Applied and Industrial Mathematics Research Group

About

Members

Research Areas

Publications

Grants

PhD Opportunities and Scholarships

Contact

Areas of Research

Bushfire Modelling

(Rod Weber, Geoff Mercer, Jason Sharples, Wendy Anderson, Phil Zylstra, Stephen Wilkes)

• fireline growth
• spread rates
• meteorology in the high country and its effects on fire spread
• impacts of fire on vegetation
• spread and patterns in discontinuous fuels

Modelling of many aspects of bushfires from the growth of the fireline, fuel dependent spread rates, impacts on live vegetation and determining damage criteria. Members of the group are actively involved with the Bushfire CRC.

Combustion Theory

(Harvi Sidhu, Geoff Mercer, Rod Weber, Simon Watt, Vladimir Gubernov)

• combustion waves
  • stability
  • initiation
  • multistep reactions
  • Evans function analysis
• chemical reactors
• models of composting
• polymers

Investigation of combustion waves in both solid and gaseous fuels using a broad variety of both numerical and analytic approaches. This work ranges over new combustion wave solutions for chain branching models, stability analysis using Evans function methods, critical initial conditions for combustion to take place and the effects of ambient temperature and heat losses on combustion waves. Others aspects related to combustion studied include chemical reactors (batch and continual flow), models of industrial composting, landfill and waste water treatment.

Defence Applications

(Geoff Mercer, Harvi Sidhu, Nadeem Ansari, Steve Barry)

• minimising detection by enemy radar
• safest routes through minefields
• dynamic route changes in real time to minimise risk
• optimal route for aerial surveillance of ships
• effects of classification range and turning radius on optimal routes
• travelling salesman problem applied to aerial surveillance

Different aspect of travel through a risk environment are studied. Determining the minimal detection route through an area under radar surveillance using differential equation based models. This has application to Unmanned Air Vehicle (UAV) deployment and design issues. Calculation of the safest route through a minefield when information on the location of the mines is only discovered once travel is underway. Solutions must be able to be calculated in real time. Many aspects of the aerial surveillance of maritime regions including use of a modified dynamic travelling salesman problem to determine the visiting order of detected but as yet unclassified ships and aspects of the airplanes capabilities such as turning radius. This is joint work with DSTO Air Operations Division.

Dynamical Systems

(Harvi Sidhu, Geoff Mercer, Richard Pennifold)

• analysing chaotic behaviour
• dynamics in ecology
• spread of diseases
• estuary behaviour
• forced systems

We utilize methods and techniques from nonlinear dynamics theory such as bifurcation and singularity theories to investigate complex real-world phenomena such as population interactions in ecology, spread of diseases, dynamics of shallow estuaries under drought conditions and forced systems. We also investigate new methods to quantify chaotic behaviour in dynamical systems.

Modelling extreme temperature effects on living tissue

(Geoff Mercer, Harvi Sidhu, Steve Barry, Nadeem Ansari)

• skin burns
  • models of skin burns subject to fire exposure
  • automotive airbags
  • design of firefighter clothing to minimise skin burn
• the effect of cold water on a swimmers core temperature
• modelling hypothermia
• wart freezing

Human skin and subcutaneous tissue is a complex organ designed to efficiently cope with a wide range of temperatures and conditions. However, at extremely high temperatures, such as exposures during fires or explosions, the skin is unable to transport the heat away fast enough and burns occur. Similarly, at cold temperatures, the skin is unable to insulate properly causing long term heat loss and hypothermia. We look at various models of heat transfer through the skin and subcutanious tissue to better understand this behaviour.

Industrial Process Modelling

(Geoff Mercer, Harvi Sidhu, Steve Barry James Caunce, Simon Watt)

• wool scouring
• porous filtering
• wastewater treatment
• compost
• bioreactors
• bloom in chocolate
• submarine battery charging
• wine fermentation

Many different industrial processes are studied with in the research group. These research areas have often been initiated by members attendance at the annual Mathematics in Industry Study Group.

Mathematics In Industry Study Group

(Geoff Mercer, Harvi Sidhu, Steve Barry, Rod Weber, James Caunce, Roslyn Hickson, Richard Pennifold)

Members of the AIMRG are actively involved in the annual Mathematics in Industry Study Group (MISG). They have, and continue to, moderate many problems at the MISG. This provides a rich source of new and exciting research areas of direct relevance to industry.

Plant and Disease Spread

(Steve Barry, Geoff Mercer, Harvi Sidhu, Roslyn Hickson)

• models of weed spread
• intervention strategies
• seed banks
• flood events

There are several current models to simulate the spreading of weeds (or any population) in the environment, involving reaction-diffusion equations, integro-difference equations, cellular automata systems, SIR ordinary differential equation, stochastic differential equations, among others. We are currently developing PLANTSIM, a Matlab based package, which allows users to simulate and compare numerous population spread simulation models in either real or artificial situations. A key feature is the Graphical User Interface which allows users to manipulate the complex parameter data sets involved in real simulations. PLANTSIM allows the user to overlay, visualise and manipulate parameter data on satellite imagery, and then run a collection of different simulation routines, with output automatically visualised in a variety of formats with key results summarised and graphed in generated LaTeX and pdf files.

Additional work is being done on formulating new models for weed spread, particularly along river systems. This is being applied to the spread of Lippia in the Murray-Darling system.

Poroelasticity

(Steve Barry, Geoff Mercer)

• injections
• swelling
• drug delivery
• water extraction

Poroelasticity is the modelling of how fluid moves through elastic porous materials, such as consolidation of soils or compression of biological soft tissue. We investigate various methods for solving the nonlinear diffusion equations governing poroelasicity and how to appy this to various industrial and biological systems.

Spraying of Agrichemicals

(Geoff Mercer)

• spray drift management
• spray retention on plant leaves
• droplet impaction models
• uptake and diffusion through leaf cuticles
• minimising environmental impacts of agrichemical sprays

The study of many aspects of the spraying of agrichemicals on to plants with the aim of developing more efficent spray techniques and formulations so that reduced spray volumes can be used for the same efficacy. This has major environmental consequences leading to less pollution, lower residues in the plants and lower chemical usage. Models for the diffusion of agrichemicals through plant leaves are being developed that take into account the varying nature of different plant cuticle structures. Droplet impaction models that predict the droplet spread over the leaf surface and possible bounce of the droplets are under investigation. Spray drift mitigation by suitable shelterbelt design is also being studied. This is joint wok with the agrichemical research company Plant Protection Chemistry New Zealand.

Stefan problems with two moving boundaries -- modelling swelling processes

(Steve Barry, James Caunce, Geoff Mercer, Harvi Sidhu)

• cooking of whole grains
• swelling of polymer implants in drug delivery
• exact and asymptotic solutions of Stefan problems
• swelling of grease layers on wool fibres

During the cooking of whole grains, or the swelling of grease, water diffuses into the outside of the grain causing the outer boundary to swell. This creates a partially swollen region which expands inwards and outwards over time. This then leads to a diffusion problem where the two boundaries defining the diffusive region move (a Stefan problem). We consider modelling this process and finding exact, numerical and asymptotic solutions to the system.