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.
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
High Dimensional Computation and Uncertainty. This project aims to establish powerful computational methods for high-dimensional problems - methods that are rigorous, and carefully tailored to specific applications, from physics, environment, manufacturing and finance, and often driven by uncertainty. The project will generate new knowledge in the area of high-dimensional computation, and develop technological innovations in key areas of science and industry. Expected outcomes include improved c ....High Dimensional Computation and Uncertainty. This project aims to establish powerful computational methods for high-dimensional problems - methods that are rigorous, and carefully tailored to specific applications, from physics, environment, manufacturing and finance, and often driven by uncertainty. The project will generate new knowledge in the area of high-dimensional computation, and develop technological innovations in key areas of science and industry. Expected outcomes include improved control of uncertainty in industry, enhanced international and interdisciplinary collaborations, and significant publications and presentations in international forums. The technological advancements will help boost Australia's position as a world leader in innovation.Read moreRead less
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.
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.
An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.Read moreRead less
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.
Very high dimensional computation - the new frontier in numerical analysis. High-dimensional problems, involving hundreds or thousands of variables, arise in applications from finance, health statistics and oil reservoir modelling to physics and chemistry. This project aims to develop the science of high-dimensional computation, as driven by important applications such as the flow of groundwater through a porous material.