Deep Coal Mining. The occurrence of progressively larger gas outbursts, coal bumps, and the potential for the catastrophic collapse of coal pillars is of increasing importance as mining drives deeper in seams rich in methane and other hydrocarbons. This study will address this issue by examining the roles of stress level, strain-rate, gas desorption rate, and drained and undrained gas and liquid pressures in the dynamic failure of coal, while simultaneously evaluating the promise and fidelity of ....Deep Coal Mining. The occurrence of progressively larger gas outbursts, coal bumps, and the potential for the catastrophic collapse of coal pillars is of increasing importance as mining drives deeper in seams rich in methane and other hydrocarbons. This study will address this issue by examining the roles of stress level, strain-rate, gas desorption rate, and drained and undrained gas and liquid pressures in the dynamic failure of coal, while simultaneously evaluating the promise and fidelity of a variety of hazard indices and precursive signals.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
Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in ....Representations of dynamical systems, amenability, and proper actions. Mathematicians study abstract objects by representing them in terms of well-understood concrete models, and need to know when a representation is faithful, in the sense that the model contains complete information. Dynamical systems are an abstraction of physical systems suitable for studying time evolution and symmetries. The project aims to determine when important representations of dynamical systems are faithful, or, in mathematical language, when the dynamical system is amenable. The proposed strategy involves extending Rieffel's notion of proper actions; the construction should be of wide applicability apart from the intended applications to amenability.Read moreRead less
The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problem ....The structure of quantum groups. We propose to study the structure of mathematical objects used in describing symmetries of micro-scale phenomena. The project will significantly develop already well established Australian-Korean cooperation in this exciting and rapidly growing area of research. The results will be immediately applicable to related fields of mathematics, most notably to noncommutative geometry. In the long run, the outcomes will help in better understanding of fundamental problems of modern quantum physics.Read moreRead less
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
Ditopic receptors for the cooperative binding of cations and anions. This project is concerned with the design, synthesis and investigation of new receptor molecules that are capable of simultaneously binding metal cations and anions in a cooperative fashion. The new systems are based on a macrocyclic platform which acts as the metal binding site together with side-arms incorporating functional groups that are designed to cooperatively interact with a suitable anion. Potential applications exist ....Ditopic receptors for the cooperative binding of cations and anions. This project is concerned with the design, synthesis and investigation of new receptor molecules that are capable of simultaneously binding metal cations and anions in a cooperative fashion. The new systems are based on a macrocyclic platform which acts as the metal binding site together with side-arms incorporating functional groups that are designed to cooperatively interact with a suitable anion. Potential applications exist for this category of ditopic receptors in mineral processing where the ability to extract a metal as its metal salt may lead to more efficient solvent extraction processes.Read moreRead less
The Genesis and Tectonic Setting of Iron Oxide Associated Mineralisation in Germany and South Australia. FeOx associated mineralisations are not restricted to Olympic Dam and Ernest Henry types but occur in various geological settings, e.g. the Mt Painter and Olary region, S A. Ocurrences in Central Europe (Erzgebirge, Harz/Calvörde) contain U and other metals, their structural setting is well recorded. Together with the Bergakademie Freiberg, Germany, and the University of Nancy, France, these ....The Genesis and Tectonic Setting of Iron Oxide Associated Mineralisation in Germany and South Australia. FeOx associated mineralisations are not restricted to Olympic Dam and Ernest Henry types but occur in various geological settings, e.g. the Mt Painter and Olary region, S A. Ocurrences in Central Europe (Erzgebirge, Harz/Calvörde) contain U and other metals, their structural setting is well recorded. Together with the Bergakademie Freiberg, Germany, and the University of Nancy, France, these mineralisations shall be investigated with modern geological and geochemical methods to develop a unifying model for the genesis of iron oxide associated U-metal-REE deposits. This will help identifying exploration targets and distinguish different types of mineralisation upon their genetic setting.Read moreRead less