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
New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deter ....New mathematics to quantify fluctuations and extremes in dynamical systems. Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.Read moreRead less
Mathematical modelling can provide vital information on the effectiveness and practical implementation of microbicides and vaccines against HIV. This project will produce mathematical models of the earliest stages of HIV infection suitable for investigation of the implementation of vaccines and microbicides. It will provide a framework to investigate why these interventions have performed poorly to date, and how these may be better implemented.
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
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 geometric theory for travelling waves in advection-reaction-diffusion models. Cell migration patterns often develop distinct sharp interfaces between identifiably different cell populations within a tissue. This research will develop new geometric methods for the mathematical analysis of cell migration models, and will design diagnostic tools to identify key parameters that cause and control these patterns and interfaces.
Governance of Agile Software Development Projects. The aim of the project is to generate theoretical knowledge on how to govern agile teams effectively. Effective governance of software development projects is essential for companies to protect their information technology investments. Nowadays, companies have migrated to agile software development where requirements and solutions evolve iteratively and change frequently; yet formal approaches to governance (eg steering committee and detailed pl ....Governance of Agile Software Development Projects. The aim of the project is to generate theoretical knowledge on how to govern agile teams effectively. Effective governance of software development projects is essential for companies to protect their information technology investments. Nowadays, companies have migrated to agile software development where requirements and solutions evolve iteratively and change frequently; yet formal approaches to governance (eg steering committee and detailed plans) are ineffective and impede flexibility, agility and creativity. This project aims to identify informal governance approaches for agile projects based on team embeddedness and network theory. With this knowledge, management could ensure projects deliver value at an acceptable cost, quality and timescale.Read moreRead less
Governing vs. opposition parties and the global financial crisis: Comparing the United Kingdom and Australia. The Australian Prime Minister has described the global financial crisis as the 'equivalent of a rolling national security crisis'. Our project, which examines the pressures upon political parties to adopt an adversarial approach to crises as an election approaches, benefits the nation by enhancing our understanding of how political systems cope with crisis. Should governing and oppositio ....Governing vs. opposition parties and the global financial crisis: Comparing the United Kingdom and Australia. The Australian Prime Minister has described the global financial crisis as the 'equivalent of a rolling national security crisis'. Our project, which examines the pressures upon political parties to adopt an adversarial approach to crises as an election approaches, benefits the nation by enhancing our understanding of how political systems cope with crisis. Should governing and opposition parties unite in order to tackle the national crisis and portray consensus to the outside world? Or should they continue to engage in routine adversary criticism, facilitating dialogue and providing a 'check' on a centralised response? Our research will help develop an understanding of Australia's capacity to respond to major economic threats.Read moreRead less
Stability Analysis of Power System with Massive Power Electronic Devices. The decarbonization of Australia's power systems is to integrate massive renewable energy sources which are interfaced with many power electronic devices (PEDs). The fast and complex dynamics of PEDs have significantly changed the nature of the power system, which limits the applicability of existing tools and methods to assess its stability. The goal of this project is to gain a comprehensive insight into the stability of ....Stability Analysis of Power System with Massive Power Electronic Devices. The decarbonization of Australia's power systems is to integrate massive renewable energy sources which are interfaced with many power electronic devices (PEDs). The fast and complex dynamics of PEDs have significantly changed the nature of the power system, which limits the applicability of existing tools and methods to assess its stability. The goal of this project is to gain a comprehensive insight into the stability of a futuristic power system with high penetration of PEDs. The intended outcomes will be a model and data jointly driven methodology for high-efficient and real-time stability assessment. The methodology developed in this project will support Australia's transition to a stable, secure, and low-carbon power grid.Read moreRead less
Attracting, preparing, and sustaining quality teachers in early education. This project aims to address the chronic shortage of early childhood teachers in Australia, which is compromising quality and return on investment in early education. The project expects to generate new understandings about this specialist teacher workforce through an innovative, ecological, longitudinal design that will track early childhood teachers’ career trajectories and develop a world-first tool to assess early chi ....Attracting, preparing, and sustaining quality teachers in early education. This project aims to address the chronic shortage of early childhood teachers in Australia, which is compromising quality and return on investment in early education. The project expects to generate new understandings about this specialist teacher workforce through an innovative, ecological, longitudinal design that will track early childhood teachers’ career trajectories and develop a world-first tool to assess early childhood teacher quality. Findings are expected to inform policy— including the Australian Government-endorsed 10-year national Workforce Strategy and the Australian Government's Early Years Strategy— to support the future sustained supply of a quality early childhood teacher workforce and improve outcomes for young children.Read moreRead less