The Capture and Escape of Stars

The shape of galaxies depends on their orbital populations. These populations change through capture into and escape from resonance. Capture problems fall into distinct cases depending upon the shape of the potential well. To visualise the effective potential well for orbital capture, a diagrammatic approach to the resonant perturbation theory of Born is presented. These diagrams we call equiaction sections. To illustrate their use, we present examples drawn from both galactic and Solar System dynamics. The probability of capture for generic shapes of the potential well is calculated. A number of predictions are made. First, there are barred galaxies that possess two outer rings of gas and stars (type R ′ 1R ′ 2). We show how to relate changes in the pattern speed and amplitude of the bar to the strength of the two rings. Secondly, under certain conditions, small disturbances can lead to dramatic changes in orbital shape. This can be exploited as a mechanism to pump counter-rotating stars and gas into the nuclei of disk galaxies. Tidal resonant forcing of highly inclined orbits around a central mass causes a substantial increase in the likelihood of collision. Thirdly, the angular momentum of a potential well is changed by the passage of stars across or capture into the well. This can lead to the creation of holes, notches and high velocity tails in the stellar distribution function, whose form we explicitly calculate.Peer reviewe

A dense Bose fluid at zero temperature: condensation and clusters in liquid He-4

We present a full set of wave equations describing a dense Bose fluid, applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in liquid 4He is found and the fraction of condensed particles is calculated at zero temperature for a wide range of densities. The theory also yields the ground-state energy for the quantum liquid 4He in agreement to high accuracy with Monte Carlo simulations and experimental data at low pressure. We also present the derivation of a generalized Hartree-Fock equation describing roton clusters in low temperature liquid 4He, allowing us to confirm that, at low enough temperatures and for a wide range of pressures, the stable clusters consist of 13 bound atoms.Comment: 16 pages, 7 figure

Input-output relations for multiport ring cavities

Quantum input-output relations for a generic $n$-port ring cavity are obtained by modeling the ring as a cascade of $n$ interlinked beam splitters. Cavity response to a beam impinging on one port is studied as a function of the beam-splitter reflectivities and the internal phase-shifts. Interferometric sensitivity and stability are analyzed as a function of the number of ports.Comment: 6 pages, 5 figures (low-res

The assessment of pain in older people

Pain is under-recognised and under-treated in older people. It is a subjective, personal experience, only known to the person who suffers. The assessment of pain is particularly challenging in the presence of severe cognitive impairment, communication difficulties or language and cultural barriers. These guidelines set out the key components of assessing pain in older people, together with a variety of practical scales that may be used with different groups, including those with varying levels of cognitive or communication impairment. The purpose is to provide professionals with a set of practical skills to assess pain as the first step towards its effective management. The guidance has implications for all healthcare and social care staff and can be applied in all settings, including the older person’s own home, in care homes, and in hospital

Quantum-field-theoretical techniques for stochastic representation of quantum problems

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic difference equations in discretised time