Applied and Computational Mathematics

Project summary

Cells have evolved redundant strategies where the function of survival is through a small dormant subpopulation of cells within a more rapidly proliferating population. It has been suggested that these cells are responsible for the persistence of chronic infections, and the recalcitrance of certain cancers.

Acquisition of resistance to anticancer drugs is a major problem in cancer therapy and these cells could be viable targets for new therapies. Nevertheless, their transient nature and low abundance, has impeded experimental advancements. Novel ways of thinking about these issues are needed.

The underlying hypothesis is that some biological cells hedge by carrying additional regulatory and chemical machinery. This machinery may only function in response to periods of extreme stress. We will develop stochastic models driven by Wiener noise and Poisson jump noise that capture the behaviour of this machinery.

The Hamilton Jacobi Bellman theory will be used to maximize the expectation of a functional associated with the response of the cell, resulting in a system of nonlinear partial differential equations describing the hedging property of a cell that will then be solved numerically.

Project summary

This project aims to re-evaluate principles for designing marine reserves to conserve reef fish and sustain fisheries under current and future scenarios of habitat quality and population connectivity.

The project will integrate advanced genetic methods, novel field experiments and new quantitative approaches to promote population recovery, persistence and yield for a range of fish species.

It will recommend optimal reserve size, spacing and location for geographic regions subject to different levels of habitat degradation and fishing pressure.

It will benefit Australia and our regional neighbours by providing the critical science necessary for the successful management of shared coral reef assets and resources.

Project summary

This project aims to develop mathematical and computational tools to compute the energy in a given ship wake and to determine a range of properties of a ship by taking simple measurements of the water height as the ship travels past.

The expected outcomes should have direct implications for measuring damage to coastal zones by ship wakes and for surveillance of shipping channels.

Project summary

Mathematical modelling and computer simulation could offer an alternative to expensive experimental programs for agrichemical spraying of plants.

This project will use contemporary fluid mechanics to build practical mathematical models for droplet impaction, spreading and evaporation on leaf surfaces, and experimentally calibrate and validate the models.

Project summary

Existing models rely solely on stochastic simulations, and therefore provide no general mathematical insight into how properties of the crowding environment (obstacle shape, size, density) affect the migration of cells through that environment.

This project will produce mathematical analysis, mathematical calculations and exact analytical tools that quantify how the crowding environment in threedimensional living tissues affects the migration of cells within these tissues.

Long term effects will be the translation of this new mathematical knowledge into decision support tools for researchers from the life sciences.

Project summary

Mesenchymal stem cells (MSCs) can differentiate into various cell types and are therefore used as therapies to treat damaged tissues. As MSC overdose can cause a variety of adverse effects, understanding these cells becomes crucial so as to better deliver the drug.

The aim of this project is to build a mathematical modelling system to investigate the homing of MSCs in the liver. By calibrating the model to experimental data from mice, we quantify the impact of liver and MSC conditions on the two distinct homing mechanisms.

As an outcome, we published a paper in the journal ‘PeerJ’ which is recognised as one of the top five most viewed mathematical biology articles in 2018.

Read the paper here

Project summary

This project aims to examine the interaction of fundamental two-dimensional patterns such as spots and stripes in reaction-diffusion equations, by developing and extending mathematical techniques.

These fundamental planar structures form the backbone of more complex patterns and are, for example, observed in models that describe the propagation of impulses in nerve axons and the formation of vegetation patterns.

The future impact of this research will have economic and environmental benefits. For example, the project will develop a deeper understanding of interacting patterns that will provide insights into the role of vegetation in ecosystems that are undergoing desertification.

Project summary

This project aims to develop technology with the potential to disrupt computation by providing a way to solve combinatorial mathematical problems in an efficient manner.

Electronic computers have revolutionised our lives over the last half-century but there are tasks they can not do, usually those requiring multi-tasking.

This project aims to overcome some of these problems by physically using molecular parts of living things moving within specially mathematically designed networks to solve "combinatorial" mathematical problems that vex traditional computers while using far less energy than electronic devices.

This project expects to develop this nascent field into a practically useful, disruptive technology based in Australia.