Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized ran ....Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.Read moreRead less
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.Read moreRead less
Computational methods for precise reconstruction of white-matter fibre tracts in the human brain using diffusion tensor imaging. One in five Australians will experience a mental illness. This project will facilitate a new method for: (1) brain researchers to advance the fundamental understanding of mental illnesses and brain disorders; (2) medical clinicians to diagnose and assess the growing incidence of mental illness confronting Australia's ageing population, thereby addressing the ageing wel ....Computational methods for precise reconstruction of white-matter fibre tracts in the human brain using diffusion tensor imaging. One in five Australians will experience a mental illness. This project will facilitate a new method for: (1) brain researchers to advance the fundamental understanding of mental illnesses and brain disorders; (2) medical clinicians to diagnose and assess the growing incidence of mental illness confronting Australia's ageing population, thereby addressing the ageing well and ageing productively national research priority; and, (3) neurosurgeons to guide surgery via localisation of major neural tracts. In addition to contributing to the understanding, diagnosis and treatment of Australia's endemic mental health burden, this project will advance Australia's skill-base and international standing in basic scientific research.Read moreRead less
Ergodic theory and number theory. Recent advances in the theory of measured dynamical systems investigated by the proponents include new versions of entropy, and the study of spectral theory for non-singular systems. These will be further developed in this joint project with the French CNRS. The results are expected to have interesting applications in physics and number theory.
Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which real ....Entropy and maximal entropy in Markov systems. Entropy is a measure of how well-ordered a system is: chaotic systems have high entropy. Two approaches to entropy are available, via the limiting behaviour of the orbits of points, which yields topological entropy, and via the behaviour of the distributions of measures of partitions, yielding measure-theoretic entropy. The topological entropy is the least upper bound of entropies of all possible measures. We study when there is a measure which realises this bound, describing the structure of such systems via Markov and Bratteli diagrams. Our methods will be applied to new versions of entropy for non-singular systems. This will assist in the description of chaotic behaviour.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
Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace de ....Dynamics of eigenvalue/eigenspace algorithms with applications to signal processing. Many problems in signal and systems lead naturally to an eigenvalue/eigenspace determination and tracking problem; for example (acoustic) echo-cancellation, crosstalk suppression in ADSL modems, direction of arrival determination with an array of sensors, linear system identification etc. Exploiting methods from global analysis and dynamical systems theory we will study the available algorithms for eigenspace determination to characterise their computational efficiency, accuracy and effectiveness in various data scenarios. The analysis will lead to improved designs for eigenvalue/eigenspace algorithms, as well as design tools to engineer algorithms to specific situations.Read moreRead less
APEC Cooperation for Earthquake Simulation Visitors Program. This project aims to improve understanding of earthquakes through development of numerical simulation models for the earthquake generation process. Its centerpiece is a major international collaboration, achieved via a visitor exchange program between the headquarters of the APEC Cooperation for Earthquake Simulation in Australia and overseas centres of excellence. Earthquakes are one of the most costly and deadly natural disasters, a ....APEC Cooperation for Earthquake Simulation Visitors Program. This project aims to improve understanding of earthquakes through development of numerical simulation models for the earthquake generation process. Its centerpiece is a major international collaboration, achieved via a visitor exchange program between the headquarters of the APEC Cooperation for Earthquake Simulation in Australia and overseas centres of excellence. Earthquakes are one of the most costly and deadly natural disasters, and APEC member economies have a high earthquake risk. Recent analyses suggest earthquakes may dominate the loss potential in Australia. The complementary research programs offer an opportunity to achieve breakthrough advances in improved methods of earthquake forecasting and hazard quantification.Read moreRead less
Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also ....Lifting the curse of dimensionality - bringing together the quasi Monte Carlo and sparse grid methods. This project is expected to lead to improved methods for handling high-dimensional problems (i.e. problems with many variables) that arise in finance, statistics, commerce, physics, and many other fields. In turn this could lead to significant economic benefit, especially to high-value service industries such as the finance industry. By strengthening international collaboration, it will also help to maintain Australia's strong position in international research in the mathematical sciences.Read moreRead less
Performance analysis of the Unified Power Flow Controller based on multi-bridge converter. The objective of this research is to conceive a new configuration of UPFC without series injection transformers, based on two-level full-bridge modules. The conceived system can be utilized for the power systems to control the power flow through the transmission line.
The benefit is in reducing restrictions on electricity transfer links.
The project will develop a laboratory version of the novel UPFC de ....Performance analysis of the Unified Power Flow Controller based on multi-bridge converter. The objective of this research is to conceive a new configuration of UPFC without series injection transformers, based on two-level full-bridge modules. The conceived system can be utilized for the power systems to control the power flow through the transmission line.
The benefit is in reducing restrictions on electricity transfer links.
The project will develop a laboratory version of the novel UPFC demonstrating the hardware and control requirements for this form of UPFC which could reduce the costs of this corrective solution up to 30% below existing solutions.
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