MELEES - e-support or mayhem?

This paper reports on progress in developing a web-based environment to support non-specialist mathematics students taking University level Mathematics as a compulsory subject in their first and second years. The scale and diversity of the service teaching provision at Nottingham invites the use of a technology-based framework in order to make available the ‘good practice’ features developed both locally and elsewhere. Initially the two year development is focusing on: • establishing a supportive environment; • providing feedback to students, their lecturers and importantly to their home Schools; • identifying and supporting e-learning strategies; • improving student motivation. Current activities have been primarily directed to the first three bullet points

Enterococcus faecalis from healthy infants modulates inflammation through MAPK signaling pathways

10.1371/journal.pone.0097523PLoS ONE95-POLN

On the effects of mass and momentum transfer from droplets impacting on steady two-dimensional rimming flow in a horizontal cylinder

Motivated by applications in aero-engines, steady two-dimensional thin-filmflow on the inside of a circular cylinder is studied when the filmsurface is subject to mass and momentum transfer from impacting droplets. Asymptotic analysis is used systematically to identify distinguished limits that incorporate these transfer effects at leading order and to provide a new mathematical model. Applying both analytical and numerical approaches to the model, a set of stable steady, two-dimensional solutions that fit within the rational framework is determined. A number of these solutions feature steep fronts and associated recirculating pools, which are undesirable in an aeroengine since oil may be stripped away from the steep fronts when there is a core flow external to the film, and recirculation may lead to oil degradation. The model, however, provides a means of investigating whether the formation of the steep fronts on the filmsurface and of internal recirculation pools can be delayed, or inhibited altogether, by designing jets to deliver prescribed distributions of oil droplets or by the judicious siting of oil sinks. Moreover, by studying pathlines, oil-residence times can be predicted and systems optimized

Effect of possible rotor deformation on the probability of face contact for a liquid film bearing

The possibility of face contact is examined for a coaxial rotor-stator bearing in dynamic motion constrained by a highly rotating very thin liquid film. A modified Reynolds equation for pressurised flow is coupled to the bearing structure leading to determination of the bearing gap from solving a nonlinear second-order non-autonomous ordinary differential equation. Periodic solutions are found via a mapping solver. Rotor deformation is parametrised by a coning angle and considered a random variable. The method of derived distributions is used to quantify variation in coning angle and examine the probability of rotor-stator contact. Additionally, effects of possible destabilising random aspects on the axial rotor oscillations are investigated. Exact solutions for probability of contact are obtained for various bearing configurations.</p

Study of aero-engine oil-air separators

For aero-engines, oil-air separation is a key function, and one approach to assessing separator effectiveness is computational fluid dynamics (CFD). The two-phase flow is complex and oil can be present in different forms (for example, droplets, mist, film). However, necessary modelling simplifications may affect solution accuracy and range of validity. This article presents a modelling methodology for oil-air separators; the effect of simplifications is discussed and their relative magnitude assessed. Comparison with available experimental data is presented. It is concluded that although simplification has an impact, the significant features of the oil-air separator are predicted with sufficient accuracy to allow design comparisons. Two separator configurations, one internal to a bearing chamber and one external, are modelled and the data presented. Flow fields are compared and the effectiveness of the separators in removing oil droplets prior to impact on the breather (primary separation) presented. The separation performance of the external design is largely independent of shaft speed, with all droplets >3 μm removed before impact on the breather. The critical droplet diameter of the internal design is larger, varying with breather configuration and shaft speed but the power loss is an order of magnitude lower than for the external design

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the possible consequences of chaotic dynamics for memory processing and learning

Effect of random forcing on fluid lubricated bearing

A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation for incompressible flow and is coupled to the axial displacement of the bearing faces as modelled by spring-mass-damper systems. Representative dynamics of a highly rotating bearing subject to external potentially destabilising random forcing is developed. An external force characterised by a noise term is imposed on the rotor, where both white noise and coloured noise are considered. For industrial applications it is important to evaluate potential bearing failure that can arise when the face clearance becomes sufficiently small. Therefore, a quantity of interest is the average time for the face clearance to reach a prescribed tolerance. A computational technique to evaluate the bearing characteristics is implemented based on a simple random walk for a Dirichlet problem for a linear parabolic partial differential equation combined with a Monte Carlo technique. Results of numerical experiments are presented, to give indicative predictions of possible face contact, which has the potential to result in bearing failure