Research Interests (attention students)

I have assisted with the running of the first two Industrial Mathematics weeks to be held in Indonesia at ITB Bandung, in Feb 98 and July 2000. Many interesting problems from industry arose out of these meetings. For further details about the problems that arose see `Industrial Mathematics Week 98, Indonesia': The Australian Mathematical Society Gazette, Vol 25, Number 2, June 98, and Proceedings Institut Teknologi Bandung ISSN 0125-9350, Vol 33, 2001. I will be assisting in running the first MISG to be held in South Africa in Johannesburg in January 2004.

Below is a list of problems that I am currently working on that would be suitable for Honours or post graduate student work. Being a modeller I often work with individuals and groups outside mathematics. Papers related to this work can be found in my publication list. Other material is available on request. The problems that I've worked on have come from many companies, small and big, concerned with improving their competitive edge. As a modeller my interest lies with the sums and the students, not the money. Companies that I've worked with include Uncle Toby's, BHP, Hardie, CRA, ICI, duPont, British Steel, BrewTech, Mouldflow, Age Developments, Unilever, LNEC. I also work with colleagues in Engineering and Physics and from medicine.

• Heart Attacks: Early detection of Large infarcts through monitoring of Tropmin-T. Damage of the heart muscle (a heart attack) usually caused by a vessel blockage may be detected by monitoring the release of an enzyme Tropmin-T into the bloodstream. The pattern of release will depend on the extent and location of the damage so that an understanding of relationship will enable doctors to better treat the condition. Early intervention is evidently important. Dr Abbey Perumpanani is a doctor at Sir Charles Gairdner hospital, and also a PhD in mathematics, has data and will jointly supervise this project. Interested students should contact Martin Hazelton or myself.
• Malting. (Brewtech) The main task in the brewing process is the conversion of the starch in barley grains into alcohol. This process involves malting, milling, mashing, boiling and fermentation. Germination occurs during malting producing enzymes that break down starch molecules into sugars which are converted to alcohol by adding yeast during fermentation. An understanding of the production, diffusion and reaction processes occuring during germination is thus of interest to the brewer as well as the biologist and modeller.
• The AAR reaction in dams. Concrete suffers from an `ageing process' due to a chemical reaction between active silica present in aggregates and alkalais present in cement. This reaction produces a gel which swells and thus affects the strength of concrete structures in general, and in dams in particular. This problem comes from LNEC, Portugal
• Hardieboard: Problems arise in the production of hardieboard. Essentially hardieboard is a cement mixture that is laid out in sheets. Thin sheets need to be joined together to produce useful thick sheets for construction. The problem is a moisture diffusion, surface tension, gravity problem. For further information click here.
• The flotation process: Foams can be used for separating out valuable minerals. Ofter unwanted materal is floated to the foam surface as well as the valuable material. How to improve the process? Foams are also used for building materials, and are important for food products, beer and icecream.
• Mike Trefy and Lloyd Townley, (http://www.dwr.csiro.au) at CSIRO WA have a number of interesting and important environmental problems involving transport of water and pollutants through soil. Joint supervision would be appropriate for these studies.
• Radiation Propagation over the Ocean (with Brett Nener, Engineering). The propagation of light rays over the ocean is strongly influenced by the presence of water droplets generated by the action of wind on water waves and by temperature and humidity variations. The aim is to produce a usefully simple mathematical model to determine accurately the propagation of light rays over large distances in known conditions, and to use this model for solving the inverse problem.
• Inverse Problems. Various groups at the UWA are involved in inverse problems, and joint supervision is encouraged. The basic aim of this work is to use wave propagation methods (sound, EM radiation, light) to determine the physical structure of an unseen object. In Western Australia, where valuable minerals are abundant, ore detection is of special interest, but the same problems arise in medical areas (detection of anatomical abnormalities). For further details from my colleagues check out Lyle Noakes from Maths, Brett Nener from Electrical Engineering, and Ryszard Kozera from Computer Science.
• Surface tension effects in a wedge. Dip coating is a common practice in industrial processes. If the object is partially dipped, surface tension effects determine the shape of the wetted surface. Often the aim is to reduce the curvature of the wetted interface. For details click here.
• Ice Cream models. Ice cream manufacturers would like to ensure that their final product tastes good and can withstand the (thermal) buffeting that occurs during storage and transport. Ice cream is a partially frozen mixture of water, air, cream fat, and other natural indegrients introduced to stabilize the final product. Thermal buffeting can change the structure.
• Ice Accretion on Aircraft Wings (British Aerospace). During holding ice can build up on aircraft wings. This can reduce lift and increase drag. Lubrication theory models need to be developed to determine the buildup under glazing conditions.
• Railway Wheel Squeal (ARTC): Vibrations that have their origin in the slip/sick contact between train and the rails cause the squealing noise heard when a train negotiates a curve. How to reduce this?
• Badminton racquet design. The aim is to design the racquet to fit the player by adjusting the racquet parameters.
• Cancer research models.
  

Student Supervision

I am happy to supervise both honours and Ph D students in all of the topics indicated above, and other suitable industrial or medical modelling topics. I encourage student to do cross discipline work with joint supervision. We have an active research Continuum Mechanics and Industrial Mathematics Group at UWA working with colleagues at Murdoch University, Curtin University, and various CSIRO groups, and other interstate and overseas groups, with a continual stream of visitors.

At present I am supervising: