The principle of equivalence and projective structure in space-times

This paper discusses the extent to which one can determine the space-time metric from a knowledge of a certain subset of the (unparametrised) geodesics of its Levi-Civita connection, that is, from the experimental evidence of the equivalence principle. It is shown that, if the space-time concerned is known to be vacuum, then the Levi-Civita connection is uniquely determined and its associated metric is uniquely determined up to a choice of units of measurement, by the specification of these geodesics. It is further demonstrated that if two space-times share the same unparametrised geodesics and only one is assumed vacuum then their Levi-Civita connections are again equal (and so the other metric is also a vacuum metric) and the first result above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit

On the Theory of Killing Orbits in Space-Time

This paper gives a theoretical discussion of the orbits and isotropies which arise in a space-time which admits a Lie algebra of Killing vector fields. The submanifold structure of the orbits is explored together with their induced Killing vector structure. A general decomposition of a space-time in terms of the nature and dimension of its orbits is given and the concept of stability and instability for orbits introduced. A general relation is shown linking the dimensions of the Killing algebra, the orbits and the isotropies. The well-behaved nature of "stable" orbits and the possible miss-behaviour of the "unstable" ones is pointed out and, in particular, the fact that independent Killing vector fields in space-time may not induce independent such vector fields on unstable orbits. Several examples are presented to exhibit these features. Finally, an appendix is given which revisits and attempts to clarify the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur

The effect of swirl recovery vanes on the cruise noise of an advanced propeller

The SR-7A propeller was acoustically tested with and without downstream swirl recovery vanes to determine if any extra noise was caused by the interaction of the propeller wakes and vortices with these vanes. No additional noise was observed at the cruise condition over the angular range tested. The presence of the swirl recovery vanes did unload the propeller and some small peak noise reductions were observed from lower propeller loading noise. The propeller was also tested alone to investigate the behavior of the peak propeller noise with helical tip Mach number. As observed before on other propellers, the peak noise first rose with helical tip Mach number and then leveled off or decreased at higher helical tip Mach numbers. Detailed pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse as the helical tip Mach number is increased. This cancellation appears to be responsible for the peak noise behavior at high helical tip Mach numbers

Recirculation effects produced by a pair of heated jets impinging on a ground plane

Exhaust recirculation effects produced by two heated jets impinging on ground plan

Detailed noise measurements on the SR-7A propeller: Tone behavior with helical tip Mach number

Detailed noise measurements were taken on the SR-7A propeller to investigate the behavior of the noise with helical tip Mach number and then to level off as Mach number was increased further. This behavior was further investigated by obtaining detailed pressure-time histories of data. The pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse which results in the noise leveling off as the helical tip Mach number is increased. This second pulse appears to originate on the same blade as the primary pulse and is in some way connected to the blade itself. This leaves open the possibility of redesigning the blade to improve the cancellation; thereby, the propeller noise is reduced

Limits of the energy-momentum tensor in general relativity

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page

Recent developments in the application of risk analysis to waste technologies.

The European waste sector is undergoing a period of unprecedented change driven by business consolidation, new legislation and heightened public and government scrutiny. One feature is the transition of the sector towards a process industry with increased pre-treatment of wastes prior to the disposal of residues and the co-location of technologies at single sites, often also for resource recovery and residuals management. Waste technologies such as in-vessel composting, the thermal treatment of clinical waste, the stabilisation of hazardous wastes, biomass gasification, sludge combustion and the use of wastes as fuel, present operators and regulators with new challenges as to their safe and environmentally responsible operation. A second feature of recent change is an increased regulatory emphasis on public and ecosystem health and the need for assessments of risk to and from waste installations. Public confidence in waste management, secured in part through enforcement of the planning and permitting regimes and sound operational performance, is central to establishing the infrastructure of new waste technologies. Well-informed risk management plays a critical role. We discuss recent developments in risk analysis within the sector and the future needs of risk analysis that are required to respond to the new waste and resource management agenda

Hydrodynamic Self-Consistent Field Theory for Inhomogeneous Polymer Melts

We introduce a mesoscale technique for simulating the structure and rheology of block copolymer melts and blends in hydrodynamic flows. The technique couples dynamic self consistent field theory (DSCFT) with continuum hydrodynamics and flow penalization to simulate polymeric fluid flows in channels of arbitrary geometry. We demonstrate the method by studying phase separation of an ABC triblock copolymer melt in a sub-micron channel with neutral wall wetting conditions. We find that surface wetting effects and shear effects compete, producing wall-perpendicular lamellae in the absence of flow, and wall-parallel lamellae in cases where the shear rate exceeds some critical Weissenberg number.Comment: Revised as per peer revie

Anomalous Hall effect in superconductors with spin-orbit interaction

We calculate the anomalous Hall conductance of superconductors with spin-orbit interaction and with either uniform or local magnetization. In the first case we consider a uniform ferromagnetic ordering in a spin triplet superconductor, while in the second case we consider a conventional s-wave spin singlet superconductor with a magnetic impurity (or a diluted set of magnetic impurities). In the latter case we show that the anomalous Hall conductance can be used to track the quantum phase transition, that occurs when the spin coupling between the impurity and electronic spin density exceeds a certain critical value. In both cases we find that for large spin-orbit coupling the superconductivity is destroyed and the Hall conductance oscillates strongly.Comment: 10 pages, 6 figure