The impact of environmental variability on Atlantic mackerel Scomber scombrus larval abundance to the west of the British Isles

The value of the Continuous Plankton Recorder (CPR) fish larvae dataset, with its extensive spatio-temporal coverage, has been recently demonstrated with studies on long-term changes over decadal scales in the abundance and distribution of fish larvae in relation to physical and biological factors in the North Sea. We used a similar approach in the west and southwest area of the UK shelf and applied a principal component analysis (PCA) using 7 biotic and abiotic parameters, combined with Hierarchical Cluster Analysis (HCA), to investigate the impact of environmental changes in the west and southwest area of the UK shelf on mackerel larvae during the period 1960–2004. The analysis revealed 3 main periods of time (1960–1968; 1969–1994; 1995–2004) reflecting 3 different ecosystem states. The results suggest a transition from an ecosystem characterized by low temperature, high salinity, high abundances of zooplankton and the larger phytoplankton groups, to a system characterized by higher temperature, lower salinities, lower abundances of zooplankton and larger phytoplankton and higher abundances of the small phytoplankton species. Analysis revealed a very weak positive correlation between the Second principal component and mackerel larvae yearly abundance, attributed to the North Atlantic Oscillation (NAO). The results presented here are in broad accord with recent investigations that link climatic variability and dynamics of mackerel reproduction. However, the growing body of literature that documents statistical correlations between environment and mackerel needs to be supplemented by local process studies, to gain more insight and to be able to predict mackerel response to climate change scenarios. Utilising the strength of the CPR dataset, namely its unique temporal coverage, in an analysis where other data (such as egg surveys) are drawn in to compensate for the spatial issues could prove to be the way forward

Scattering from Singular Potentials in Quantum Mechanics

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known.Comment: 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completenes

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Supernova 1987A: Rotation and a Binary Companion

In this paper we provide a possible link between the structure of the bipolar nebula surrounding SN1987A and the properties of its progenitor star. A Wind Blwon Bubble (WBB) scenario is emplyed, in which a fast, tenuous wind from a Blue Supergiant expands into a slow, dense wind, expelled during an earlier Red Supergiant phase. The bipolar shapre develops due to a pole-to-equator density contrast in the slow wind (ie, the slow wind forms a slow torus). We use the Wind Compressed Disk (WCD) model of Bjorkman & Cassinelli (1992) to determine the shape of the slow torus. In the WCD scenario, the shape of the torus is determined by the rotation of the progenitor star. We then use a self-similar semi-analytical method for wind blown bubble evolution to determine the shape of the resulting bipolar nebula. We find that the union of the wind-compressed-disk and bipolar-wind-blown- bubble models allows us to recover the salient properties of SN1987A's circumstellar nebula. In particular, the size, speed and density of SN1987A's inner ring are easily reproduced in our calculations. An exploration of parameter space shows the the red supergiant progenitor must be been rotating at > 0.3 of its breakup speed. We conclude that the progenitor was most likely spun up by a merger with a binary companion. Using a simple model for the binary merger we find that the companion is likely to have had a mass > 0.5 M_sun.Comment: 30 pages, 4 figure

Mapping the economic value of landslide regulation by forests

The role of forests in regulating landslide risks is well established but estimates of the economic value of this ecosystem service are limited. In order to incorporate the role of forests for landslide risk mitigation in spatial planning and other decision-making contexts, there is a need for spatially explicit information regarding the value of this service. We develop a methodological framework to combine bio-physical modelling of natural hazard risk and socio-economic exposure in a predictive model to estimate and map of the economic value of forest regulation of landslides. This method is applied in a case study of Adjara Autonomous Republic of Georgia to examine alternative scenarios for forest management and associated land cover change. The approach produces credible spatially explicit results to inform policy decisions regarding investment in forest management; and has the potential for replication in other data scarce regions

Anti-HBs re-seroconversion after liver transplantation in a patient with past HBV infection receiving a HBsAg positive graft

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