Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limit ....Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limitations and the convergence properties of the proposed
algorithms. The outcomes will be widely applicable in modelling of
large scale and complex data as is encountered in areas of
bioinformatics, physics and experimental studies of complex systems.
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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
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
Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linea ....Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linear scaling electronic structure codes, methods that are critical to the study of nano- and bio-materials, and are therefore of great importance to our economic future and medical well being. The project will build expertise within Australia in the area of interval arithmetic, an area that is currently poorly represented.Read moreRead less
NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's p ....NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's plates move and
interact now and in the past and how the structure of the continents
arose.
Not only is this intrinsically interesting, it
will also be of immediate practical benefit to geological modelers.Read moreRead less
Black Hole Accretion: The Effects of Magnetic Fields and Radiation. This project represents a significant contribution by Australian researchers to one of Science's Big Questions: How do Black Holes channel gravitational energy into radiation at many different energies and into high speed outflows. It offers Australian Astronomy an opportunity to expand its endeavours into the rapidly growing and high profile areas of high-energy and computational astrophysics, injecting new expertise into the i ....Black Hole Accretion: The Effects of Magnetic Fields and Radiation. This project represents a significant contribution by Australian researchers to one of Science's Big Questions: How do Black Holes channel gravitational energy into radiation at many different energies and into high speed outflows. It offers Australian Astronomy an opportunity to expand its endeavours into the rapidly growing and high profile areas of high-energy and computational astrophysics, injecting new expertise into the interpretation of multi-wavelength data on accreting black holes. We will train a new cohort of internationally competitive students and early career researchers, equipping them with the advanced computational and modelling skills that are in increasingly higher demand in many technology-based industries.Read moreRead less
The link between the deep Earth and its dynamic surface. Modelling the two-way interaction of plate tectonics with the actions of erosion and sedimentation gives a fundamentally new view of the dynamics of our planet and the importance of the surface on the deep interior. It will improve our understanding of the formation of sedimentary basins, their evolution and their preservation over geological time.
A semiclassical approach to spectral theory. Spectral theory is the branch of mathematics dealing with natural frequencies (eigenvalues) and modes of vibration (eigenfunctions) of systems arising in geometry, quantum physics and engineering. As such, they have important applications in seismic and medical imaging, nanotechnology, and optical communications. This project aims to use recently developed mathematical tools to advance our understanding of high energy eigenvalues and eigenfunctions, a ....A semiclassical approach to spectral theory. Spectral theory is the branch of mathematics dealing with natural frequencies (eigenvalues) and modes of vibration (eigenfunctions) of systems arising in geometry, quantum physics and engineering. As such, they have important applications in seismic and medical imaging, nanotechnology, and optical communications. This project aims to use recently developed mathematical tools to advance our understanding of high energy eigenvalues and eigenfunctions, as well as new algorithms for numerically computing them.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