical and planar (slab) symmetry, crossing the stellar wind material. From the results of the simulations, we derive estimates of the particle acceleration efficiency, using first order Fermi acceleration theory, and give some insight on the possible radiative outcomes. We find that, during jet launching, the jet head generates a strong shock in the wind. During and after this process, strong recollimation shocks can occur due to the initial overpressure of the jet with its environment. The conditions in all these shocks are convenient to accelerate particles up to $\sim$ TeV energies, which can lead to leptonic (synchrotron and inverse Compton) and hadronic (proton-proton) radiation. In principle, the cylindrical jet simulations show that the jet is stable, and can escape from the system even for relatively low power. However, when accounting for the wind ram pressure, the jet can be bent and disrupted for power \la 10^{36} erg s$^{-1}$.Comment: Accepted for publication in Astronomy & Astrophysic