GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative featur ....GEOMETRIC NUMERICAL INTEGRATION. Many scientific phenomena in physics, astronomy, and chemistry, are modelled by ordinary differential equations (ODEs). Often these equations have no solution in closed form, and one relies on numerical integration. Traditionally this is done using Runge-Kutta methods or linear multistep methods. In the last decade, however, we (and others) have discovered novel classes of so-called "geometric" numerical integration methods that preserve qualititative features of certain ODE's exactly (in contrast to traditional methods), leading to crucial stability improvements. Extending concepts from dynamical systems theory and traditional numerical ODEs, this project will improve, extend and systematize this new field of geometric integration.Read moreRead less
Geometric Integration. This project gives an important boost to Australia's strength in the niche area of geometric numerical integration,in the face of strong international competition. It gathers 7 world experts from 5 countries to create new computer programs to improve calculations in dynamics, with applications ranging from astronomy, physics, chemistry, biology, and meteorology to finance. It strengthens Australia's links with the mathematical software industry, and will lead to world-clas ....Geometric Integration. This project gives an important boost to Australia's strength in the niche area of geometric numerical integration,in the face of strong international competition. It gathers 7 world experts from 5 countries to create new computer programs to improve calculations in dynamics, with applications ranging from astronomy, physics, chemistry, biology, and meteorology to finance. It strengthens Australia's links with the mathematical software industry, and will lead to world-class graduates and research training.Read moreRead less
Geometric numerical integration of differential equations. Differential equations (DEs) play a central role in modelling scientific phenomena in physics, biology, chemistry, astronomy, meteorology, and geoscience. We have developed new ways of solving DEs, using geometric integration, which have significant advantages over traditional methods because of the crucial nonlinear stability they provide.
This project, combining 7 world experts from 6 countries and 1 early career researcher, will pl ....Geometric numerical integration of differential equations. Differential equations (DEs) play a central role in modelling scientific phenomena in physics, biology, chemistry, astronomy, meteorology, and geoscience. We have developed new ways of solving DEs, using geometric integration, which have significant advantages over traditional methods because of the crucial nonlinear stability they provide.
This project, combining 7 world experts from 6 countries and 1 early career researcher, will place Australia at the forefront of this intensive international activity.
It will significantly strengthen Australia's links with the mathematical software industry (e.g. Wolfram Research, Inc), and will lead to world class graduates and research training.
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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
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.
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Investigation of 1/f noise mechanisms in HgCdTe heterostructure IR photodiodes. Since the performance of any photon detector is defined by its signal to noise ratio, the reduction of noise generating mechanisms is equally important to improvement of the signal. In this project we propose to carry out, for the first time, a comprehensive analysis of noise generating mechanisms in HgCdTe detectors using recently developed, two-dimensional analysis procedure. The main objective of this project is t ....Investigation of 1/f noise mechanisms in HgCdTe heterostructure IR photodiodes. Since the performance of any photon detector is defined by its signal to noise ratio, the reduction of noise generating mechanisms is equally important to improvement of the signal. In this project we propose to carry out, for the first time, a comprehensive analysis of noise generating mechanisms in HgCdTe detectors using recently developed, two-dimensional analysis procedure. The main objective of this project is to prove that 1/f noise in HgCdTe photodetectors is caused by dark current fluctuations in the high electric field regions of the detector structure. The primary outcome of this work will be the first comprehensive two-dimensional device model that can predict 1/f noise in a semiconductor device.Read moreRead less
Nucleosynthesis today and tomorrow. Australia is a recognised world leader in understanding the interiors of stars and how they make the elements seen all around us, from Carbon to Gold and beyond. This project combines Australian theoreticians with the world's largest telescopes and computers, as well as the latest laboratory instruments and techniques, to further our understanding of where all the elements originated.
Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will ....Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will (i) develop numerical techniques to extend these piece-wise Beltrami states far away from axisymmetry (ii) develop practical tests to determine when existence breaks down (iii) analyze the frequency spectrum of small oscillations about such equilibria (iv) extend the model to two-fluid MHD.Read moreRead less
The role of magnetic fields in star formation. Recently we have performed the world's first calculations of star cluster formation that incorporate the effects of magnetic fields and radiation. This research has recently been brought back to Australia and the goal of this proposal is to extend our competitive edge in this area.
Whilst calculations of the formation of stars gives us fundamental understanding about a very basic physical process in the universe (namely, the conversion of gas into s ....The role of magnetic fields in star formation. Recently we have performed the world's first calculations of star cluster formation that incorporate the effects of magnetic fields and radiation. This research has recently been brought back to Australia and the goal of this proposal is to extend our competitive edge in this area.
Whilst calculations of the formation of stars gives us fundamental understanding about a very basic physical process in the universe (namely, the conversion of gas into stars), the equations we solve and the methods used to solve them, are the same as those used to describe many gases and fluids on earth. Solving these equations in difficult astrophysical regimes develops new methodology which translates readily to earth-bound problems.Read moreRead less
Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscal ....Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel methodology will explore this stumbling block, and promises to radically change the modeling, exploration and understanding of multiscale complex system behaviour.Read moreRead less