Stochastic methods in mathematical geophysical fluid dynamics. We will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical
climate forecasting. We will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisti ....Stochastic methods in mathematical geophysical fluid dynamics. We will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical
climate forecasting. We will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisticated mathematics, this project investigates how to parameterize the fast and small processes by using stochastic processes in a controllable and adaptive way.Read moreRead less
Western Australia severe weather prediction: optimising forecasts using new data sources and improved high-resolution models. WA suffers unusually high exposure to severe tropical and extra-tropical weather, from its size and geographical location. This project will develop enhanced data assimilation and modelling techniques, using emerging high-resolution satellite and other data to improve the timeliness, accuracy and reliability of weather forecasts for WA. Outcomes include: improved forecas ....Western Australia severe weather prediction: optimising forecasts using new data sources and improved high-resolution models. WA suffers unusually high exposure to severe tropical and extra-tropical weather, from its size and geographical location. This project will develop enhanced data assimilation and modelling techniques, using emerging high-resolution satellite and other data to improve the timeliness, accuracy and reliability of weather forecasts for WA. Outcomes include: improved forecast systems for predicting severe weather affecting WA (and consequently Australia), and ensemble forecast systems that provide valuable probabilistic information, such as confidence limits in the forecasts. Better forecasts issued earlier for severe weather events will allow appropriate planning and management measures, thereby reducing their present high social and economic cost.Read moreRead less
Stochastic Methods in Mathematical Geophysical Fluid Dynamics. The project will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical climate forecasting. The project will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scale ....Stochastic Methods in Mathematical Geophysical Fluid Dynamics. The project will develop analytical and numerical methods for long-term weather forecasting and climate modelling. The project deals with the mathematical aspects and fundamental mechanisms underpinning numerical climate forecasting. The project will develop new methodology for accurate modelling of the important and dominant slow global processes without explicitly resolving the precise detail of the weather of each day at all scales. Using sophisticated mathematics, this project investigates how to parameterize the fast and small processes by using stochastic processes in a controllable and adaptive way.Read moreRead less
Geometric Methods in Geophysical Fluid Dynamics. The need for a reliable weather forecast has never been more evident. This project addresses fundamental problems which are obstacles to more accurate weather forecasts. The dynamics of the atmosphere and the oceans is inherently complex. The complexity of the flow is confined though by conservation laws. This observation has not yet been used in current weather models. These conservation laws will be the guiding principle for the design of a stab ....Geometric Methods in Geophysical Fluid Dynamics. The need for a reliable weather forecast has never been more evident. This project addresses fundamental problems which are obstacles to more accurate weather forecasts. The dynamics of the atmosphere and the oceans is inherently complex. The complexity of the flow is confined though by conservation laws. This observation has not yet been used in current weather models. These conservation laws will be the guiding principle for the design of a stable numerical integration scheme.
Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will ....Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will include all these effects to answer timely
and important astronomical
questions such as: can planets survive life in
a cluster? how do interactions between stars
affect the chemical enrichment of
clusters and galaxies?Read moreRead less
New and computationally feasible methods of constructing efficient and exact confidence limits from count data. Biological and health science data is commonly in the form of counts. The statistical analysis of such data should be (a) efficient i.e. it should not, in effect, throw away valuable data, (b) exact i.e. it should have precisely known statistical properties and (c) computationally feasible. Kabaila and Lloyd (1997-2001) have proposed and analysed a radically new method of confidence li ....New and computationally feasible methods of constructing efficient and exact confidence limits from count data. Biological and health science data is commonly in the form of counts. The statistical analysis of such data should be (a) efficient i.e. it should not, in effect, throw away valuable data, (b) exact i.e. it should have precisely known statistical properties and (c) computationally feasible. Kabaila and Lloyd (1997-2001) have proposed and analysed a radically new method of confidence limit construction which, for the first time, possesses all of these requirements. The purpose of the project is to establish further theoretical support for the new method, to develop efficient computational algorithms and to write easy-to-use computer programs for its practical use.Read moreRead less
ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.Read moreRead less
Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also ....Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also applicable to microscopic systems. The expressions will determine the probability that finite sized systems will violate the Second Law for small periods of time and will therefore contribute to development of a fundamental understanding of microscopic systems and the development of nanotechnology.
Read moreRead less
Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these dev ....Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these developments by: generalizing a theorem which relates transport coefficients to chaoticity; detailed studies of the influence of thermostatting mechanisms on nonequilibrium chaoticity and fluctuations, and by understanding the range of applicability of a nonequilibrium fluctuation theorem for non-isoenergetic systems.Read moreRead less