Advanced Computational and Analytic Studies in Lattice Statistical Mechanics and Applications. Lattice Statistical Mechanics is one of the current success stories of Australian Science with a significant international presence. The applicants represent a centre of excellence, particularly in the area of combining computational and analytic studies for maximum scientific benefit. The programme of research maximises Australia's investment in this human resource by focussing on an integrated set of ....Advanced Computational and Analytic Studies in Lattice Statistical Mechanics and Applications. Lattice Statistical Mechanics is one of the current success stories of Australian Science with a significant international presence. The applicants represent a centre of excellence, particularly in the area of combining computational and analytic studies for maximum scientific benefit. The programme of research maximises Australia's investment in this human resource by focussing on an integrated set of projects comprising a diverse and innovative group of applications in areas such as polymer science, DNA denaturation, combinatorics and the study of traffic flows. The underlying theme is always the utility of lattice statistical mechanics in 21st century science.Read moreRead less
Key combinatorial problems in lattice statistical mechanics. The enumeration of lattice animals is a famous open problem in combinatorics. These discrete structures also underpin our understanding of many physical phenomena, including polymer collapse and percolation in random media, through the integral part they play in many models in statistical mechanics and theoretical chemistry.
The project aims to answer some key open problems in this area using exact and numerical techniques. We expe ....Key combinatorial problems in lattice statistical mechanics. The enumeration of lattice animals is a famous open problem in combinatorics. These discrete structures also underpin our understanding of many physical phenomena, including polymer collapse and percolation in random media, through the integral part they play in many models in statistical mechanics and theoretical chemistry.
The project aims to answer some key open problems in this area using exact and numerical techniques. We expect that this will lead to proofs of the insolvability of certain problems, new exact solutions of others, and a greater understanding of the effect of topology and geometry on the behaviour of these models.Read moreRead less
Exact dynamics of the asymmetric exclusion process with boundaries. This project offers an opportunity for a postgraduate student to participate in world-class research. It further strengthens collaborative ties with the renowned department of theoretical physics at Oxford University. The outcomes of this project are expected to provide valuable fundamental information for any applied science in which transport plays a crucial role.
Hecke algebras and hidden symmetries in quantum spin chains. This project further strenghtens collaborative ties with Prof. Rittenberg who is a leading figure in statistical mechanics. Rittenberg is Scientific Director of one of the best journals, and has been instrumental in advocating and advancing Australia's influence in the field. All this on top of his original scientific input which we have become used to in the past years.
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
Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of th ....Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of the modern methods in the theory require expertise in mathematics as well as a high level of programming skills. This combination provides a unique training ground for higher degree students aiming at careers in financial mathematics, weather/climate forecasting and internet security.
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Conformal invariance and stationary states. Universal properties in nonequilibrium processes, such as scaling of space and time, suggest the existence of a fundamental, model independent theory describing such phenomena. An analogous theory for equilibrium phenomena exists, namely conformal field theory, and is extremely important for our understanding. Using recent insights this project aims at formulating such a theory for universal nonequilibrium behaviour.
Searching for solvability in Statistical Mechanics and beyond using advanced Enumerative Combinatorics. Standard models in lattice statistical mechanics provide basic models of a large variety of physical systems from polymers to the spread of forest fires. The ability to write down some kind of solution to these problems provides inestimable insight into their generic and universal behaviour. This project aims to expand the types of "solution" that mathematicians and physicists can write down.
Polynomial representations of the Hecke algebra. This project will offer a great opportunity for talented students to engage in internationally competitive research in mathematics. In addition, through international collaboration, this project will be able to deliver an online database with software libraries which will be a world benchmark for computation with multivariate polynomials.
Statistical Topology and its Application to Deriving New Geometric Invariants. This project will offer a great opportunity for talented students to engage in internationally competitive research. Statistical topology, which combines ideas in topology, geometry and statistical mechanics is becoming a rapidly increasing branch of mathematics, with many emerging applications in bio-informatics, computer science and theoretical physics.