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

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

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

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

Closed-form sums for some perturbation series involving associated Laguerre polynomials

Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2), where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 + lambda/x^alpha 0 0, A >= 0. It is proved that the series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 + (1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m, m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page

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

First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the k-space Berry phase of occupied Bloch states. The theory is able to account for both dc and magneto-optical Hall conductivities with no adjustable parameters.Comment: 4 pages, 6 figures, author list correcte

Cartographic research in EREP program for small scale mapping

The author has identified the following significant results. Skylab photography is suitable for producing planimetric maps with graphical representation of landform at scales up to 1:100,000. It cannot supply all the detail necessary for maps at this scale, but it may be used to produce a sound framework which can be completed by detail from other sources. Its principal cartographic use is for original mapping of undeveloped areas of the world, but it would also be useful for the revision of existing maps and for monitoring extensive urban changes