Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

The life history and ecology of black scabbardfish (Aphanopus carbo Lowe 1839) in the north-east Atlantic

The black scabbardfish is a deep water species that supports commercial fisheries across a large area of the NE Atlantic shelf. The life history of black scabbardfish is poorly understood and a major unresolved issue is population structure. In this study it was used a combination of methodologies to get further knowledge in the life history and population structure of A. carbo over its wide distribution range in the Northeast Atlantic. The new knowledge acquired during this study, will increase our ability to better manage this species in the NE Atlantic. It has been postulated that fish caught to the west of the British Isles are pre-adults that migrate further south (to Madeira) for spawning, implying a single panmictic population. In this study, specimens of Aphanopus carbo were sampled between September 2008 and May 2010 from two different areas: NW Scotland (French trawlers and deep water surveys) and Madeira Islands (longliners commercial landings). Geographical differences in reproductive state of scabbardfish were evident, supportive of a north-south migration theory. In the northern area, all specimens found were immature, while in Madeira all maturity stages were observed. In Madeira, spawning occurred during the fourth quarter, with peak maturity in October (males) and in November (females). The age of this species has proven difficult and has led to different and contradictory age and growth estimates. For this study, we used two reading interpretations to determine age and estimate the growth parameters. To the west of the British Isles, specimens reached a lower maximum age and had a higher growth rate than those caught off Madeira. These differences are consistent with the theory of a single population of black scabbardfish in the NE Atlantic, highly segregate, with smaller, immature and younger fish caught to the west of the British Isles and bigger and mature caught in Madeira Islands. The feeding ecology showed strong evidence that the diet of black scabbardfish is associated with the spawning migration of blue whiting, which may support a northerly feeding migration theory for black scabbardfish. The stable isotope analyses in the muscle of black scabbardfish identified that black scabbardfish feeds on species with epipelagic and benthopelagic affinities. Comparison with stable isotope analysis in Madeira samples indicated that black scabbardfish feed at a similar trophic level and has the same trophic niche width in both areas, assuming similar baseline isotope compositions. Otolith stable isotopes (oxygen - δ18O and nitrogen - δ15N) analyses were used as a tool to clarify migratory behaviour. Otolith isotope ratios can provide insight into whether adults caught around Madeira fed in an isotopically depleted northerly ecosystem (NW Scotland) during their pre-adult period and then migrate towards south to spawn. Overall, the results support a south-north migration of pre adult fish from spawning areas around Madeira and a north-south migration from the west of Scotland to the spawning areas. Given its life cycle there is an urgent need that the management process recognizes the existence of a continuous widely distributed stock of black scabbardfish between the west of the British Isles and Madeira. The results highlight large scale dispersal in this species which needs to be treated as a highly migratory species and be managed as a single population.

Biomethane production from food waste and organic residues

Anaerobic digestion (AD) of biodegradable waste is an environmentally and economically sustainable solution which incorporates waste treatment and energy recovery. The organic fraction of municipal solid waste (OFMSW), which comprises mostly of food waste, is highly degradable under anaerobic conditions. Biogas produced from OFMSW, when upgraded to biomethane, is recognised as one of the most sustainable renewable biofuels and can also be one of the cheapest sources of biomethane if a gate fee is associated with the substrate. OFMSW is a complex and heterogeneous material which may have widely different characteristics depending on the source of origin and collection system used. The research presented in this thesis investigates the potential energy resource from a wide range of organic waste streams through field and laboratory research on real world samples. OFMSW samples collected from a range of sources generated methane yields ranging from 75 to 160 m3 per tonne. Higher methane yields are associated with source segregated food waste from commercial catering premises as opposed to domestic sources. The inclusion of garden waste reduces the specific methane yield from household organic waste. In continuous AD trials it was found that a conventional continuously stirred tank reactor (CSTR) gave the highest specific methane yields at a moderate organic loading rate of 2 kg volatile solids (VS) m-3 digester day-1 and a hydraulic retention time of 30 days. The average specific methane yield obtained at this loading rate in continuous digestion was 560 ± 29 L CH4 kg-1 VS which exceeded the biomethane potential test result by 5%. The low carbon to nitrogen ratio (C: N <14:1) associated with canteen food waste lead to increasing concentrations of volatile fatty acids in line with high concentrations of ammonia nitrogen at higher organic loading rates. At an organic loading rate of 4 kg VS m-3day-1 the specific methane yield dropped considerably (381 L CH4 kg-1 VS), the pH rose to 8.1 and free ammonia (NH3 ) concentrations reached toxicity levels towards the end of the trial (ca. 950 mg L-1). A novel two phase AD reactor configuration consisting of a series of sequentially fed leach bed reactors connected to an upflow anaerobic sludge blanket (UASB) demonstrated a high rate of organic matter decay but resulted in lower specific methane yields (384 L CH4 kg-1 VS) than the conventional CSTR system.