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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
Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscal ....Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel methodology will explore this stumbling block, and promises to radically change the modeling, exploration and understanding of multiscale complex system behaviour.Read moreRead less
ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.Read moreRead less
Robust fluid mixing through topological chaos. The Australian chemicals and plastics industry has an annual turnover of over $20 billion and employs over 77,000 people; fluid mixing is fundamental to this industry, yet the industry is recognised as underinvesting in research and development in this essential area. Furthermore, frontier technologies such as biotechnology and the next generation of smart materials also crucially rely on fluid mixing. This project aims to evaluate a new paradigm ( ....Robust fluid mixing through topological chaos. The Australian chemicals and plastics industry has an annual turnover of over $20 billion and employs over 77,000 people; fluid mixing is fundamental to this industry, yet the industry is recognised as underinvesting in research and development in this essential area. Furthermore, frontier technologies such as biotechnology and the next generation of smart materials also crucially rely on fluid mixing. This project aims to evaluate a new paradigm (topological chaos) for the design of mixers, to provide better and more robust mixers that work from microscopic to industrial scales.Read moreRead less
Advanced studies of QCD and the strong interaction. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associa ....Advanced studies of QCD and the strong interaction. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associates of high quality, who will benefit from participating in these state-of-the-art studies and from the advanced training in modelling, high-performance computer simulation and visualisation. This training will have major economic benefits for and provide strong links to Australian industry.Read moreRead less
Strong Interaction Physics from Lattice QCD. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associates of h ....Strong Interaction Physics from Lattice QCD. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associates of high quality, who will benefit from participating in these state-of-the-art studies and from the advanced training in modeling, high-performance computer simulation and visualisation. This training will have major economic benefits for and provide strong links to Australian industry.Read moreRead less
Systematically model the large-scale complexity of turbulent floods and thin film flows. This project continues development of new models, and computer
simulation, of turbulent flood, river and estuarine flow. The models
will be based systematically upon established turbulence models to
resolve accurately the complex physical processes. The development of
new and robust computer models for thin layers of coating fluid will
aid many industrial processes. We also aim to provide correct ini ....Systematically model the large-scale complexity of turbulent floods and thin film flows. This project continues development of new models, and computer
simulation, of turbulent flood, river and estuarine flow. The models
will be based systematically upon established turbulence models to
resolve accurately the complex physical processes. The development of
new and robust computer models for thin layers of coating fluid will
aid many industrial processes. We also aim to provide correct initial
conditions and boundary conditions for simpler cases of the above
flows. The approach leads to a greater understanding of the range of
applicability of the models through better estimating the errors in the
modelling process. The project develops a fundamental enabling
methodology for engineering and the sciences.
Read moreRead less
Modelling of multiscale systems in engineering and science supports large-scale equation-free simulations and analysis. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are known, but the closures to translate microscale ....Modelling of multiscale systems in engineering and science supports large-scale equation-free simulations and analysis. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel, equation free, computational methodologies will circumvent this stumbling block, and promises to radically change the modeling, exploration and understanding of complex system behavior. We continue to develop this powerful computational methodology. Read moreRead less
Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form ....Normal forms and Chern-Moser connection in the study of Cauchy-Riemann Manifolds. This research project is aimed at a systematic study of Cauchy-Riemann manifolds, their holomorphic mappings and automorphisms, by means of a unifying approach based on
Chern-Moser type normal forms. The importance of Cauchy-Riemann manifolds stems from the fact that they bridge complex structure and holomorphy with the Riemannian nature of real manifolds. Construction of an analogue of the Chern-Moser normal form for multicodimensional Levi-nondegenerate CR-manifolds and extension of CR-mappings between them are major goals in complex analysis. Identification of Chern-Moser chains and equivariant linearisation of isotropy automorphisms are major goals in geometry.Read moreRead less
Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ult ....Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ultimate goal is to find the appropriate K-theory classifying D-branes in arbitrary closed string backgrounds or, similarly, classifying boundary Conformal Field Theories. It has already emerged that the K-theory of C*-algebras will play an important role.Read moreRead less