The role of low-energy excited states in solar-energy capture. This project aims to determine the nature and role of the lowest-energy excited states in most natural photosynthetic reaction centres and light-harvesting complexes. The lowest-energy states of bacterial reaction centres are critical to function and are used as a paradigm in artificial organic solar-energy capture, but for most photosystems their nature remains unknown. The project aims to answer the critical question of why they do ....The role of low-energy excited states in solar-energy capture. This project aims to determine the nature and role of the lowest-energy excited states in most natural photosynthetic reaction centres and light-harvesting complexes. The lowest-energy states of bacterial reaction centres are critical to function and are used as a paradigm in artificial organic solar-energy capture, but for most photosystems their nature remains unknown. The project aims to answer the critical question of why they do not actually prevent function. It is expected that both the outcomes obtained and techniques developed will be directly relevant to solar-energy device design. The project will apply five existing, complimentary and purposely built spectrometers as well as quantum electronic and nuclear simulation techniques to identify and characterise three key systems.Read moreRead less
Enabling three dimensional stochastic geological modelling. This project aims to develop technologies to mitigate three dimensional (3D) geological risk in resources management. This project expects to create new knowledge and methods in the field of 3D geological modelling through the innovative application of mathematical methods, structural geology concepts and probabilistic programming. The expected outcomes are an enhanced capability to model the subsurface, characterise model uncertainty a ....Enabling three dimensional stochastic geological modelling. This project aims to develop technologies to mitigate three dimensional (3D) geological risk in resources management. This project expects to create new knowledge and methods in the field of 3D geological modelling through the innovative application of mathematical methods, structural geology concepts and probabilistic programming. The expected outcomes are an enhanced capability to model the subsurface, characterise model uncertainty and test multiple geological scenarios. This enhanced capability is important for the future of Australia's subsurface management, including urban geology and our continuously growing sustainable resources industry.Read moreRead less
HARMONIC ANALYSIS AND BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS. It is of the utmost necessity for Australia to develop the theoretical
expertise needed in the current era. The type of mathematics under
investigation here is closely allied to that needed in much of the
current boom in communication technology and medical research. The
training which would be provided to the research associates is
considerable, and would flow on to produce the expertise needed to
keep the coming gen ....HARMONIC ANALYSIS AND BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS. It is of the utmost necessity for Australia to develop the theoretical
expertise needed in the current era. The type of mathematics under
investigation here is closely allied to that needed in much of the
current boom in communication technology and medical research. The
training which would be provided to the research associates is
considerable, and would flow on to produce the expertise needed to
keep the coming generation involved in modern technological development. I will maintain my large collaborative effort with
leading mathematicians from the US, France and other countries, thus
helping to keep Australia at the forefront of a significant field of
research.Read moreRead less
HARMONIC ANALYSIS OF ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS. It is of the utmost necessity for Australia to develop the theoretical expertise needed in the current era. The type of mathematics under investigation here is closely allied to that needed in much of the current boom in communication technology and medical research. The training which would be provided to the research associates is considerable, and would flow on to produce the expertise needed to keep the coming generation invol ....HARMONIC ANALYSIS OF ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS. It is of the utmost necessity for Australia to develop the theoretical expertise needed in the current era. The type of mathematics under investigation here is closely allied to that needed in much of the current boom in communication technology and medical research. The training which would be provided to the research associates is considerable, and would flow on to produce the expertise needed to keep the coming generation involved in modern technological development. I will maintain my active collaborative effort with leading mathematicians from the US, France and other countries, thus helping to keep Australia at the forefront of a significant field of research.Read moreRead less
Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Sc ....Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations. Read moreRead less
Physics of Risk: new tools to survey the Australian market and beyond. The lives of most Australians depend on the dynamics of financial markets that affects investments, savings, business, employment, growth, wealth and -ultimately- the daily functioning of our society. Understanding, monitoring and managing the dynamics of financial markets is of crucial importance to policy-makers, financial institutions and businesses that are increasingly faced with managing risk, planning strategies and ta ....Physics of Risk: new tools to survey the Australian market and beyond. The lives of most Australians depend on the dynamics of financial markets that affects investments, savings, business, employment, growth, wealth and -ultimately- the daily functioning of our society. Understanding, monitoring and managing the dynamics of financial markets is of crucial importance to policy-makers, financial institutions and businesses that are increasingly faced with managing risk, planning strategies and taking decisions in an increasingly complex market-place. The project is also of importance to the continued evolution of physics in this country contributing to the emergence of a strong new area of statistical physics concerned with the ?real world? in a manner hitherto unknown.Read moreRead less
HARMONIC ANALYSIS, BOUNDARY VALUE PROBLEMS, AND MAXWELL'S EQUATIONS IN LIPSCHITZ DOMAINS. Boundary value problems for partial differential equations arise naturally when physical problems are expressed in mathematical terms. This project concerns the systematic development of the harmonic analysis of partial differential operators, and of the corresponding boundary integrals in order to solve such problems on irregular regions. Particular emphasis is given to studying the behaviour of electrom ....HARMONIC ANALYSIS, BOUNDARY VALUE PROBLEMS, AND MAXWELL'S EQUATIONS IN LIPSCHITZ DOMAINS. Boundary value problems for partial differential equations arise naturally when physical problems are expressed in mathematical terms. This project concerns the systematic development of the harmonic analysis of partial differential operators, and of the corresponding boundary integrals in order to solve such problems on irregular regions. Particular emphasis is given to studying the behaviour of electromagnetic waves both inside and outside irregularly shaped surfaces, and their propagation through it.Read moreRead less
Harmonic analysis of differential operators in Banach spaces. This proposal aims to develop harmonic analysis (the mathematical tools used in digital music and photography) in new contexts. It focuses on boundary value problems (the theory behind medical or geological imaging) and stochastic equations (which describe phenomena with random components such as the behaviour of financial markets).
Three-dimensional Bayesian Modelling of Geological and Geophysical data. The project aims to develop technologies enabling rapid informed decision-making related to the management of natural resources, including critical metals, copper and water. This new technology will support a greener future, securing our energy future, our access to clean water and reduce the mining footprint. Expected outcomes include an enhanced capability in interoperable, integrated three-dimensional geological and geop ....Three-dimensional Bayesian Modelling of Geological and Geophysical data. The project aims to develop technologies enabling rapid informed decision-making related to the management of natural resources, including critical metals, copper and water. This new technology will support a greener future, securing our energy future, our access to clean water and reduce the mining footprint. Expected outcomes include an enhanced capability in interoperable, integrated three-dimensional geological and geophysical modelling in order to predictively characterise sub-surface geology. The outcome will be an open-source forecasting dashboard enabling decision making while considering underlying risk related to resource extractions and management with significant benefits to the Australian society (lower emissions, clean water).Read moreRead less