Sigma, tau and Abelian functions of algebraic curves

We compare and contrast three different methods for the construction of the differential relations satisfied by the fundamental Abelian functions associated with an algebraic curve. We realize these Abelian functions as logarithmic derivatives of the associated sigma function. In two of the methods, the use of the tau function, expressed in terms of the sigma function, is central to the construction of differential relations between the Abelian functions.Comment: 25 page

D-instanton sums for matter hypermultiplets

We calculate some non-perturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi-Yau threefold, near conifold singularities. We find a non-trivial deformation of the (real) 4n-dimensional hypermultiplet moduli space metric due to the infinite number of D-instantons, under the assumption of n tri-holomorphic commuting isometries of the metric, in the hyper-K"ahler limit (i.e. in the absence of gravitational corrections).Comment: 11 pages, no figure

Rotating non-asymptotically flat black rings in charged dilaton gravity

We derive new rotating, non-asymptotically flat black ring solutions in five-dimensional Einstein-Maxwell-dilaton gravity with dilaton coupling constant $\alpha=\sqrt{8/3}$ which arises from a six-dimensional Kaluza-Klein theory. As a limiting case we also find new rotating, non-asymptotically flat five-dimensional black holes. The solutions are analyzed and the mass, angular momentum and charge are computed. A Smarr-like relation is found. It is shown that the first law of black hole thermodynamics is satisfied.Comment: 21 pages, LaTeX; v2 a reference added, typos correcte

Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)

The classifications of holonomy groups in Lorentzian and in Euclidean signature are quite different. A group of interest in Lorentzian signature in n dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2). Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg, and a single four-dimensional example with a non-zero cosmological constant was exhibited by Ghanam and Thompson. Here we reduce the problem of finding the general $n$-dimensional Einstein metric of SIM(n-2) holonomy, with and without a cosmological constant, to solving a set linear generalised Laplace and Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit examples may be constructed in terms of generalised harmonic functions. A dimensional reduction of these multi-centre solutions gives new time-dependent Kaluza-Klein black holes and monopoles, including time-dependent black holes in a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page

Vacuum decay via Lorentzian wormholes

We speculate about the spacetime description due to the presence of Lorentzian wormholes (handles in spacetime joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete spacetimes should be actually negligible in our physical Universe

Gravitational lensing in the Kerr-Randers optical geometry

A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a suitable osculating Riemannian manifold, adapted from a construction by Naz\i m, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.Comment: 7 pages, 1 figure. Accepted by Gen. Rel. Grav. Version 2: change of notation in sec.

Applications of the Gauss-Bonnet theorem to gravitational lensing

In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.Comment: 10 pages, 1 figure, IoP styl

Feeding and vertical migration of the chaetognath Sagitta friderici (Ritter Zahony, 1911) in the southern Benguela during spring 1987, with notes on seasonal variability of feeding ecology

The feeding biology and the vertical migration of Sagitta friderici were examined over 24 h at two stations in the southern Benguela during spring (October) 1987. Together with studies conducted during summer (February 1991) and winter (May 1984), they serve to allow valuable generalizations of the biology and ecology of this abundant chaetognath. Populations migrate vertically and feed nocturnally, although the timing and the extent of migration vary between studies. S.friderici exhibits ontogenetic layering and the cross-shelf distribution of maturity stages differs, suggesting that it is able to take advantage of cross-shelf water movement in order to maintain populations in the nearshore waters of the West Coast. S.friderici prey almost exclusively on copepodg (cannibalism is rare), and there is a positive relationship between the lengths of predator and prey that is influenced by the size structure of the prey environment. This casts doubt on the validity of a chaetognath species-specific relationship between predator and prey size. S. friderici selects its prey on the basis of size, and not species. Daily ration is related linearly to prey density, so reflecting the low density of prey and providing support for theoretical predictions regarding ingestion rates under oceanic conditions. The impact of S. friderici predation on the copepod assemblage is generally less than 3% of the standing stock, although it could be much higher under conditions of low copepod biomass and poor secondary production

Variable cavity volume tooling for high-performance resin infusion moulding

This article describes the research carried out by Warwick under the BAE Systems/EPSRC programme ‘Flapless Aerial Vehicles Integrated Interdisciplinary Research – FLAVIIR’. Warwick's aim in FLAVIIR was to develop low-cost innovative tooling technologies to enable the affordable manufacture of complex composite aerospace structures and to help realize the aim of the Grand Challenge of maintenance-free, low-cost unmanned aerial vehicle manufacture. This article focuses on the evaluation of a novel tooling process (variable cavity tooling) to enable the complete infusion of resin throughout non-crimp fabric within a mould cavity under low (0.1 MPa) injection pressure. The contribution of the primary processing parameters to the mechanical properties of a carbon composite component (bulk-head lug section), and the interactions between parameters, was determined. The initial mould gap (di) was identified as having the most significant effect on all measured mechanical properties, but complex interactions between di, n (number of fabric layers), and vc (mould closure rate) were observed. The process capability was low due to the manual processing, but was improved through process optimization, and delivered properties comparable to high-pressure resin transfer moulding