Assessment in mathematics: A multimedia resource for preservice teachers

It is commonly accepted that teachers teach the way they were taught and that innovation is difficult to achieve. In this project, the theoretical framework of situated cognition or situated learning has been used to design an interactive multimedia resource that allows preservice teachers to become aware of different assessment strategies in mathematics education, and how to apply them. The resource enables users to encounter the authentic use of a range of assessment strategies and to view their interpretations from multiple perspectives which include the teacher's decision-making processes, the child's thinking, expert opinion and written documentation

Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Quantum Hamiltonian for gravitational collapse

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.Comment: 17 pages, published version (minor changes

The inefficiency of re-weighted sampling and the curse of system size in high order path integration

Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques -- which is based on re-weighted sampling -- is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average

HST imaging of hyperluminous infrared galaxies

We present HST WFPC2 I band imaging for a sample of 9 Hyperluminous Infrared Galaxies spanning a redshift range 0.45 < z < 1.34. Three of the sample have morphologies showing evidence for interactions, six are QSOs. Host galaxies in the QSOs are reliably detected out to z ~ 0.8. The detected QSO host galaxies have an elliptical morphology with scalelengths spanning 6.5 < r_{e}(Kpc) < 88 and absolute k corrected magnitudes spanning -24.5 < M_{I} < -25.2. There is no clear correlation between the IR power source and the optical morphology. None of the sources in the sample, including F15307+3252, show any evidence for gravitational lensing. We infer that the IR luminosities are thus real. Based on these results, and previous studies of HLIRGs, we conclude that this class of object is broadly consistent with being a simple extrapolation of the ULIRG population to higher luminosities; ULIRGs being mainly violently interacting systems powered by starbursts and/or AGN. Only a small number of sources whose infrared luminosities exceed 10^{13}Lsun are intrinsically less luminous objects which have been boosted by gravitational lensing.Comment: 16 Pages. Accepted for publication in MNRA

The effects of magnetic-field geometry on longitudinal oscillations of solar prominences: Cross-sectional area variation for thin tubes

Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filament-channel magnetic structure that supports the cool prominence plasma against gravity. Our pendulum model, in which the restoring force is the gravity projected along the dipped field lines of the magnetic structure, best explains these oscillations. However, several factors can influence the longitudinal oscillations, potentially invalidating the pendulum model. The aim of this work is to study the influence of large-scale variations in the magnetic field strength along the field lines, i.e., variations of the cross-sectional area along the flux tubes supporting prominence threads. We studied the normal modes of several flux tube configurations, using linear perturbation analysis, to assess the influence of different geometrical parameters on the oscillation properties. We found that the influence of the symmetric and asymmetric expansion factors on longitudinal oscillations is small.}{We conclude that the longitudinal oscillations are not significantly influenced by variations of the cross-section of the flux tubes, validating the pendulum model in this context.Comment: Accepted for publication in Astronomy & Astrophysic