A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

A computational model for the cooling phase of injection moulding

This paper discusses the approaches and techniques used to build a realistic numerical model to analyse the cooling phase of the injection moulding process. The procedures employed to select an appropriate mesh and the boundary and initial conditions for the problem are discussed and justified. The final model is validated using direct comparisons with experimental results generated in an earlier study. The model is shown to be a useful tool for further studies aimed at optimising the cooling phase of the injection moulding process. Using the numerical model provides additional information relating to changes in conditions throughout the process, which otherwise could not be deduced or assessed experimentally. These results, and other benefits related to the use of the model, are also discussed in the paper. © 2007 Elsevier B.V. All rights reserved.