Co‐operative cross‐platform courseware development

The UKMCC (UK Mathematics Courseware Consortium) is a Consortium funded under TLTP (Training and Learning Technology Programme) to produce courseware for service mathematics teaching, using the SEFI (Société Européenne pour la Formation des Ingénieurs) syllabus. There are agreed courseware design guidelines and a simple courseware management system which allows cross‐referencing. Courseware is divided into modules, with an author as implementer for each. On any one hardware platform, a variety of authoring languages is possible. Across hardware platforms, the design guidelines ensure that conversion is possible, and will preserve look and feel. We argue here that these arrangements provide a basis for continued co‐operation between authors and future development as the technology changes

Constraints on the Growth and Spin of the Supermassive Black Hole in M32 From High Cadence Visible Light Observations

We present 1-second cadence observations of M32 (NGC221) with the CHIMERA instrument at the Hale 200-inch telescope of the Palomar Observatory. Using field stars as a baseline for relative photometry, we are able to construct a light curve of the nucleus in the g-prime and r-prime band with 1sigma=36 milli-mag photometric stability. We derive a temporal power spectrum for the nucleus and find no evidence for a time-variable signal above the noise as would be expected if the nuclear black hole were accreting gas. Thus, we are unable to constrain the spin of the black hole although future work will use this powerful instrument to target more actively accreting black holes. Given the black hole mass of (2.5+/-0.5)*10^6 Msun inferred from stellar kinematics, the absence of a contribution from a nuclear time-variable signal places an upper limit on the accretion rate which is 4.6*10^{-8} of the Eddington rate, a factor of two more stringent than past upper limits from HST. The low mass of the black hole despite the high stellar density suggests that the gas liberated by stellar interactions was primarily at early cosmic times when the low-mass black hole had a small Eddington luminosity. This is at least partly driven by a top-heavy stellar initial mass function at early cosmic times which is an efficient producer of stellar mass black holes. The implication is that supermassive black holes likely arise from seeds formed through the coalescence of 3-100 Msun mass black holes that then accrete gas produced through stellar interaction processes.Comment: 8 pages, 3 figures, submitted to the Astrophysical Journal, comments welcom

Resistance of superconducting nanowires connected to normal metal leads

We study experimentally the low temperature resistance of superconducting nanowires connected to normal metal reservoirs. We find that a substantial fraction of the nanowires is resistive, down to the lowest temperature measured, indicative of an intrinsic boundary resistance due to the Andreev-conversion of normal current to supercurrent. The results are successfully analyzed in terms of the kinetic equations for diffusive superconductors

First principles study of intrinsic point defects in hexagonal barium titanate

Density functional theory (DFT) calculations have been used to study the nature of intrinsic defects in the hexagonal polymorph of barium titanate. Defect formation energies are derived for multiple charge states and due consideration is given to finite-size effects (elastic and electrostatic) and the band gap error in defective cells. Correct treatment of the chemical potential of atomic oxygen means that it is possible to circumvent the usual errors associated with the inaccuracy of DFT calculations on the oxygen dimer. Results confirm that both mono- and di-vacancies exist in their nominal charge states over the majority of the band gap. Oxygen vacancies are found to dominate the system in metal-rich conditions with face sharing oxygen vacancies being preferred over corner sharing oxygen vacancies. In oxygen-rich conditions, the dominant vacancy found depends on the Fermi level. Binding energies also show the preference for metal-oxygen di-vacancy formation. Calculated equilibrium concentrations of vacancies in the system are presented for numerous temperatures. Comparisons are drawn with the cubic polymorph as well as with previous potential-based simulations and experimental results

Compton Scattering in Ultra-Strong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime

This paper explores the effects of strong magnetic fields on the Compton scattering of relativistic electrons. Recent studies of upscattering and energy loss by relativistic electrons that have used the non-relativistic, magnetic Thomson cross section for resonant scattering or the Klein-Nishina cross section for non-resonant scattering do not account for the relativistic quantum effects of strong fields ($> 4 \times 10^{12}$ G). We have derived a simplified expression for the exact QED scattering cross section for the broadly-applicable case where relativistic electrons move along the magnetic field. To facilitate applications to astrophysical models, we have also developed compact approximate expressions for both the differential and total polarization-dependent cross sections, with the latter representing well the exact total QED cross section even at the high fields believed to be present in environments near the stellar surfaces of Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars. We find that strong magnetic fields significantly lower the Compton scattering cross section below and at the resonance, when the incident photon energy exceeds $m_ec^2$ in the electron rest frame. The cross section is strongly dependent on the polarization of the final scattered photon. Below the cyclotron fundamental, mostly photons of perpendicular polarization are produced in scatterings, a situation that also arises above this resonance for sub-critical fields. However, an interesting discovery is that for super-critical fields, a preponderance of photons of parallel polarization results from scatterings above the cyclotron fundamental. This characteristic is both a relativistic and magnetic effect not present in the Thomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for publication in The Astrophysical Journa

Colloidal brazil nut effect in sediments of binary charged suspensions

Equilibrium sedimentation density profiles of charged binary colloidal suspensions are calculated by computer simulations and density functional theory. For deionized samples, we predict a colloidal ``brazil nut'' effect: heavy colloidal particles sediment on top of the lighter ones provided that their mass per charge is smaller than that of the lighter ones. This effect is verifiable in settling experiments.Comment: 4 pages, 4 figure

Superfluid Friction and Late-time Thermal Evolution of Neutron Stars

The recent temperature measurements of the two older isolated neutron stars PSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr, respectively) indicate that these objects are heated. A promising candidate heat source is friction between the neutron star crust and the superfluid it is thought to contain. We study the effects of superfluid friction on the long-term thermal and rotational evolution of a neutron star. Differential rotation velocities between the superfluid and the crust (averaged over the inner crust moment of inertia) of $\bar\omega\sim 0.6$ rad s$^{-1}$ for PSR 1929+10 and $\sim 0.02$ rad s$^{-1}$ for PSR 0950+08 would account for their observed temperatures. These differential velocities could be sustained by pinning of superfluid vortices to the inner crust lattice with strengths of $\sim$ 1 MeV per nucleus. Pinned vortices can creep outward through thermal fluctuations or quantum tunneling. For thermally-activated creep, the coupling between the superfluid and crust is highly sensitive to temperature. If pinning maintains large differential rotation ($\sim 10$ rad s$^{-1}$), a feedback instability could occur in stars younger than $\sim 10^5$ yr causing oscillations of the temperature and spin-down rate over a period of $\sim 0.3 t_{\rm age}$. For stars older than $\sim 10^6$ yr, however, vortex creep occurs through quantum tunneling, and the creep velocity is too insensitive to temperature for a thermal-rotational instability to occur. These older stars could be heated through a steady process of superfluid friction.Comment: 26 pages, 1 figure, submitted to Ap