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 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

Self-similar static solutions admitting a two-space of constant curvature

A recent result by Haggag and Hajj-Boutros is reviewed within the framework of self-similar space-times, extending, in some sense, their results and presenting a family of metrics consisting of all the static spherically symmetric perfect fluid solutions admitting a homothety.Comment: 6 page

Development of EM-CCD-based X-ray detector for synchrotron applications

A high speed, low noise camera system for crystallography and X-ray imaging applications is developed and successfully demonstrated. By coupling an electron-multiplying (EM)-CCD to a 3:1 fibre-optic taper and a CsI(Tl) scintillator, it was possible to detect hard X-rays. This novel approach to hard X-ray imaging takes advantage of sub-electron equivalent readout noise performance at high pixel readout frequencies of EM-CCD detectors with the increase in the imaging area that is offered through the use of a fibre-optic taper. Compared with the industry state of the art, based on CCD camera systems, a high frame rate for a full-frame readout (50 ms) and a lower readout noise (<1 electron root mean square) across a range of X-ray energies (6–18 keV) were achieved

Kadanoff-Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation

A recently developed method for incorporating initial binary correlations into the Kadanoff-Baym equations (KBE) is used to derive a generalized T-matrix approximation for the self-energies. It is shown that the T-matrix obtains additional contributions arising from initial correlations. Using these results and taking the time-diagonal limit of the KBE, a generalized quantum kinetic equation in binary collision approximation is derived. This equation is a far-reaching generalization of Boltzmann-type kinetic equations: it selfconsistently includes memory effects (retardation, off-shell T-matrices) as well as many-particle effects (damping, in-medium T-Matrices) and spin-statistics effects (Pauli-blocking).Comment: 9 pages, 7 figures, corrected misprints in eqs. 48-5

Planetary nebulae after common-envelope phases initiated by low-mass red giants

It is likely that at least some planetary nebulae are composed of matter which was ejected from a binary star system during common-envelope (CE) evolution. For these planetary nebulae the ionizing component is the hot and luminous remnant of a giant which had its envelope ejected by a companion in the process of spiralling-in to its current short-period orbit. A large fraction of CE phases which end with ejection of the envelope are thought to be initiated by low-mass red giants, giants with inert, degenerate helium cores. We discuss the possible end-of-CE structures of such stars and their subsequent evolution to investigate for which structures planetary nebulae are formed. We assume that a planetary nebula forms if the remnant reaches an effective temperature greater than 30 kK within 10^4 yr of ejecting its envelope. We assume that the composition profile is unchanged during the CE phase so that possible remnant structures are parametrized by the end-of-CE core mass, envelope mass and entropy profile. We find that planetary nebulae are expected in post-CE systems with core masses greater than about 0.3 solar masses if remnants end the CE phase in thermal equilibrium. We show that whether the remnant undergoes a pre-white dwarf plateau phase depends on the prescribed end-of-CE envelope mass. Thus, observing a young post-CE system would constrain the end-of CE envelope mass and post-CE evolution.Comment: Published in MNRAS. 12 pages, 12 figures. Minor changes to match published versio

The Greek financial crisis: growing imbalances and sovereign spreads

We discuss the origins of the Greek financial crisis as manifested in the growing fiscal and current-account deficits since euro-area entry in 2001. We then provide an investigation of spreads on Greek relative to German long-term government debt. Using monthly data over the period 2000 to 2010, we estimate a cointegrating relationship between spreads and their long-term fundamental determinants, and compare the spreads predicted by this estimated relationship with actual spreads. We find periods of both undershooting and overshooting of spreads compared to what is predicted by the economic fundamentals.Greek financial crisis; sovereign spreads

Transient dynamics of a flexible rotor with squeeze film dampers

A series of simulated blade loss tests are reported on a test rotor designed to operate above its second bending critical speed. A series of analyses were performed which predicted the transient behavior of the test rig for each of the blade loss tests. The scope of the program included the investigation of transient rotor dynamics of a flexible rotor system, similar to modern flexible jet engine rotors, both with and without squeeze film dampers. The results substantiate the effectiveness of squeeze film dampers and document the ability of available analytical methods to predict their effectiveness and behavior

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