Dynamic Analysis and Control for Hybrid Systems and Networks. Hybrid systems are now accepted as the best way to model many high-tech situations in transport, energy management, networking, household and industrial automation. This project will develop the theoretical tools needed to ensure such systems operate stably and efficiently despite imperfections and outside disturbances.
Modelling, forecasting, and control for econometrics based on generalized dynamic factor models: a system theoretic approach. The project will provide a tool that will assist organizations wishing to understand the dynamics of a national economy to model it, and to forecast future econometric time series values. Such ability will provide another tool to econometric managers, including the Reserve Bank , Treasury and fund managers, that should benefit the Australian nation.
Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an i ....Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an important contribution towards building a strong local knowledge base by addressing the problem of understanding the glassy state. The knowledge base can then serve as a springboard for possible high tech applications in materials science and engineering.Read moreRead less
Studies of turbulence and coherent structures in quasi two-dimensional plasmas and fluids. One of the most celebrated but least understood complex systems in nature is turbulent flow. This cross-disciplinary project aims to contribute to basic scientific knowledge of a class of turbulent flows, known as quasi two-dimensional fluids, that typically exhibit self-organizing properties, stable sheared flow, and relatively weak dissipation. The significance lies in the proposed testing, by modelling ....Studies of turbulence and coherent structures in quasi two-dimensional plasmas and fluids. One of the most celebrated but least understood complex systems in nature is turbulent flow. This cross-disciplinary project aims to contribute to basic scientific knowledge of a class of turbulent flows, known as quasi two-dimensional fluids, that typically exhibit self-organizing properties, stable sheared flow, and relatively weak dissipation. The significance lies in the proposed testing, by modelling and simulation studies, of the well-grounded hypothesis that suppression of turbulence by sheared flow is a universal phenomenon in such fluids, and that it can be exploited to control transport of fluid constituents. Applications of this new knowledge will be developed.Read moreRead less
A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less
Interactions of Human and Machine Intelligence in Modern Economic Systems. Much of modern economic systems are driven by machine-machine and machine-human interactions that happens rapidly at large scale. But such interactions are often opaque and can have negative or catastrophic consequences, such as market plunges with no apparent economic reasons in financial trading, content recommendations that promote extremism, algorithms in gig economy leading to worker exploitation and wasted resources ....Interactions of Human and Machine Intelligence in Modern Economic Systems. Much of modern economic systems are driven by machine-machine and machine-human interactions that happens rapidly at large scale. But such interactions are often opaque and can have negative or catastrophic consequences, such as market plunges with no apparent economic reasons in financial trading, content recommendations that promote extremism, algorithms in gig economy leading to worker exploitation and wasted resources. This project aims for new theoretical results and algorithms at the intersection computational economics, game theory, and dynamical systems, that establish conditions under which the economic systems are stable, propose mechanisms that make the interactions more fair, transparent and aligned with human values.Read moreRead less
Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of di ....Navigating tipping points in complex dynamical systems. This project aims to use applied mathematics to investigate the onset of tipping points in dynamical systems. Working with clinicians and practicing engineers, the project aims to contribute to the development of new treatment regimes for dynamical diseases and develop improved management strategies for resource focussed engineering industries. This should provide significant benefit to many areas, including the personalised treatment of disease.Read moreRead less
Rogue waves in oceans and optical fibres. Rogue waves can sink large ships in the ocean. They appear more commonly than previously thought. Optical rogue waves, the laboratory counterparts of extreme ocean waves, will allow the project to study the main features of the phenomenon, provide the theoretical explanation for their existence and potentially help to eliminate these catastrophic events.
Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomeno ....Exploding solitons. This project builds on previous work in which the existence of exploding solitons was confirmed. Explosions occur regularly in a variety of systems with continuous supply and dissipation of energy. Exploding solitons are more common than ordinary dissipative solitons and occupy large areas in the parameter space. They can be generated relatively easily, however the phenomenon is highly complex. This project aims to further understand exploding solitons so that the phenomenon can be used for the generation of pulses with wide spectral output similar to `supercontinuum’ radiation. Research in this direction will provide the basis for building powerful laser sources with wide spectral output.Read moreRead less