38,174 research outputs found
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
- …