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

Flight testing the fixed-wing configuration of the Rotor Systems Research Aircraft (RSRA)

The Rotor Systems Research Aircraft (RSRA) is a unique research aircraft designed to flight test advanced helicopter rotor system. Its principal flight test configuration is as a compound helicopter. The fixed wing configuration of the RSRA was primarily considered an energy fly-home mode in the event it became necessary to sever an unstable rotor system in flight. While it had always been planned to flight test the fixed wing configuration, the selection of the RSRA as the flight test bed for the X-wing rotor accelerated this schedule. This paper discusses the build-up to, and the test of, the RSRA fixed wing configuration. It is written primarily from the test pilot's perspective

A strong constitutive ethylene-response phenotype conferred on Arabidopsis plants containing null mutations in the ethylene receptors ETR1 and ERS1

Background: The ethylene receptor family of Arabidopsis consists of five members, falling into two subfamilies. Subfamily 1 is composed of ETR1 and ERS1, and subfamily 2 is composed of ETR2, ERS2, and EIN4. Although mutations have been isolated in the genes encoding all five family members, the only previous insertion allele of ERS1 (ers1-2) is a partial loss-of-function mutation based on our analysis. The purpose of this study was to determine the extent of signaling mediated by subfamily-1 ethylene receptors through isolation and characterization of null mutations. Results: We isolated new T-DNA insertion alleles of subfamily 1 members ERS1 and ETR1 (ers1-3 and etr1-9, respectively), both of which are null mutations based on molecular, biochemical, and genetic analyses. Single mutants show an ethylene response similar to wild type, although both mutants are slightly hypersensitive to ethylene. Double mutants of ers1-3 with etr1-9, as well as with the previously isolated etr1-7, display a constitutive ethylene-response phenotype more pronounced than that observed with any previously characterized combination of ethylene receptor mutations. Dark-grown etr1-9;ers1-3 and etr1-7;ers1-3 seedlings display a constitutive triple-response phenotype. Light-grown etr1-9;ers1-3 and etr1-7;ers1-3 plants are dwarfed, largely sterile, exhibit premature leaf senescence, and develop novel filamentous structures at the base of the flower. A reduced level of ethylene response was still uncovered in the double mutants, indicating that subfamily 2 receptors can independently contribute to signaling, with evidence suggesting that this is due to their interaction with the Raf-like kinase CTR1. Conclusion: Our results are consistent with the ethylene receptors acting as redundant negative regulators of ethylene signaling, but with subfamily 1 receptors playing the predominant role. Loss of a single member of subfamily 1 is largely compensated for by the activity of the other member, but loss of both subfamily members results in a strong constitutive ethylene-response phenotype. The role of subfamily 1 members is greater than previously suspected and analysis of the double mutant null for both ETR1 and ERS1 uncovers novel roles for the receptors not previously characterized

Takeoff/approach noise for a model counterrotation propeller with a forward-swept upstream rotor

A scale model of a counterrotating propeller with forward-swept blades in the forward rotor and aft-swept blades in the aft rotor (designated F39/A31) has been tested in the NASA Lewis 9- by 15-Foot Anechoic Wind Tunnel. This paper presents aeroacoustic results at a takeoff/approach condition of Mach 0.20. Laser Doppler velocimeter results taken in a plane between the two rotors are also included to quantify the interaction flow field. The intention of the forward-swept design is to reduce the magnitude of the forward rotor tip vortex and/or wakes which impinge on the aft rotor, thus lowering the interaction tone levels. A reference model propeller (designated F31/A31), having aft-swept blades in both rotors, was also tested. Aeroelastic performance of the F39/A31 propeller was disappointing. The forward rotor tip region tended to untwist toward higher effective blade angles under load. The forward rotor also exhibited steady state blade flutter at speeds and loadings well below the design condition. The noise results, based on sideline acoustic data, show that the interaction tone levels were up to 8 dB higher with the forward-swept design compared to those for the reference propeller at similar operating conditions, with these tone level differences extending down to lower propeller speeds where flutter did not occur. These acoustic results are for a poorly-performing forward-swept propeller. It is quite possible that a properly-designed forward-swept propeller would exhibit substantial interaction tone level reductions

Comment on Ricci Collineations for type B warped space-times

We present two counterexamples to the paper by Carot et al. in Gen. Rel. Grav. 1997, 29, 1223 and show that the results obtained are correct but not general.Comment: LaTex, 3 pages, Eq. (9) and reference added, typos corrected; Gen. Rel. Grav (to appear

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