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
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include po ....New mathematics for lipids and cells: structured models for atherosclerosis. The project aims to create new mathematical theory for immune cell behaviour which leads to heart attacks and strokes. This includes formulation and analysis of new types of mathematical models for atherosclerotic plaque development, leading to the creation of new mathematical tools to investigate cell fate in plaques and to generate new hypotheses for experimental research. Expected outcomes of this project include powerful and reliable mathematical models ready for application, and national and international collaborations with scientists and mathematicians. This should provide significant benefits including increased capacity to use mathematical models in vascular biology and training young researchers in interdisciplinary methods.Read moreRead less
Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
Special Research Initiatives - Grant ID: SR0354716
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainabilit ....Energetically Open Systems Research Network Study. Conceptual frameworks arising in the physical sciences, such as non-equilibrium statistical mechanics and thermodynamics, synergetics, chaos and dynamical systems theory, are seminal in the emerging science of complexity. This study will lay the groundwork for a network to link Australian and overseas research on these fundamental concepts, and their application within the context of entropy-producing systems vital to the long-term sustainability of the earth - oceans, atmosphere, biosphere, CO2-free energy production, space and solar environment. The network would facilitate the development of young investigators and be linked into wider complex systems networks such as the CSIRO Centre for Complex Systems Science.Read moreRead less
Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a frame ....Liquidity in financial markets. This project aims to develop a theory which models the effect of liquidity on option prices under different market conditions. Economic or financial crises are inevitable and affect economics. During or after a major financial crisis, market liquidity usually becomes risky and needs to be studied. Through both empirical and theoretical explorations, this project will quantify and measure liquidity risk and its effect on the options markets. It will develop a framework to help market regulators manage illiquidity, enhance the efficiency of option trading in illiquid markets and help in the detection of market manipulation.Read moreRead less
From individuals to mass organisation: aggregation, synchronisation and collective movement in locusts. By combining field biology, robotics and mathematics, this project will determine how animals flock or swarm and, in particular, how locust nymphs control their collective movement over their lifetime. The mathematical models derived during the project will be directly applied to controlling outbreaks of locusts in Australia, South and North Africa.
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
New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less