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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.

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

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

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.

A unifying framework for generalised distributed-order fractional models

Project leaders
Dates

2018-2020

Project summary
This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media.

Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.

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.

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.

Image-based multiscale modelling of transport phenomena in porous media

Project leader

Professor Ian Turner

Dates

2015-2017

Project summary
This project aims to develop an innovative general framework to build multiphase porous media transport models directly from electron microscope images of the underlying microstructure. Leading edge experimental, computational and applied mathematical techniques are proposed to drive this novel approach of multiscale modelling, employable across numerous fields of science and engineering.

The central theme of developing an efficient and accurate multiscale model for simulating transport in heterogeneous porous media is expected to find application in the drying, timber and crop industries, and governmental agencies managing pollution in groundwater resources. This insight is likely to be invaluable for designing new industrial technologies and optimising current operations.

Two-scale numerical modelling of coupled transport in heterogeneous media

Project leader

Dr Elliot Carr

Dates

2015-2017

Project summary
Groundwater constitutes a vital part of water resources in Australia, however, the quality of this water is susceptible to contamination. This project aims to develop an innovative two-scale mathematical model for contaminant transport that accounts for small-scale heterogeneities found in the unsaturated zone of an aquifer located between the ground surface and the underlying groundwater.

The work will develop valuable environmental insights, a simulation tool that will help in making decisions regarding the future management of Australian groundwater resources, and a general two-scale modelling and simulation framework for other important environmental and industrial problems involving coupled transport in heterogeneous media.

New mathematical models for capturing heterogeneity of human brain tissue

Project leader

Dr Qianqian Yang

Dates

2015-2017

Project summary
This project aims to understand the impact of the heterogeneity of brain tissue on Magnetic Resonance Imaging (MRI) data in both healthy and diseased human brains, and to extract and quantify information on heterogeneity from the data.

A key goal is to develop novel mathematical and computational approaches to model the heterogeneity of the human brain. The work also aims to identify new biomarkers for classifying different brain diseases, based on the extent of heterogeneity across different brain tissue.

Results will be validated against extensive MRI scanning data of patients. This project aims to advance state-of-the-art techniques in human brain MRI data analysis.

New data-driven mathematical models of collective cell motion

Project leader

Professor Matthew Simpson

Dates

2013-2017

Project summary
Cancer and chronic wounds are a national, and indeed, international health problem set to worsen as our population ages. Predictive and interpretive tools are required to improve our understanding of collective cell migration in relation to cancer and chronic wounds.

This project will produce new validated mathematical tools for predicting collective cell migration in a general framework that can deal with application-specific details, such as the role of cell shape and cell size.

Although cell shape and size are known to affect collective cell migration, standard mathematical models ignore these details. This project will produce new predictive mathematical modelling tools that are validated by new experimental data.

Interdisciplinary and inter-institution projects

Novel multiscale model to investigate mechanical properties of cartilage

Project leaders
Dates

2018-2020

Project summary
This project aims to develop a new multiscale model to investigate anisotropic and inhomogeneous mechanical properties of cartilage. It has been found that the mechanical properties of cartilage highly depend on its microstructures and components.

The new model is proposed based on a new constitutive relation in the macroscale and a novel algorithm to obtain local stress distributions in the microscale as well as through rigorous experimental validations. This model will be a powerful tool to understand cartilage mechanical properties. It will accelerate the design of mechanically viable artificial cartilage biomaterial, which will provide significant economic benefits and place Australia in the forefront of modelling and biomaterials.

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Partnerships

Our industry and community partners have included:

Industry and community

Universities and institutes

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Our topics

Are you looking to study at a higher or more detailed level? We are currently looking for students to research topics at a variety of study levels, including PhD, Masters, Honours or the Vacation Research Experience Scheme (VRES).
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Our experts

We host an expert team of researchers and teaching staff, including Head of School and discipline leaders. Our discipline brings together a diverse team of experts who deliver world-class education and achieve breakthroughs in research.

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