Modelling large urban transport networks using stochastic cellular automata. Urban traffic congestion is a major social, economic and environmental problem, and to overcome it we need reliable and flexible mathematical models of traffic flow. This project will introduce and study new mathematical traffic models, and use them to study innovative traffic signal systems for our arterial roads, freeways, and tram routes.
Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what i ....Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what is the best one can do? Secondly to provide then tight error bounds for the control design;
thirdly to develop new methods for some hitherto unresolved problems in system identification.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE180101098
Funder
Australian Research Council
Funding Amount
$374,200.00
Summary
New mathematical theory for fluid motion on surfaces with holes. This project aims to develop new explicit mathematical results to enhance the understanding of potential theory – a fundamental area of mathematics - on surfaces with complicating geometrical properties. There are very few such fundamental results on complicated curved surfaces, such as those with holes. This project should provide a toolbox for solving many different mathematical problems on curved surfaces. The new results should ....New mathematical theory for fluid motion on surfaces with holes. This project aims to develop new explicit mathematical results to enhance the understanding of potential theory – a fundamental area of mathematics - on surfaces with complicating geometrical properties. There are very few such fundamental results on complicated curved surfaces, such as those with holes. This project should provide a toolbox for solving many different mathematical problems on curved surfaces. The new results should also have application to the analysis of fluid flows over porous media and practical engineering structures.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL110100020
Funder
Australian Research Council
Funding Amount
$3,057,554.00
Summary
Consensus, estimation and control in complex large-scale quantum systems. Australia has considerable strengths in quantum technology research and as these technologies advance, the issue of control becomes a critical one. This project will strengthen Australia's position in quantum technology by developing new methodologies for designing high performance controllers and estimators for complex quantum systems.
Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscal ....Suspension flows and particle focusing in curved geometries. The project aims to develop fast predictive tools to investigate suspension flows in curved channels and thin ducts and the effect of channel geometry on the focusing of particles by weight to different regions of the channel. Interaction between particles and fluid in suspension flows is a fundamental problem that is little understood but which is important in a wide range of problems in nature and industry (eg for design of microscale segregation devices for separation of different cells in a blood sample, and of macroscale devices for separation of mineral particles from crushed ore). At present, the description of these processes is qualitative, with quantitative understanding seen as a challenge without intensive computation. The project plans to develop, solve and validate mathematical models to give a quantitative understanding of these processes.Read moreRead less
Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular ....Algebraically informed models of biological sequence evolution. To make sense of the patterns they see in the natural world, biologists across fields as diverse as genetics, epidemiology and biogeography need an accurate picture of evolutionary history. DNA sequences provide an exciting means to establish this picture of the past, but to decode it successfully requires mathematical models of how DNA evolves. Mathematical inconsistencies have been identified with current approaches. In particular, understanding the effect of natural selection in different parts of the tree of life requires models that behave robustly in the face of shifting evolutionary processes. This project aims to use insights from algebraic methods to construct mathematically consistent models of wide biological utility.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130100423
Funder
Australian Research Council
Funding Amount
$369,061.00
Summary
Group theory and phylogenetics: exploiting symmetry to uncover evolutionary history. Using advanced algebra, structural symmetries inherent in phylogenetic methods will be studied and improved approaches will be derived. DNA sequences contain a wealth of information about evolutionary events that occurred millions of years ago, but extracting this information requires the application of robust methods.
Discovery Early Career Researcher Award - Grant ID: DE130100031
Funder
Australian Research Council
Funding Amount
$333,684.00
Summary
Mathematical modelling of the complex mechanics of biological materials and their role in tissue function and development. The mechanics of biological materials is complicated because they consist of many components such as fibres, proteins and polymers. We aim to use mathematical tools to understand how these components interact in tissues such as the spinal disc which will aid the development of new treatments to reverse the effects of injury, disease or aging.
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
Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of ....Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of the art mathematical techniques in exponential asymptotics to address this deficiency in the classical theory, and provide a deeper understanding of pattern formation, instabilities and wave propagation on the interface between two fluids.Read moreRead less