Measuring gravitational lens time delays using low-resolution radio monitoring observations

Obtaining lensing time delay measurements requires long-term monitoring campaigns with a high enough resolution (< 1 arcsec) to separate the multiple images. In the radio, a limited number of high-resolution interferometer arrays make these observations difficult to schedule. To overcome this problem, we propose a technique for measuring gravitational time delays which relies on monitoring the total flux density with low-resolution but high-sensitivity radio telescopes to follow the variation of the brighter image. This is then used to trigger high-resolution observations in optimal numbers which then reveal the variation in the fainter image. We present simulations to assess the efficiency of this method together with a pilot project observing radio lens systems with the Westerbork Synthesis Radio Telescope (WSRT) to trigger Very Large Array (VLA) observations. This new method is promising for measuring time delays because it uses relatively small amounts of time on high-resolution telescopes. This will be important because instruments that have high sensitivity but limited resolution, together with an optimum usage of followup high-resolution observations from appropriate radio telescopes may in the future be useful for gravitational lensing time delay measurements by means of this new method.Comment: 10 pages, 7 figures, accepted by MNRA

Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap

We show that the dynamics of particles in a one-dimensional harmonic trap with hard-core interactions can be solvable for certain arrangements of unequal masses. For any number of particles, there exist two families of unequal mass particles that have integrable dynamics, and there are additional exceptional cases for three, four and five particles. The integrable mass families are classified by Coxeter reflection groups and the corresponding solutions are Bethe ansatz-like superpositions of hyperspherical harmonics in the relative hyperangular coordinates that are then restricted to sectors of fixed particle order. We also provide evidence for superintegrability of these Coxeter mass families and conjecture maximal superintegrability.Comment: 9.5+4.5 pages, 5 figures, 2 tables; v3: a few corrections and addition

Recruiting and retaining children and families' social workers. The potential of work discussion groups

Current difficulties with the recruitment and retention of children and families' social workers have been formally acknowledged. However, although initiatives which focus on remuneration and career progression are clearly welcome, research and evidence from practice highlights how social workers themselves place high value on the availability of good quality supervision. Yet, questions remain about whether first-line managers have the time or are even in the best position to offer this support. This article draws on the experience and evaluation of one particular model of supervision — 'work discussion groups' —and explores its impact with residential social work staff and teachers as well as the potential for further developments of this kind

ULAS J234311.93-005034.0: A gravitational lens system selected from UKIDSS and SDSS

We report the discovery of a new gravitational lens system. This object, ULAS J234311.93-005034.0, is the first to be selected by using the new UKIRT Infrared Deep Sky Survey (UKIDSS), together with the Sloan Digital Sky Survey (SDSS). The ULAS J234311.93-005034.0 system contains a quasar at redshift 0.788 which is doubly imaged, with separation 1.4". The two quasar images have the same redshift and similar, though not identical, spectra. The lensing galaxy is detected by subtracting point-spread functions from R-band images taken with the Keck telescope. The lensing galaxy can also be detected by subtracting the spectra of the A and B images, since more of the galaxy light is likely to be present in the latter. No redshift is determined from the galaxy, although the shape of its spectrum suggests a redshift of about 0.3. The object's lens status is secure, due to the identification of two objects with the same redshift together with a lensing galaxy. Our imaging suggests that the lens is found in a cluster environment, in which candidate arc-like structures, that require confirmation, are visible in the vicinity. Further discoveries of lenses from the UKIDSS survey are likely as part of this programme, due to the depth of UKIDSS and its generally good seeing conditions.Comment: Accepted by MNRA

Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields

The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the distortion can be calculated analytically. We examine the specific examples of fields with cylindrical and spherical symmetry in detail assuming the ion distributions to be of a generally Gaussian form. The effects of differing diffusion coefficients in the transverse and longitudinal directions are included

The dynamics of digits: Calculating pi with Galperin's billiards

In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number $\pi$. This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of $\pi$ in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be $\pi$ itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls' positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of $\pi$ with Galperin billiards, including curious cases with irrational number bases.Comment: 30 pages, 13 figure

Cooperative resonance linewidth narrowing in a planar metamaterial

We theoretically analyze the experimental observations of a spectral line collapse in a metamaterial array of asymmetric split ring resonators [Fedotov et al., Phys. Rev. Lett. 104, 223901 (2010)]. We show that the ensemble of closely-spaced resonators exhibits cooperative response, explaining the observed system-size dependent narrowing of the transmission resonance linewidth. We further show that this cooperative narrowing depends sensitively on the lattice spacing and that significantly stronger narrowing could be achieved in media with suppressed ohmic losses.Comment: 19 pages, 6 figures, to appear in New Journal of Physic