What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms ....What predictions can I trust? Stability of chaotic random dynamical systems. This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.Read moreRead less
Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particl ....Computational modelling of nanofluids for industrial applications. The use of nanoparticles in heat transfer fluids, then known as nanofluids, increases their specific heat and thermal conductivity. Recent experimental works highlight that anomalous transport phenomena are evident in nanofluids that cannot be adequately described by classical conservation laws. We will extend these conservation laws to incorporate fractional operators to capture the fluid memory effects and the impact of particle clustering. Computational modelling and experimental investigations will be undertaken to identify the heat transfer mechanisms of various nanofluids. The outcomes of the work will increase knowledge on nanofluids and offer a significant opportunity to improve the efficiency of many thermal engineering systems.Read moreRead less
New mathematics for understanding complex patterns in the natural sciences. 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 futu ....New mathematics for understanding complex patterns in the natural sciences. 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.Read moreRead less
Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynami ....Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynamics. The project should provide benefits to industries where highly organised behaviours are important, for example those interested in robot swarming, optimal transportation, and epidemic management. It should also benefit Australian students and researchers with novel overseas training opportunities.Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
A theory of communicative practices within financial internet discussion site communities. This project aims to use online financial investment communities to identify factors that drive communication and influence knowledge co-creation, examine how systematic variations in these factors influence investor decision making, and develop a mid-range theory for explaining and predicting the influence of online communication patterns on individual decisions and market outcomes. By developing and vali ....A theory of communicative practices within financial internet discussion site communities. This project aims to use online financial investment communities to identify factors that drive communication and influence knowledge co-creation, examine how systematic variations in these factors influence investor decision making, and develop a mid-range theory for explaining and predicting the influence of online communication patterns on individual decisions and market outcomes. By developing and validating a new mid-range theory, initially in the financial investment context, this project will provide significant benefits, such as help to secure Australia’s place in a changing world through improved information flow.Read moreRead less
Discontinued Use of Social Media: Dichotomy of Rational & Emotional Choices. This project aims to gain a better understanding of discontinued use of social media. For businesses and governments, social media serves as a dynamic channel for engagement, value co-creation, and business analytics marketing that is lost when users choose to discontinue its use. This project will generate new knowledge of rational and emotional decision criteria, enabling design features of social media, and their com ....Discontinued Use of Social Media: Dichotomy of Rational & Emotional Choices. This project aims to gain a better understanding of discontinued use of social media. For businesses and governments, social media serves as a dynamic channel for engagement, value co-creation, and business analytics marketing that is lost when users choose to discontinue its use. This project will generate new knowledge of rational and emotional decision criteria, enabling design features of social media, and their complex effects on discontinued use of social media. The expected outcome of this project is an integrated theory of social media discontinuance. The project findings provide significant benefits, such as strategic capabilities and actionable knowledge for businesses and governments to mitigate social media discontinued use.Read moreRead less
Trusted business processes. This project aims to use conceptual design, process modelling and co-design approaches to create a structured approach for the management of trust. With a focus on business processes, it is intended to develop research- informed methods in order to (1) identify and specify trust concerns and opportunities, (2) model these within a common process modelling language and (3) propose patterns for how to mitigate trust concerns and how to benefit from opportunities. If suc ....Trusted business processes. This project aims to use conceptual design, process modelling and co-design approaches to create a structured approach for the management of trust. With a focus on business processes, it is intended to develop research- informed methods in order to (1) identify and specify trust concerns and opportunities, (2) model these within a common process modelling language and (3) propose patterns for how to mitigate trust concerns and how to benefit from opportunities. If successful, this would lead to an operational, and world first, detailed trust methodology for organisations in all sectors. As a result, Australian customers would engage with business processes with reduced trust concerns and experience increased integrity and benevolence.Read moreRead less
The recirculation of myeloid dendritic cells. This project aims to understand dendritic cell recirculation. It will use virological tools to track dendritic cell migration, and identify key decision points. Expected outcomes include enhanced capacity in basic research and greater interdisciplinary collaboration between virology and immunology research groups. Significant benefits will include a new understanding of how G protein coupled receptor signalling and other tissue cues guide dendritic c ....The recirculation of myeloid dendritic cells. This project aims to understand dendritic cell recirculation. It will use virological tools to track dendritic cell migration, and identify key decision points. Expected outcomes include enhanced capacity in basic research and greater interdisciplinary collaboration between virology and immunology research groups. Significant benefits will include a new understanding of how G protein coupled receptor signalling and other tissue cues guide dendritic cell recirculation, and what consequences the recirculation has for immune cell function. This understanding will significantly advance our basic understanding of the immune system.Read moreRead less