Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Lensing Properties of Cored Galaxy Models

A method is developed to evaluate the magnifications of the images of galaxies with lensing potentials stratified on similar concentric ellipses. A simple contour integral is provided which enables the sums of the magnifications of even parity or odd parity or the central image to be easily calculated. The sums for pairs of images vary considerably with source position, while the signed sums can be remarkably uniform inside the tangential caustic in the absence of naked cusps. For a family of models in which the potential is a power-law of the elliptic radius, the number of visible images is found as a function of flattening, external shear and core radius. The magnification of the central image depends on the core radius and the slope of the potential. For typical source and lens redshifts, the missing central image leads to strong constraints; the mass distribution in the lensing galaxy must be nearly cusped, and the cusp must be isothermal or stronger. This is in accord with the cuspy cores seen in high resolution photometry of nearby, massive, early-type galaxies, which typically have the surface density falling like distance^{-1.3} outside a break radius of a few hundred parsecs. Cuspy cores by themselves can provide an explanation of the missing central images. Dark matter at large radii may alter the slope of the projected density; provided the slope remains isothermal or steeper and the break radius remains small, then the central image remains unobservable. The sensitivity of the radio maps must be increased fifty-fold to find the central images in abundance.Comment: 42 pages, 11 figures, ApJ in pres

Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

Roll diffusion bonding of titanium alloy panels

Roll diffusion bonding technique is used for fabricating T-stiffened panel assemblies from titanium alloy. The single unit fabrication exhibits excellent strength characteristics under tensile and compressive loads. This program is applied to structures in which weight/strength ratio and integral construction are important considerations

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

Technical guidelines for economic valuation of inland small-scale fisheries in developing countries

These ôTechnical Guidelines for Economic Valuation of Inland Small-scale Fisheries in Developing Countriesö are one of the outputs of the project on ôFood security and poverty alleviation through improved valuation and governance of river fisheries in Africaö. The guidelines draw upon research results and experience gained during the course of the project. The project was coordinated and implemented by the WorldFish Center and was carried out in cooperation with the National Agricultural Research Institutes (NARs) from the participating countries: the Nigeria Institute for Freshwater Fisheries Research, the Departments of Fishery of Niger, Malawi and Zambia, and the Cameroonian MinistΦre de lÆElevage, des PΩches et de lÆIndustrie Animale; and three advanced research institutes (ARIs): the Leibniz University of Hannover in Germany, the Institute for Sustainable Development and Aquatic Resources in UK, and the University of Cape Town in South Africa.Rural development, Sustainable development, Livelihoods, Economic analysis, Research, Artisanal fishing

Localized energy for wave equations with degenerate trapping

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of regularity is a common way to incorporate such. When trapping is sufficiently weak, a logarithmic loss of regularity suffices. Here, by studying a warped product manifold introduced by Christianson and Wunsch, we encounter the first explicit example of a situation where an estimate with an algebraic loss of regularity exists and this loss is sharp. Due to the global-in-time nature of the estimate for the wave equation, the situation is more complicated than for the Schr\"{o}dinger equation. An initial estimate with sub-optimal loss is first obtained, where extra care is required due to the low frequency contributions. An improved estimate is then established using energy functionals that are inspired by WKB analysis. Finally, it is shown that the loss cannot be improved by any power by saturating the estimate with a quasimode.Comment: 18 page

Classical and quantum time dependent solutions in string theory

Using the ontological interpretation of quantum mechanics in a particular sense, we obtain the classical behaviour of the scale factor and two scalar fields, derived from a string effective action for the FRW time dependent model. Besides, the Wheeler-DeWitt equation is solved exactly. We speculate that the same procedure could also be applied to S-branes.Comment: 11 pages, To appear in Int. J. Mod. Phys.

Astrometric Microlensing as a Method of Discovering and Characterizing Extra-Solar Planets

We introduce a new method of searching for and characterizing extra-solar planets. We show that by monitoring the center-of-light motion of microlensing alerts using the next generation of high precision astrometric instruments the probability of detecting a planet orbiting the lens is high. We show that adding astrometric information to the photometric microlensing lightcurve greatly helps in determining the planetary mass and semi-major axis. We introduce astrometric maps as a new way for calculating astrometric motion and planet detection probabilities. Finite source effects are important for low mass planets, but even Earth mass planets can give detectable signals.Comment: 9 pages includes 8 postscript figures, AAS Latex, submitted to Ap