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
Derivation and calculation of onsager transport coefficients in mass transport and thermotransport. The transport of matter and heat within solids has a profound effect on the functional properties of engineering components. The current description of mass and heat transport has major failings which then lead to major failings for property predictions. This project will establish a new mathematical framework that will redress the problems.
Mathematics in the round - the challenge of computational analysis on spheres. Real world problems formulated on spheres (including physical problems for the whole earth) provide many difficult challenges. This project aims at developing algorithms to solve problems on spheres in two and higher dimensions, with applications ranging from geophysics to signal analysis.
Theory and applications of three dimensional fractal transformations. The purpose of this project is to develop the theory and algorithms for a new class of continuous mappings between fractals. Outcomes include a better understanding of fractals, substantially better algorithms for fractal compression and many new applications.
Australian Laureate Fellowships - Grant ID: FL120100094
Funder
Australian Research Council
Funding Amount
$3,184,657.00
Summary
Geometric construction of critical solutions of nonlinear systems. Whether we are looking at waves on a beach, the dispersal of herds of animals in a landscape, or the interaction of black holes, their patterns of movement rely on rules expressed by non-linear mathematical models. This project will aim to create new mathematical methods to describe the solutions of non-linear systems, which are ubiquitous in modern science.
Towards a science of high dimensional computation. This project aims to establish scientifically precise methods for high dimensional problems - methods that are mathematically rigorous, empirically tested, and carefully tailored to specific modern applications across physics, environment, and finance. This project expects to generate new knowledge in the area of high dimensional computation and to develop technological innovations in key areas of science and industry. Expected outcomes of this ....Towards a science of high dimensional computation. This project aims to establish scientifically precise methods for high dimensional problems - methods that are mathematically rigorous, empirically tested, and carefully tailored to specific modern applications across physics, environment, and finance. This project expects to generate new knowledge in the area of high dimensional computation and to develop technological innovations in key areas of science and industry. Expected outcomes of this project include enhanced international and interdisciplinary collaborations, and significant publications and presentations in international forums. These technological advancements will help boost Australia’s position as a world leader in creativity and innovation.Read moreRead less
Novel technology for enhanced coal seam gas production utilising mechanisms of stimulated cleat permeability through graded particle injection. This cross-disciplinary project will develop a new integrated technology for well productivity enhancement in coal seam gas, shale, tight gas and geothermal reservoirs - the world’s fastest growing unconventional clean energy resources. It will improve our understanding of the multi scale physics of natural gas and energy production.
Critical solutions of nonlinear systems. Whether we are looking at waves on a beach, the dispersal of herds of animals in a landscape, or the interaction of black holes, their patterns of movement rely on rules expressed by nonlinear mathematical models. This project aims to create new mathematical methods to describe critical solutions of nonlinear systems, which are ubiquitous in modern science.
Discovery Early Career Researcher Award - Grant ID: DE170100171
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to i ....Towards a mathematical description of magneto-hydrodynamic turbulence. The project aims to better predict magneto-hydrodynamic turbulence than existing empirical models. Turbulence in high-speed flows of electrically conductive fluid sustains magnetic fields in various engineering, geophysical, and astrophysical flows. However, investigations into magneto-hydrodynamic flows have been limited to slow flows, and the application of the results to the actual problems hindered. This project aims to improve magneto-hydrodynamic flow control in future energy-generating technology, using theoretical and numerical tools that are mathematically consistent with the high-speed limit of the governing equations. More efficient electric generators could improve Australia’s future energy supply with fewer emissions of global warming gases.Read moreRead less
Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend ....Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend the toolbox of methods for such problems utilising ideas from Banach spaces, convex analysis, parallel computing and optimisation. This project is expected to make a substantial contribution to a better understanding of inverse problems and their solution procedures.Read moreRead less