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
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
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
Function and evolution of optical structures in nature. Designing optical structures that simultaneously satisfy multiple and conflicting criteria and satisfy difficult manufacturing constraints is technologically challenging. However, Nature has been doing this for millions of years. This project is a systematic study of optical structures in one of Nature's most diverse range of species: butterflies. The microstructures inside butterfly scales have an amazing diversity of geometries that produ ....Function and evolution of optical structures in nature. Designing optical structures that simultaneously satisfy multiple and conflicting criteria and satisfy difficult manufacturing constraints is technologically challenging. However, Nature has been doing this for millions of years. This project is a systematic study of optical structures in one of Nature's most diverse range of species: butterflies. The microstructures inside butterfly scales have an amazing diversity of geometries that produce structural colour and are amongst the most complex naturally occurring optical structures produced by a single cell.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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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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