Two studies in process modelling: injection moulding and resin film infusion

This paper discusses two problems from important areas of processmodelling, namely injection moulding and resin film infusion.The first comes from the food-processing sector, and involvesthe filling of tubs with liquid foodstuffs. The approach takenhere is computational, with the foodstuffs modelled as incompressibleviscous (Newtonian or non-Newtonian) fluids. In practice, theliquids have multiple free surfaces; the correct treatment ofthese surfaces is a crucial element of the modelling herein. Resin film infusion is one of the preferred processes for themanufacture of composite materials. In essence it involves squeezinga viscous incompressible fluid into a woven carbon-fibre matrix.With the matrix treated as a porous medium, and with exothermicreactions (and consequent thermal effects) neglected, simpleanalytical results are obtainable which can be verified by straightforwardengineering experiments.     

Residues in toric varieties

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y.     

The numerical solution of an inverse scattering problem for acoustic waves

In a previous paper, the authors presented a dual space methodfor the numerical solution of the two-dimensional inverse scatteringproblem for acoustic waves in an inhomogeneous medium. Here,by making major modifications to the dual space method, a dramaticimprovement in the numerical performance of this method is achievedfor solving the inverse scattering problem.     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

Statistical geometry of hard sphere systems: exact relations for first-order phase transitions in multicomponent systems

Statistical geometry provides exact relations between the thermophysical properties of hard sphere systems and various geometric quantities. Utilizing recently derived relations that describe multicomponent hard sphere systems, we derive two new expressions which place rigorous constraints on the behaviour of geometric quantities across a first-order phase transition. Some implications of these constraints for a binary mixture of additive hard spheres are discussed.