Debris disc candidates in systems with transiting planets

Debris discs are known to exist around many planet-host stars, but no debris dust has been found so far in systems with transiting planets. Using publicly available catalogues, we searched for infrared excesses in such systems. In the recently published Wide-Field Infrared Survey Explorer (WISE) catalogue, we found 52 stars with transiting planets. Two systems with one transiting "hot Jupiter" each, TrES-2 and XO-5, exhibit small excesses both at 12 and 22 microns at a > 3 sigma level. Provided that one or both of these detections are real, the frequency of warm excesses in systems with transiting planets of 2-4 % is comparable to that around solar-type stars probed at similar wavelengths with Spitzer's MIPS and IRS instruments. Modelling suggests that the observed excesses would stem from dust rings with radii of several AU. The inferred amount of dust is close to the maximum expected theoretically from a collisional cascade in asteroid belt analogues. If confirmed, the presence of debris discs in systems with transiting planets may put important constraints onto formation and migration scenarios of hot Jupiters.Comment: Accepted for publication in MNRAS Letter

Stability and error analysis for a diffuse interface approach to an advection-diffusion equation on a moving surface

In this paper we analyze a fully discrete numerical scheme for solving a parabolic PDE on a moving surface. The method is based on a diffuse interface approach that involves a level set description of the moving surface. Under suitable conditions on the spatial grid size, the time step and the interface width we obtain stability and error bounds with respect to natural norms. Furthermore, we present test calculations that confirm our analysis

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

A composite functional equation from algebraic aspect

In this paper we discuss the composite functional equation f(x+2f(y))=f(x)+y+f(y) on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes

In this article we present a system of coupled bulk-surface reaction-diffusion equations on exponentially evolving volumes. Detailed linear stability analysis of the homogeneous steady state is carried out. It turns out that due to the nature of the coupling (linear Robin-type boundary conditions) the characterisation of the dispersion relation in the absence and presence of spatial variation (i.e. diffusion), can be decomposed as a product of the dispersion relation of the bulk and surface models thereby allowing detailed analytical tractability. As a result we state and prove the conditions for diffusion-driven instability for systems of coupled bulk-surface reaction-diffusion equations. Furthermore, we plot explicit evolving parameter spaces for the case of an exponential growth. By selecting parameter values from the parameter spaces, we exhibit pattern formation in the bulk and on the surface in complete agreement with theoretical predictions

37^th plenary meeting report of the scientific, technical and economic committee for fisheries (PLEN-11-02)

The Scientific, Technical and Economic Committee for Fisheries hold its 37th plenary on 11-15 July 2011 in Copenhagen (Denmark). The terms of reference included both issues assessments of STECF Expert Working Group reports and additional requests submitted to the STECF by the Commission. Topics dealt with ranged from fisheries economics to management plan evaluation issues

Using model selection to choose a size-based condition index that is consistent with operational welfare indicators

Quantitative and qualitative measures of fish health and welfare are essential for management of both wild capture and aquaculture species. These measures include morphometric body condition indices, energetic condition, and aquaculture operational welfare indicators (OWI). Measures vary in ease of measurement (and may require destructive sampling), and it is critical to know how well they correlate with fish health and welfare so appropriate management decisions can be based on them. Lumpfish (Cyclopterus lumpus) is a new farming species that needs non-destructive OWIs to be developed and validated. In this study, we developed a C. lumpus fin damage score. Four different body condition indexes based on individual weight relative to either length-weight relationships, or relative to other fish in its local environment were tested (using model selection) as predictors of individual fin damage. Results showed severity of fin damage was predicted by small size relative to the other individuals in the tank or cage. Body condition based on length-weight relationship was not found to predict fin damage, indicating that using established indices from fisheries or from other species would not predict welfare risks from fin damage. Implications are that especially in hatchery conditions grading will improve the condition index, and is expected to mitigate fin damage, but that low weight at length was not of use in predicting fin damage. Model selection to choose between a suite of possible indices proved powerful, and should be considered in other applications where an easily measured index is needed to correlate with other health measures