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Applied and Computational Mathematics

Overview

We focus on developing and analysing mathematical models and solving mathematical problems using numerical methods and computer simulation.

Our applied and computational mathematics discipline is devoted to:

  • teaching mathematics with an emphasis on mathematical modelling and numerical simulation
  • research to develop new fundamental knowledge in mathematics
  • applying new models, algorithms and software to solve complex problems for our partners in academia, industry and government.
Professor Scott McCue
Discipline Leader, Applied and Computational Mathematics

Our experts

Our discipline brings together a diverse team of experts who deliver world-class education and achieve breakthroughs in research.

Explore our staff profiles to discover the amazing work our researchers are contributing to.

Meet our experts

Professor Kevin Burrage
Position
Professor of Computational Maths
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Statistics
Email
Professor Fawang Liu
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Professor Scott McCue
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research field
Applied Mathematics
Email
Professor Timothy Moroney
Position
Professor in Mathematics
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research field
Numerical and Computational Mathematics
Email
Professor Matthew Simpson
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Other Mathematical Sciences
Email
Professor Ian Turner
Position
Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Associate Professor Michael Bode
Position
Associate Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Associate Professor Petrus van Heijster
Position
Associate Professor
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Pure Mathematics
Numerical and Computational Mathematics
Email
Associate Professor Dan Nicolau
Position
Future Fellow
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Dr Pamela Burrage
Position
Senior Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Numerical and Computational Mathematics
Applied Mathematics
Email
Dr Elliot Carr
Position
Senior Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email
Dr Robyn Araujo
Position
Lecturer
Division / Faculty
Applied and Computational Mathematics,
School of Mathematical Sciences
Research fields
Applied Mathematics
Numerical and Computational Mathematics
Email

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Teaching

We offer a major that provides students the opportunity to combine their studies in mathematics with real-world applications and computational simulations.

Students can use these computer simulation and visualisation techniques in many research projects, from bone fracture and wound healing to modelling saltwater intrusion in coastal systems.

Bachelor of Mathematics (Applied and Computational Mathematics)

Industry learning

Students in our capstone unit have worked with Australasian Groundwater and Environmental Consultants (AGE) to model and analyse groundwater flow in aquifer systems used for crop irrigation across regional Queensland.

Through a combination of mathematical modelling and computational algorithms, students simulated different groundwater pumping scenarios and devised strategies to ensure this natural resource was being used sustainably.

This project brought together three years of learning in modelling and computation and provided valuable experience in teamwork, communication, the nature and language of industry projects.

Research

In the Australian Government's 2018 Excellence in Research for Australia (ERA) framework, our research in both Applied Mathematics and Numerical and Computational Mathematics have been ranked at the highest possible level of 'well above world standard.'

Our discipline’s research has contributed to new advancements and insights into a wide variety of practical applications, including:

  • agrichemical spraying of plants
  • battery technology
  • coal seam gas production
  • electrical activity of the heart
  • growth of cancerous tumours
  • management of coastal aquifers.
  • sugar cane production
  • wood drying processes
  • wound healing.

Research themes

Mathematical modelling of physical processes with industrial applications

  • electrochemical systems and solar cells
  • fluid dynamics, bubbles and droplets
  • heat and mass transfer
  • hydrology and groundwater flow
  • multi-scaled modelling
  • porous materials
  • phase-change phenomena
  • transport theory.

Computational simulation of large, multi-scaled or complex systems

  • computational efficiency
  • high performance computing
  • parallel computing with GPU hardware
  • numerical linear algebra
  • numerical methods
  • quantifying uncertainty
  • scientific computing and visualisation
  • stochastic simulation.

Modelling processes in biology, ecology and medicine

  • cardiac modelling
  • collective cell motion
  • computational biology
  • fracture healing
  • gene regulation
  • infectious disease modelling
  • intra-cellular processes
  • pattern formation
  • regulation of musculoskeletal tissues
  • tissue engineering
  • tumour growth and invasion
  • wound healing processes.

New mathematical techniques and analysis of mathematical models

  • analysis of differential equations
  • analysis of stochastic models
  • applied complex analysis
  • asymptotic analysis and perturbation methods
  • geometric singular perturbation theory
  • mathematical cryptology
  • numerical analysis.

Projects

Cellular Hedging

Project leaders
Dates

2018-2019

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.

Conserving coral reef fish and sustaining fisheries in the Anthropocene

Project leader
Dates

2019-2021

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.

Mathematical and computational analysis of ship wakes

Project leaders
Dates

2018-2020

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.

Mathematical and computational models for agrichemical retention on plants

Project leader

Professor Scott McCue

Dates

2016-2019

Project summary
This project aims to build interactive software that simulates agrichemical spraying for multiple virtual plants reconstructed from scanned data.

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.

Mathematical models of cell migration in three-dimensional living tissues

Project leader

Professor Matthew Simpson

Dates

2017-2020

Project summary
This project aims to develop mathematical models of cell migration in crowded, living tissues.

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.

Modelling the homing of therapeutic mesenchymal stem cells in mice

Project leader
Dates

2018

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

New mathematics for understanding complex patterns in the natural sciences

Project leader
Dates

2019-2021

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.

Scalable biocomputing on networks: design and mathematical foundations

Project leader
Dates

2019-2021

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.

View our student topics

Partnerships

Our industry and community partners have included:

Industry and community

Universities and institutes

Ask us about becoming a partner

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