Regularity estimates up to the boundary for elliptic systems of difference equations

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations

Orbital parameters, chemical composition, and magnetic field of the Ap binary HD 98088

HD 98088 is a synchronised, double-lined spectroscopic binary system with a magnetic Ap primary component and an Am secondary component. We study this rare system using high-resolution MuSiCoS spectropolarimetric data, to gain insight into the effect of binarity on the origin of stellar magnetism and the formation of chemical peculiarities in A-type stars. Using a new collection of 29 high-resolution Stokes VQU spectra we re-derive the orbital and stellar physical parameters and conduct the first disentangling of spectroscopic observations of the system to conduct spectral analysis of the individual stellar components. From this analysis we determine the projected rotational velocities of the stars and conduct a detailed chemical abundance analysis of each component using both the SYNTH3 and ZEEMAN spectrum synthesis codes. The surface abundances of the primary component are typical of a cool Ap star, while those of the secondary component are typical of an Am star. We present the first magnetic analysis of both components using modern data. Using Least-Squares Deconvolution, we extract the longitudinal magnetic field strength of the primary component, which is observed to vary between +1170 and -920 G with a period consistent with the orbital period. There is no field detected in the secondary component. The magnetic field in the primary is predominantly dipolar, with the positive pole oriented approximately towards the secondary.Comment: Accepted for publication by MNRAS, 17 pages, 12 figure

Magnetic field, chemical composition and line profile variability of the peculiar eclipsing binary star AR Aur

AR Aur is the only eclipsing binary known to contain a HgMn star, making it an ideal case for a detailed study of the HgMn phenomenon. HgMn stars are a poorly understood class of chemically peculiar stars, which have traditionally been thought not to possess significant magnetic fields. However, the recent discovery of line profile variability in some HgMn stars, apparently attributable to surface abundance patches, has brought this belief into question. In this paper we investigate the chemical abundances, line profile variability, and magnetic field of the primary and secondary of the AR Aur system, using a series of high resolution spectropolarimetric observations. We find the primary is indeed a HgMn star, and present the most precise abundances yet determined for this star. We find the secondary is a weak Am star, and is possibly still on the pre-main sequence. Line profile variability was observed in a range of lines in the primary, and is attributed to inhomogeneous surface distributions of some elements. No magnetic field was detected in any observation of either stars, with an upper limit on the longitudinal magnetic field in both stars of 100 G. Modeling of the phase-resolve longitudinal field measurements leads to a 3 sigma upper limit on any dipole surface magnetic field of about 400 G.Comment: Accepted for publication in MNRAS, 11 pages, 9 figure

The prediction and management of aquatic nitrogen pollution across Europe: an introduction to the Integrated Nitrogen in European Catchments project (INCA)

Excess nitrogen in soils, fresh water, estuarine and marine systems contributes to nutrient enrichment in key ecosystems throughout Europe, often leading to detrimental environmental impacts, such as soil acidification or the eutrophication of water bodies. The Integrated Nitrogenmodel for European Catchments (INCA) project aims to develop a generic version of the Integrated Nitrogen in Catchments (INCA) model to simulate the retention and transport of nitrogen within river systems, thereby providing a tool to aid the understanding of nitrogen dynamics and for river-basin management/policy-making. To facilitate the development of the model, 10 partners have tested the INCA model with data collected in study sites located in eight European countries as part of the INCA project. This paper summarises the key nitrogen issues within Europe, describes the main aims and methodology of the INCA project, and sets the project in the context of the current major research initiatives at a European level.</p> <p style='line-height: 20px;'><b>Keywords: </b>Europe, European Union, nitrogen, nitrate, ammonium, river basin management, modelling, water chemistry, acidification, eutrophication, Water Framework Directive, INCA