Curvature dependences of wave propagation in reaction–diffusion models

Overview

Reaction–diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wavefronts. These waves have important applications in many physical, ecological and biological systems. Our group has recently provided new theoretical and numerical analyses to elucidate the influence of curvature for the diffusion and reaction of entities, such as chemical compounds, biological cells, or individuals in a population.

In this project, you will extend these mathematical and/or numerical analyses to new situations, such as the progression and stability of fronts with small perturbations, the interaction of fronts with obstacles of various geometries, Fisher–Stefan reaction–diffusion models, and multispecies models. These investigations will provide new understandings of the survival and extinction of populations in complex environments.

Research engagement

You will be exposed to leading-edge research from the literature, and have the opportunity to develop novel mathematical models informed by experimental data, and to develop bespoke computer code to numerically simulate the models.

Research activities

You will work closely and meet regularly with the supervisory team to carry out all aspects of the project, including engaging with key literature, developing new mathematical models, performing mathematical analyses and numerical simulations, and comparing with experimental observations.

Research skills

Research skills you will acquire include reading and understanding specialised literature on mathematical modelling of biological systems, applying established and novel mathematical modelling frameworks and critically analysing results obtained. You will also develop skills in presenting your results to a general and specialist audience.

Outcomes

The outcomes of this projects are new understandings of the influence of geometry for the survival and extinction of populations in complex environments, with applications to ecology, developmental biology, and tumour growth.

Skills and experience

This project can be tailored to suit research students at VRES, Honours, Masters, and PhD level. Some proficiency in differential equations and computer modelling is expected. No prior knowledge of biology is required.

Start date

2 November, 2026

End date

19 February, 2027

Location

Gardens Point, QUT

Additional information

The supervisory team may take some leave over the summer break. Suitable dates will be arranged within this period.

Keywords

• Mathematical modelling
• Population models
• Survival and extinction

Contact

Pascal Buenzli

x81558

pascal.buenzli@qut.edu.au