Applied Mathematical Modelling

Link to Applied Mathematics and Statistics Research Report 09/10 (pdf file)

This group undertakes research in the application of mathematical methods to model real-world systems, including those that are directly relevant to industry.

• Industrial Mathematics
• Nonlinear dynamics: fundamentals and applications/simulations
• Wool scouring
• Ecological modelling
• Exercise physiology
• Determining optimal path in a threat environment
• Statistical comparisons of running and triathlon results
• Pesticide Spraying
  

Industrial Mathematics

Brief Description: We have a strong involvement in the annual Mathematics-in-Industry Study Group (MISG), assisting Australian and New Zealand industry to solve challenging problems. Recent problems include the control of chocolate bloom, reduction of iron oxide/coal pellets to pure iron in a fast heat reduction process, heat transfer in a steel ladle, moisture content in iron-ore and coal stockpiles, coating of spectacle lenses, microwave drying of photographic emulsions, flow of granular sugar-cane residue, sorting of coal and maximising the output in a bioreactor.

Staff members: Steve Barry, Geoff Mercer, Harvi Sidhu and Rod Weber

Nonlinear dynamics: fundamentals and applications/simulations

Brief Description: We utilize methods and techniques from nonlinear dynamics theory to investigate complex real-world phenomena such as population interactions, dynamics of shallow estuaries under drought conditions, forced oscillations and the dynamics of molecular motion.

Staff members: Dennis Isbister and Harvi Sidhu

Wool scouring

Brief Description: Wool scouring is the process of cleaning wool once it has been sheared from a sheep. This involves washing the wool in a series of bowls, with squeeze rollers expelling water from the wool at the end of each bowl. Presently we are modelling:

• the movement of dirt within each bowl
• the swelling of grease on the wool fibre
• the water flow through the wool during the squeeze rolling
• the drying of wet patches within the wool after scouring

Most of these models involve differential-equation models based on momentum and mass transport.

Staff members: Steve Barry and Geoff Mercer

Ecological modelling

Brief Description: There are two projects which are currently been investigated. One involves the grazing of herbivores, while the other centres around scaling problems involving trees and forests, with the aim of studying carbon sequestration. The latter project is part of the CRC for Greenhouse Accounting. This work is being undertaken with collaboration with Dr Belinda Barnes from the Ecosystems Group in the Research School of Biological Sciences at ANU.

Staff member: Harvi Sidhu

Exercise physiology

Brief Description: When an person exercises, their heart rate depends on many things such as their fitness level, how hard they are working, how long they have been working, their glucose levels etc. Essentially these reduce to the following key factors:

• Work rate.
• Muscle glycogen levels.
• Oxygen transport and available oxygen. Transport rates of sugars (glucose glycogen etc) between liver and muscle glycogen stores.

While there have been some crude models of these factors in the literature, none has tried to combine them into a sophisticated differential-equation-based model. Our aim is to be able to model the performance of long-distance runners and, by being able to predict heart rate and glycogen levels as a function of work and time, to develop feeding and work-rate strategies to improve long-term performance. This will have applicability not only to for training and racing of competitive and recreational athletes, but also to occupations requiring long-term work output such as in the military. Data are provided by GPS/heart rate tracking equipment tested on runners in a variety of terrains.

Staff members: Steve Barry and Geoff Mercer

Determining optimal path in a threat environment

Brief Description: We investigate the use of the continuous formulation (as opposed to the traditional discrete methods) to determine paths through a hostile environment, with the aim to minimize the risk of detection. These paths are often subject to given constraints such as maximum travel time and fuel usage. We are collaborating with Dr Jane Sexton from DSTO on this project.

Staff members: Geoff Mercer, Harvi Sidhu, Zlatko Jovanoski and Nadeem Ansari

Statistical comparisons of running and triathlon results

Brief Description: When an athlete races, they use three methods to find out how well they did. They consider their overall time, their position with respect to the whole field and their position with respect to some colleagues. For example, 'I ran 40:50 for the 10 km which was slow, and I came 120th out of 200 which is not good, but I beat John and Fred who usually beat me, so perhaps I did okay after all.' Time is often not a good measure, as conditions between races vary. Similarly, the people running the race may vary. However, comparison between similar colleagues can be a good measure. Triathlons and cross-country races are particularly difficult for comparisons because of the large variations in course length, style, and competitors.

The aim of this project is to improve on the 'colleague-comparison' method, by comparing everybody's performance against all other people who have run earlier races. This will provide statistical measures of performance regardless of variations in conditions and crowd sample. This can be further improved by weighting performances with respect to age, gender and length of race. Ultimately we aim to produce a model which will transform each race result into one equivalent to a 25 year old male doing a set course (say a flat 10 km run), hence allowing a much better comparison of results across distances, courses, ages and gender. Several years of data for ACT triathlons are being used to assess the viability of the models.

Staff member: Steve Barry

Pesticide Spraying

(Click on image for a larger view of the following images of Flow through a Porous hedge.)

Brief Description: We investigate numerous aspects of pesticide spraying of crops including

• Spray drift capture by shelterbelts and riparian vegetation
• Modelling spray droplet trajectories and evaporation
• Models for droplet impaction on leaf surfaces: adhere, rebound or shatter
• Retention and runoff of spray on different crops

This work is in collaboration with Plant Protection Chemistry New Zealand. Opportunities exist for exciting PhD projects in this area contact Geoff Mercer

Staff members: Geoff Mercer