On the nature of the torus in the complex Lorenz equations.

The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠ 0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability)

A delay recruitment model of the cardiovascular control system.

Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.

Partial melting in an upwelling mantle column

Decompression melting of hot upwelling rock in the mantle creates a region of partial melt comprising a porous solid matrix through which magma rises buoyantly. Magma transport and the compensating matrix deformation are commonly described by two-phase compaction models, but melt production is less often incorporated. Melting is driven by the necessity to maintain thermodynamic equilibrium between mineral grains in the partial melt; the position and amount of partial melting that occur are thus thermodynamically determined. We present a consistent model for the ascent of a one-dimensional column of rock and provide solutions that reveal where and how much partial melting occurs, the positions of the boundaries of the partial melt being determined by conserving energy across them. Thermodynamic equilibrium of the boundary between partial melt and the solid lithosphere requires a boundary condition on the effective pressure (solid pressure minus melt pressure), which suggests that large effective stresses, and hence fracture, are likely to occur near the base of the lithosphere. Matrix compaction, melt separation and temperature in the partially molten region are all dependent on the effective pressure, a fact that can lead to interesting oscillatory boundary-layer structures. © 2008 The Royal Society

Designing and Building immersive education spaces using Project Wonderland: from pedagogy through to practice

This paper presents work on the JISC funded SIMiLLE project to build a culturally sensitive virtual world to support language learning. This builds on the MiRTLE project (funded by Sun Microsystems), which created a mixed-reality space for teaching and learning. The aim of the SIMiLLE project is to investigate the technical feasibility and pedagogical value of using virtual environments to provide a realistic socio-cultural setting and content for language learning interaction. The paper starts by providing some background information on the Wonderland platform and the MiRTLE project, and then outlines the requirements for SIMiLLE, and how these requirements will be supported through the use of a virtual world based on Project Wonderland. We then present our plans for the evaluation of the system, with a particular focus on the importance of incorporating pedagogy into the design of these systems, and how we can support good practice with the ever-growing use of 3D virtual environments in formalised education