An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

On the coupling of Navier–Stokes and linearised Euler equations for aeroacoustic simulation

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

Numerical simulation of vacuum dezincing of lead alloy

Removing zinc by distillation can leave the lead bullion virtually free of zinc and also produces pure zinc crystals. Batch distillation is considered in a hemispherical kettle with water-cooled lid, under high vacuum (50 Pa or less). Sufficient zinc concentration at the evaporating surface is achieved by means of a mechanical stirrer. The numerical model is based on the multiphysics simulation package PHYSICA. The fluid flow module of the code is used to simulate the action of the stirring impeller and to determine the temperature and concentration fields throughout the liquid volume including the evaporating surface. The rate of zinc evaporation and condensation is then modelled using Langmuir’s equations. Diffusion of the zinc vapour through the residual air in the vacuum gap is also taken into account. Computed results show that the mixing is sufficient and the rate-limiting step of the process is the surface evaporation driven by the difference of the equilibrium vapour pressure and the actual partial pressure of zinc vapour. However, at higher zinc concentrations, the heat transfer through the growing zinc crystal crust towards the cold steel lid may become the limiting factor because the crystallization front may reach the melting point. The computational model can be very useful in optimising the process within its safe limits.

A unified 3D model of the VAR process

A 3D time-dependent model of the VAR process has been developed using CFD techniques. The model solves the coupled field equations for fluid flow, heat transfer (including phase change) and electromagnetic field, for both the electrode and the ingot. The motion of the electic arc 'preferred spot' can be specified based on observations. Correlations are sought between the local gap height, resulting from instantaneous liquid pool surface shape and electrode tip shape, and the arc motion. The detailed behaviour of the melting film on the electrode tip is studies using a spectral free surface technique, which allows investigation of the drops' detachment and drip shorts.

Research supervision and psychotherapeutic theory: bridging the research-practice-gap

Research supervision in the field of counselling and psychotherapy is a fruitful area for investigation in view of the fact that the research supervisory relationship is powerful and highly charged, whether consciously acknowledged or not. Researchers trained as counsellors and psychotherapists possess the skills to facilitate the emergence of, and work creatively with, impasses and crises, both in the research itself and the supervisory relationship, as a result of their training and experience in dealing with crisis and catharsis in clinical work. This paper will demonstrate these points using a case vignette from my work as a supervisor of research dissertations undertaken by students on a Masters in Therapeutic Counselling course. Drawing on narrative analysis, clinical supervision theory and discursive analysis it will look at the strengths and weaknesses of a 'psychotherapeutic' approach to research supervision.

Bridging the gap with teamwork: collaborative leadership for communities of practice in the learning and skills sector

Collaborative approaches in leadership and management are increasingly acknowledged to play a key role in successful institutions in the learning and skills sector (LSS) (Ofsted, 2004). Such approaches may be important in bridging the potential 'distance' (psychological, cultural, interactional and geographical) (Collinson, 2005) that may exist between 'leaders' and 'followers', fostering more democratic communal solidarity. This paper reports on a 2006-07 research project funded by the Centre for Excellence in Leadership (CEL) that aimed to collect and analyse data on 'collaborative leadership' (CL) in the learning and skills sector. The project investigated collaborative leadership and its potential for benefiting staff through trust and knowledge-sharing in communities of practice (CoPs). The project forms part of longer-term educational research investigating leadership in a collaborative inquiry process (Jameson et al., 2006). The research examined the potential for CL to benefit institutions, analysing respondents' understanding of and resistance to collaborative practices. Quantitative and qualitative data from senior managers and lecturers was analysed using electronic data in SPSS and Tropes Zoom. The project aimed to recommend systems and practices for more inclusive, diverse leadership (Lumby et al., 2005). Collaborative leadership has increasingly gained international prominence as emphasis shifted towards team leadership beyond zero-sum 'leadership'/ 'followership' polarities into more mature conceptions of shared leadership spaces, within which synergistic leadership spaces can be mediated. The relevance of collaboration within the LSS has been highlighted following a spate of recent government-driven policy developments in FE. The promotion of CL addresses concerns about the apparent 'remoteness' of some senior managers, and the 'neo-management' control of professionals which can increase 'distance' between leaders and 'followers' and may de-professionalise staff in an already disempowered sector. Positive benefit from 'collaborative advantage' tends to be assumed in idealistic interpretations of CL, but potential 'collaborative inertia' may be problematic in a sector characterised by rapid top-down policy changes and continuous external audit and surveillance. Constant pressure for achievement against goals leaves little time for democratic group negotiations, despite the desires of leaders to create a more collaborative ethos. Yet prior models of intentional communities of practice potentially offer promise for CL practice to improve group performance despite multiple constraints. The CAMEL CoP model (JISC infoNet, 2006) was linked to the project, providing one practical way of implementing CL within situated professional networks.The project found that a good understanding of CL was demonstrated by most respondents, who thought it could enable staff to share power and work in partnership to build trust and conjoin skills, abilities and experience to achieve common goals for the good of the sector. However, although most respondents expressed agreement with the concept and ideals of CL, many thought this was currently an idealistically democratic, unachievable pipe dream in the LSS. Many respondents expressed concerns with the 'audit culture' and authoritarian management structures in FE. While there was a strong desire to see greater levels of implementation of CL, and 'collaborative advantage' from the 'knowledge sharing benefit potential' of team leadership, respondents also strongly advised against the pitfalls of 'collaborative inertia'. A 'distance' between senior leadership views and those of staff lower down the hierarchy regarding aspects of leadership performance in the sector was reported. Finally, the project found that more research is needed to investigate CL and develop innovative methods of practical implementation within autonomous communities of professional practice.