A nonlinear equation for ionic diffusion in a strong binary electrolyte

The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description consists of a diffusion equation for each species augmented by transport due to a self consistent electrostatic field determined by the Poisson equation. This mathematical framework also describes other important problems in physics such as electron and hole diffusion across semi-conductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here we derive a more general theory by exploiting the ratio of Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear integro-differential equation which replaces the classical linear equation for ambipolar diffusion but reduces to it in the appropriate limit. Through numerical integration of the full set of equations it is shown that this nonlinear equation provides a better approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur

A dual-beam actinic light source for photosynthesis research

Simulation of photosynthetic process in plants is accomplished by using two separate and identical optical channels that provide independently adjustable wavelengths (filters), shutter sequencing, and control intensity of illumination. In addition to experiments using electron paramagnetic resonance spectroscopy, system may be applicable to other types of research in photosynthetic field

Magnetic shell enhancements during magnetic disturbances

Magnetic shell enhancements during magnetic field disturbances from Langmuir probe observations of electron density on Ariel I satellit

Open-mindedness can decrease persuasion amongst adolescents: The role of self-affirmation

Objectives Self-affirmation (e.g., by reflecting on important personal values) has been found to promote more open-minded appraisal of threatening health messages in at-risk adults. However, it is unclear how self-affirmation affects adolescents and whether it has differential effects on the impact of these messages amongst those at relatively lower and higher risk. The current study explored moderation by risk. Design Participants were randomly assigned to either a self-affirmation or a control condition before receiving a health message concerning physical activity. Methods Older adolescents (N = 125) completed a self-affirmation or control writing task before reading about the health consequences of not meeting recommendations to be physically active for at least 60 min daily. Most of the sample did not achieve these levels of activity (98%, N = 123). Consequently, the message informed these participants that – unless they changed their behaviour – they would be at higher risk of heart disease. Participants completed measures of responses to the message and behaviour-specific cognitions (e.g., self-efficacy) for meeting the recommendations. Results For relatively inactive participants, self-affirmation was associated with increased persuasion. However, for those who were moderately active (but not meeting recommendations), those in the self-affirmation condition were less persuaded by the message. Conclusions Whilst self-affirmation can increase message acceptance, there are circumstances when the open-mindedness it induces may decrease persuasion. The evidence provided in this study suggests that caution may be needed when recommendations are challenging and it could be considered reasonable to be sceptical about the need to change behaviour

Short turn-around intercontinental clock synchronization using very-long-baseline interferometry

During the past year work was accomplished to bring into regular operation a VLBI system for making intercontinental clock comparisons with a turn around of a few days from the time of data taking. Earlier VLBI systems required several weeks to produce results. The present system, which is not yet complete, incorporates a number of refinements not available in earlier systems, such as dual frequency inosopheric delay cancellation and wider synthesized bandwidths with instrumental phase calibration

Vortex spectrum in superfluid turbulence: interpretation of a recent experiment

We discuss a recent experiment in which the spectrum of the vortex line density fluctuations has been measured in superfluid turbulence. The observed frequency dependence of the spectrum, $f^{-5/3}$, disagrees with classical vorticity spectra if, following the literature, the vortex line density is interpreted as a measure of the vorticity or enstrophy. We argue that the disagrement is solved if the vortex line density field is decomposed into a polarised field (which carries most of the energy) and an isotropic field (which is responsible for the spectrum).Comment: Submitted for publication http://crtbt.grenoble.cnrs.fr/helio/GROUP/infa.html http://www.mas.ncl.ac.uk/~ncfb

Developing mathematical thinking in the primary classroom: liberating students and teachers as learners of mathematics

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011–2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of project supported by the Scottish Government. The paper presents the background for this initiative within the context of the Scottish Curriculum for Excellence reform. Particular attention is given to the epistemological positioning of the researchers as this influenced both the curriculum design process and also the theoretical framing of the research study which are both described. The project was set up within a design research framework, which aimed to promote classroom-based action research on the part of participants through the course and also research by the university researchers into the process of curriculum development. The research questions focused on the teachers’ confidence, competence, attitudes and beliefs in relation to mathematics and their expectations and experiences of the impact on pupil learning arising from this course. Empirical data were drawn from pre- and post-course surveys, interviews and observations of the discussion forums in the online environment. Findings from this study highlight the way the course had a transformational and emancipatory impact on these teachers. They also highlight ways in which the ‘framing’ of particular aspects of the curriculum had an oppressive impact on learners in the ways that suppressed creativity and limited the exercise of learner autonomy. Furthermore, they highlight the ways in which a number of these teachers had experienced mathematics as a school subject in very negative ways, involving high levels of ‘symbolic violence’ and of being ‘labelled’

A review of peer-assisted learning to deliver interprofessional supplementary image interpretation skills.

Background Peer-assisted learning provides a means through which individuals can learn from one another through a reciprocal process. Radiographic image interpretation skills are fundamental to both diagnostic radiography students and medical students due to their shared role in preliminary evaluation of conventional radiographic images. Medical students on graduation, may not be well prepared to carry out image interpretation, since evidence suggests that they perform less well than radiographers in e.g. Accident and Emergency situations. Method A review of literature was conducted exploring the application of peer-assisted learning within diagnostic radiography and health education more widely as well as the practice of initial image interpretation. An extensive and systematic search strategy was developed which provided a range of material related to the areas. Findings An overview was obtained of the effectiveness of peer-assisted learning and the issues associated with development of image interpretation skills and a degree of discrepancy was identified between the two cohorts regarding their interpretative competence and confidence. This inconsistency may create an opportunity to apply peer-assisted learning, better preparing both disciplines for the practical application of image interpretation skills. Conclusion The review identified the lack of a substantial evidence base relating to peer-assisted learning in radiography. Peer-assisted learning is not widely embraced in an interprofessional context. Multiple positive factors of such an intervention are identified which outweigh perceived negative issues. Student teacher and learner may benefit as should the clinical service from enhanced practitioner performance. The findings justify further research to develop the evidence base

Witness for initial system-environment correlations in open system dynamics

We study the evolution of a general open quantum system when the system and its environment are initially correlated. We show that the trace distance between two states of the open system can increase above its initial value, and derive tight upper bounds for the growth of the distinguishability of open system states. This represents a generalization of the contraction property of quantum dynamical maps. The obtained inequalities can be interpreted in terms of the exchange of information between the system and the environment, and lead to a witness for system-environment correlations which can be determined through measurements on the open system alone.Comment: 4 pages, 1 figur

Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration

We study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed