Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their ....Self-assembly and complexity: networks and patterns from materials to markets. Self-assembly leads the formation of patterns without external directing agents. It is responsible for the growth of complex multiscale structures found in biology and materials science and is a crucial concept for development of viable nanotechnologies. Complex systems, from biological ecosystems to financial markets and the Internet, are also characterized by spontaneous clustering and linkages that determine their collective behaviour. The project will investigate in detail the geometry, topology, materials science and statistical physics of networks, leading to design and characterization of robust self-assembled materials and complex systems.Read moreRead less
Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent math ....Quantum Spectra. Fundamental quantum processes will play a key role in emerging technologies in the twenty-first century across diverse industries including quantum information technology, quantum computers and electronics, quantum optics, nanoscale quantum microscopes and superconductor technology. Australia has a strong base of expertise in the underpinning quantum disciplines. This project in strategic basic research within mathematical physics will develop a comprehensive and consistent mathematical description of quantum processes. This research will lead to a deeper understanding of quantum processes, keep Australia at the leading edge of international developments and increase Australia's capacity to develop and implement these new technologies.Read moreRead less
Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will ....Virtual Star Clusters: The Dynamics and Evolution of Stars and Planets. Most stars are born in star clusters. When stars age
they swell and contract, change composition,
lose mass, and in dense regions they may collide.
Further, about 50% of stars are binary pairs,
and when these swell they can merge or
transfer mass. These effects dramatically
alter the lives of stars and their chemical makeup.
By combining special
purpose computers with newly developed simulation techniques,
we will include all these effects to answer timely
and important astronomical
questions such as: can planets survive life in
a cluster? how do interactions between stars
affect the chemical enrichment of
clusters and galaxies?Read moreRead less
Some Outstanding Mechanics Problems in Layered Ferroelectromagnetic Composites with Enhanced Magnetoelectric Effect. The proposed research has high impact on both science and technology of ferroelectromagnetic materials. The outcomes will expand Australia's knowledge base and research capability in this emerging field. Relevant industries, such as smart materials and devices, can benefit from the results of this project. The theoretical, experimental and numerical results can be directly transfo ....Some Outstanding Mechanics Problems in Layered Ferroelectromagnetic Composites with Enhanced Magnetoelectric Effect. The proposed research has high impact on both science and technology of ferroelectromagnetic materials. The outcomes will expand Australia's knowledge base and research capability in this emerging field. Relevant industries, such as smart materials and devices, can benefit from the results of this project. The theoretical, experimental and numerical results can be directly transformed to design and application guidelines for the materials engineers and scientists to develop innovative and structurally/functionally reliable ferroelectromagnetic composites and their various devices and products.Read moreRead less
On the Geometry of Liquid Crystals and Biological Membranes. This project will provide fundamental insights via realistic mathematical models into two areas of technological importance in the development of certain advanced materials involving liquid crystals and biomembranes. The use of liquid crystal devices is ubiquitous in the design of optical display units. Biomembranes are of much current importance, in particular, in connection with sophisticated drug delivery systems. The design of adva ....On the Geometry of Liquid Crystals and Biological Membranes. This project will provide fundamental insights via realistic mathematical models into two areas of technological importance in the development of certain advanced materials involving liquid crystals and biomembranes. The use of liquid crystal devices is ubiquitous in the design of optical display units. Biomembranes are of much current importance, in particular, in connection with sophisticated drug delivery systems. The design of advanced `smart' materials which admit solitonic behaviour is an area at the forefront of materials science and as such is important to the continued development of an advanced technological base within Australia.Read moreRead less
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
Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught ....Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught up with these developments. Our recent papers, all published in premier journals in this field, have not only received widespread international attention but have also increased the profile of String Theory amongst Australia's mathematicians and mathematical physicists. The proposed project is expected to continue this trend.Read moreRead less
Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial the ....Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.Read moreRead less
The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less
Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading the ....Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading theoretical groups, which will greatly aid research student education. There are direct applications to experiments on molecule formation with ultra-cold fermions in the ARC Centre of Excellence for Quantum-Atom Optics.Read moreRead less