Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The mainten ....Invariants of singular spaces from noncommutative geometry. The project addresses questions of significance at the international forefront in the mathematical sciences and the ARC funds will enable research training of students and postdoctoral fellows at this very high level. International collaboration and networking is a key feature that will enhance Australia's scientific standing and provide opportunities for early career researchers to engage internationally with world leaders. The maintenance of a high quality research program at ANU enhances Australia's ability to attract international students and places the ANU in the top league of world universities. It brings with it recognition of Australia as a culturally advanced nation.Read moreRead less
Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has econom ....Markov invariants and phylogenetic tree reconstruction. The project will assist Australia to progress as an innovator in the production phylogenetic tree reconstruction techniques.
Identifying species is a difficult task with environmental, social and economic benefits to Australia. DNA evidence and phylogenetic methods clearly achieve this task. Conservation of rare species depends upon identification and hence robust phylogenetic analysis. Phylogenetically identifying fish species has economic importance as different fish species are all managed separately, having different catch limits, catch areas and market values. Using effective phylogenetic methods, epidemiologists can track the spread of a disease through a population. 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
Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The ....Linear Dynamical Quantum Networks: Synthesis and Control. Australia is recognized as a leader in the international race to develop quantum technologies of the future. This project will strengthen Australia's profile in quantum technology engineering by developing a new theory for building arbitrary complex linear quantum mechanical control systems for control tasks in quantum technology, and presenting new control system design tools to support high performance quantum communication systems. The project outcomes together with advances in experimental physics are anticipated to play an important role in the long term as enablers of viable quantum technologies that can provide new commercial opportunities for Australian hi-tech industries to benefit Australia's economy in the future.Read moreRead less
Robust and Distributed Control of Quantum Systems. Australia has considerable strengths in quantum technology research. As these technologies advance, the issue of control and in particular feedback control becomes a critical one. This research project will strengthen Australia's position in quantum technology by developing new methodologies for designing high performance robust and distributed feedback controllers for quantum systems. The project will also add to Australia's strength in quantum ....Robust and Distributed Control of Quantum Systems. Australia has considerable strengths in quantum technology research. As these technologies advance, the issue of control and in particular feedback control becomes a critical one. This research project will strengthen Australia's position in quantum technology by developing new methodologies for designing high performance robust and distributed feedback controllers for quantum systems. The project will also add to Australia's strength in quantum technology by contributing to the research training of young researchers with expertise both in control systems engineering and quantum technology. This project will help Australia reap the maximum possible benefit from the new industries to emerge from the field of quantum technology.Read moreRead less
Robust Feedback Control in Quantum Technology. Australia has considerable strengths in quantum technology research. As these technologies advance, the issue of control and in particular feedback control becomes a critical one. This research project will strengthen Australia's position in quantum technology by developing new methodologies for designing high performance robust feedback controllers for quantum systems. The project will also add to Australia's strength in quantum technology by contr ....Robust Feedback Control in Quantum Technology. Australia has considerable strengths in quantum technology research. As these technologies advance, the issue of control and in particular feedback control becomes a critical one. This research project will strengthen Australia's position in quantum technology by developing new methodologies for designing high performance robust feedback controllers for quantum systems. The project will also add to Australia's strength in quantum technology by contributing to the research training of young researchers with expertise both in control systems engineering and quantum technology. This project will help Australia reap the maximum possible benefit from the new industries to emerge from the field of quantum technology.
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Quantitative dynamics of functional magnetic resonance imaging. By modeling and verifying the dynamics of brain activity and blood flow that underlie functional magnetic resonance imaging (fMRI), this project will yield improved scientific outcomes and imaging sensitivity. The new data analysis techniques and technologies that result will yield potentially patentable intellectual property, and will increase the standing of Australia in this rapidly developing field, including via links being bu ....Quantitative dynamics of functional magnetic resonance imaging. By modeling and verifying the dynamics of brain activity and blood flow that underlie functional magnetic resonance imaging (fMRI), this project will yield improved scientific outcomes and imaging sensitivity. The new data analysis techniques and technologies that result will yield potentially patentable intellectual property, and will increase the standing of Australia in this rapidly developing field, including via links being built to leading international workers. The National Research Priority Goals of Frontier Technologies, Breakthrough Science, Smart Information Use, and Promoting an Innovation Economy will thus be advanced.Read moreRead less
A new asymptotic toolbox for nonlinear discrete systems and particle chains. This project aims to pioneer a mathematical toolbox of new asymptotic techniques for discrete systems driven by vanishingly small influences. The purpose of these techniques is to permit the asymptotic study of discrete problems in which significant effects originate due to subtle causes that are invisible to existing asymptotic methods. Discrete systems play a significant role in modern applied mathematics, and it is v ....A new asymptotic toolbox for nonlinear discrete systems and particle chains. This project aims to pioneer a mathematical toolbox of new asymptotic techniques for discrete systems driven by vanishingly small influences. The purpose of these techniques is to permit the asymptotic study of discrete problems in which significant effects originate due to subtle causes that are invisible to existing asymptotic methods. Discrete systems play a significant role in modern applied mathematics, and it is vital that mathematical tools be designed in order to explore their behaviour. The aim of this project is to open new pathways for resolving open scientific problems, providing benefits such as understanding the energy dissipation of particle chains and granular lattices contained in small-scale technological components.Read moreRead less
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
Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Exp ....Prediction of inertial particle focusing in curved microfluidic ducts. This project aims to develop mathematical models to predict migration of particles suspended in flow through curved microfluidic ducts and their focusing by size to different regions in the cross-section of the duct. New knowledge in mathematics and engineering will be generated through models that capture the two-way force balance between fluid and particles and by a novel use of asymptotics for computational efficiency. Expected outcomes are understanding of the physics that drives particle migration and the parameters that may be used to control particle focusing. This will benefit design and operation of microfluidic devices for particle sorting as required for "liquid biopsy", the isolation of cancer cells in a routine blood sample.Read moreRead less