New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuo ....New Frontiers and Advances in Discrete Integrable Systems. Integrable systems boast a long and venerable history, and have such famous members as the Kepler system, the Korteweg-de Vries equation, and the sine-Gordon equation. More recently, interest in integrable systems has expanded to include systems with discrete time, that is, ordinary difference equations (or maps) and integrable partial difference equations. These discrete integrable systems are arguably more fundamental than the continuous-time ones. Based upon recent breakthroughs this study will combine analysis, geometry, and computer algebra to expand and systematise this new interdisciplinary field of discrete integrable systems.Read moreRead less
Estimating the Topology of Low-Dimensional Data Using Deep Neural Networks. This project will expand on the superhuman visual capabilities of deep neural networks to allow us to analyse the topology of 3- and 4-dimensional manifolds. While these spaces still count as low-dimensional, 4-dimensional manifolds typically are beyond human visual comprehension. The topology of a manifold describes its essential properties such as the number of connected components, holes, tunnels and cavities of vario ....Estimating the Topology of Low-Dimensional Data Using Deep Neural Networks. This project will expand on the superhuman visual capabilities of deep neural networks to allow us to analyse the topology of 3- and 4-dimensional manifolds. While these spaces still count as low-dimensional, 4-dimensional manifolds typically are beyond human visual comprehension. The topology of a manifold describes its essential properties such as the number of connected components, holes, tunnels and cavities of various dimensions. Traditional methods from computational topology fail in large practical applications due to computational restrictions. We propose an approximation that overcomes previous limitations and can open new doors to data analysis in material science, medical imaging, dynamical systems and other applications.
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A Stress-relax Model for Stellar Flares. This project aims to improve our ability to predict solar and stellar flares by developing a theoretical model for the build-up and release of magnetic stress in stellar atmospheres. Solar flares are the most energetic events in the solar system, and together with associated coronal mass ejections can create hazardous conditions in our local space environment. Stellar flares are thousands of times more energetic and produce dangerous space weather for exo ....A Stress-relax Model for Stellar Flares. This project aims to improve our ability to predict solar and stellar flares by developing a theoretical model for the build-up and release of magnetic stress in stellar atmospheres. Solar flares are the most energetic events in the solar system, and together with associated coronal mass ejections can create hazardous conditions in our local space environment. Stellar flares are thousands of times more energetic and produce dangerous space weather for exoplanets orbiting flare stars. Expected outcomes include insight into the flare mechanism, and new approaches to flare prediction. The major potential benefit is improved solar and stellar space weather forecasting to protect human safety and infrastructure.Read moreRead less
Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-struct ....Optimal electromaterial structures for energy applications. This project aims to develop new mathematical and modelling approaches to determine optimal configurations and parameters for material structures created from three-dimensional printing of combined metals and electromaterials. Electromaterials are needed for sustainable energy, but solving coupled-systems of highly nonlinear governing equations is needed for optimal control of spatial arrangement and composition in nano and micro-structural domains. Dealing with this mathematical complexity is critical to developing high efficiency energy generation and gas storage systems. This is expected to enhance transport mechanisms within electrochemical devices and create opportunities for industry to use electrofunctional materials.Read moreRead less
Understanding the role of terrain geometry in eruptive bushfire behaviour. This project aims to improve understanding of the physical processes that cause eruptive bushfire behaviour, otherwise known as fire blow-up. Eruptive fire behaviour, characterised by rapid and unexpected escalation in fire intensity and rate of spread, is a global phenomenon that poses a major threat to fire-fighter safety and can seriously compromise bushfire suppression efforts. This project will address the role that ....Understanding the role of terrain geometry in eruptive bushfire behaviour. This project aims to improve understanding of the physical processes that cause eruptive bushfire behaviour, otherwise known as fire blow-up. Eruptive fire behaviour, characterised by rapid and unexpected escalation in fire intensity and rate of spread, is a global phenomenon that poses a major threat to fire-fighter safety and can seriously compromise bushfire suppression efforts. This project will address the role that terrain geometry plays in the incidence of fire eruption, through consideration of its effect on the attachment of flames to a surface. Expected outcomes include a dynamic fire spread modelling framework and the provision of better advice to bushfire authorities concerning fire blow-up.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL210100110
Funder
Australian Research Council
Funding Amount
$3,021,288.00
Summary
New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight i ....New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight into fundamental biomedical processes. In this way, the project expects to affect a paradigm shift in mathematical biology while strengthening Australia’s reputation as a world-leader in mathematical biology. An outcome from this project could be new mathematical models that guide decision making in the clinic.Read moreRead less