Staggered-mesh computation for aerodynamic sound

For the numerical solution of the linearized Euler equations, an optimized computational scheme is considered. It is based on fully staggered (in space and time) regular meshes and on a simple mirroring procedure at the stepwise solid walls. There is no need to define ghost points into the solid ohjects that reflect the sound waves. Test results demonstrate the accuracy of the method that may be used for aeroacoustic problems with complex geometries.

Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Ontological considerations of time, meta-predicates and temporal propositions

A natural approach to representing and reasoning about temporal propositions (i.e., statements with time-dependent truth-values) is to associate them with time elements. In the literature, there are three choices regarding the primitive for the ontology of time: (1) instantaneous points, (2) durative intervals and (3) both points and intervals. Problems may arise when one conflates different views of temporal structure and questions whether some certain types of temporal propositions can be validly and meaningfully associated with different time elements. In this paper, we shall summarize an ontological glossary with respect to time elements, and diversify a wider range of meta-predicates for ascribing temporal propositions to time elements. Based on these, we shall also devise a versatile categorization of temporal propositions, which can subsume those representative categories proposed in the literature, including that of Vendler, of McDermott, of Allen, of Shoham, of Galton and of Terenziani and Torasso. It is demonstrated that the new categorization of propositions, together with the proposed range of meta-predicates, provides the expressive power for modeling some typical temporal terms/phenomena, such as starting-instant, stopping-instant, dividing-instant, instigation, termination and intermingling etc.

Characterisation of freeze-dried wafers and solvent evaporated films as potential drug delivery systems to mucosal surfaces

Freeze-dried (lyophilised) wafers and solvent cast films from sodium alginate (ALG) and sodium carboxymethylcellulose (CMC) have been developed as potential drug delivery systems for mucosal surfaces including wounds. The wafers (ALG, CMC) and films (CMC) were prepared by freeze-drying and drying in air (solvent evaporation) respectively, aqueous gels of the polymers containing paracetamol as a model drug. Microscopic architecture was examined using scanning electron microscopy, hydration characteristics with confocal laser scanning microscopy and dynamic vapour sorption. Texture analysis was employed to investigate mechanical characteristics of the wafers during compression. Differential scanning calorimetry was used to investigate polymorphic changes of paracetamol occurring during formulation of the wafers and films. The porous freeze-dried wafers exhibited higher drug loading and water absorption capacity than the corresponding solvent evaporated films. Moisture absorption, ease of hydration and mechanical behaviour were affected by the polymer and drug concentration. Two polymorphs of paracetamol were observed in the wafers and films, due to partial conversion of the original monoclinic to the orthorhombic polymorph during the formulation process. The results showed the potential of employing the freeze-dried wafers and solvent evaporated films in diverse mucosal applications due to their ease of hydration and based on different physical mechanical properties exhibited by both type of formulations.

Modelling of the time-dependent flow behaviour of lead-free solder pastes used for flip-chip assembly applications

The market for solder paste materials in the electronic manufacturing and assembly sector is very large and consists of material and equipment suppliers and end users. These materials are used to bond electronic components (such as flip-chip, CSP and BGA) to printed circuit boards (PCB's) across a range of dimensions where the solder interconnects can be in the order of 0.05mm to 5mm in size. The non-Newtonian flow properties exhibited by solder pastes during its manufacture and printing/deposition phases have been of practical concern to surface mount engineers and researchers for many years. The printing of paste materials through very small-sized stencil apertures is known to lead to increased stencil clogging and incomplete transfer of paste to the substrate pads. At these very narrow aperture sizes the paste rheology and particle-wall interactions become crucial for consistent paste withdrawal. These non-Newtonian effects must be understood so that the new paste formulations can be optimised for consistent printing. The focus of the study reported in this paper is the characterisation of the rheological properties of solder pastes and flux mediums, and the evaluation of the effect of these properties on the pastes' printing performance at the flip-chip assembly application level. Solder pastes are known to exhibit a thixotropic behaviour, which is recognised by the decrease in apparent viscosity of paste material with time when subjected to a constant shear rate. The proper characterisation of this time-dependent theological behaviour of solder pastes is crucial for establishing the relationships between the pastes' structure and flow behaviour; and for correlating the physical parameters with paste printing performance. In this paper, we present a number of methods which have been developed for characterising the time-dependent and non-Newtonian rheological behaviour of solder pastes and flux mediums as a function of shear rates. We also present results of the study of the rheology of the solder pastes and flux mediums using the structural kinetic modelling approach, which postulates that the network structure of solder pastes breaks down irreversibly under shear, leading to time and shear dependent changes in the flow properties. Our results show that for the solder pastes used in the study, the rate and extent of thixotropy was generally found to increase with increasing shear rate. The technique demonstrated in this study has wide utility for R&D personnel involved in new paste formulation, for implementing quality control procedures used in solder paste manufacture and packaging; and for qualifying new flip-chip assembly lines