General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Application of CFD in vacuum dezincing process

Most lead bullion is refined by pyrometallurgical methods - this involves a serics of processes that remove the antimony (softening) silver (Parkes process), zinc (vacuum dezincing) and if need be, bismuth (Betterton-Kroll process). The first step, softening, removes the antimony, arsenic and tin by air oxidation in a furnace or by the Harris process. Next, in the Parkes process, zinc is added to the melt to remove the silver and gold. Insoluble zinc, silver and gold compounds are skimmed off from the melt surface. Excess zinc added during desilvering is removed from lead bullion using one of ghree methods: * Vacuum dezincing; * Chlorine dezincing; or * Harris dezincing. The present study concentrates on the Vacuum dezincing process for lead refining. The main aims of the research are to develop mathematical model(s), using Computational Fluid Dyanmics (CFD) a Surface Averaged Model (SAM), to predict the process behaviour under various operating conditions, thus providing detailed information of the process - insight into its reaction to changes of key operating parameters. Finally, the model will be used to optimise the process in terms of initial feed concentration, temperature, vacuum height cooling rate, etc.

A comprehensive copper stockpile leach model: background and model formulation

The first phase in the sign, development and implementation of a comprehensive computational model of a copper stockpile leach process is presented. The model accounts for transport phenomena through the stockpile, reaction kinetics for the important mineral species, oxgen and bacterial effects on the leach reactions, plus heat, energy and acid balances for the overall leach process. The paper describes the formulation of the leach process model and its implementation in PHYSICA+, a computational fluid dynamic (CFD) software environment. The model draws on a number of phenomena to represent the competing physical and chemical features active in the process model. The phenomena are essentially represented by a three-phased (solid liquid gas) multi-component transport system; novel algorithms and procedures are required to solve the model equations, including a methodology for dealing with multiple chemical species with different reaction rates in ore represented by multiple particle size fractions. Some initial validation results and application simulations are shown to illustrate the potential of the model.

An industrial implementation of a methodology for the optimisation of product design tolerances

Today, the key to commercial success in manufacturing is the timely development of new products that are not only functionally fit for purpose but offer high performance and quality throughout their entire lifecycle. In principle, this demands the introduction of a fully developed and optimised product from the outset. To accomplish this, manufacturing companies must leverage existing knowledge in their current technical, manufacturing and service capabilities. This is especially true in the field of tolerance selection and application, the subject area of this research. Tolerance knowledge must be readily available and deployed as an integral part of the product development process. This paper describes a methodology and framework,currently under development in a UK manufacturer, to achieve this objective.