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.
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.
A synthesis of random matrix theory for applications in mathematics, physics and engineering. Random matrix theory, matrix theory where the elements are random, or the matrix chosen from an ensemble, is driven by its ever expanding range of applications, and the richness of the mathematics being uncovered. These applications include topics of acknowledged modern day importance, for example quantum information theory, wireless communication, data analysis, signal processing and the study of algor ....A synthesis of random matrix theory for applications in mathematics, physics and engineering. Random matrix theory, matrix theory where the elements are random, or the matrix chosen from an ensemble, is driven by its ever expanding range of applications, and the richness of the mathematics being uncovered. These applications include topics of acknowledged modern day importance, for example quantum information theory, wireless communication, data analysis, signal processing and the study of algorithms. Buoyed by promising preliminary investigations, this project aims to draw together seemingly disparate techniques to tackle problems from such topics. In addition to providing solutions to these problems, these methods are expected to provide inspiration for fellow researchers.Read moreRead less
Advanced numerical and analytical techniques for exact studies in combinatorics and statistical mechanics. Exactly solved models are of immense importance in all areas of the theoretical sciences and play important roles in our understanding of complex natural and social phenomena. This project aims to develop powerful new methods that will enable mathematicians and physicists to greatly expand the types of models for which we can find a solution.
Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by t ....Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by the CI. All indications are that the new ideas relating integrable structures and random matrices underpinning this proposal will fulfil this goal. For the postdoctral researcher involved the stimulating atmosphere of discovery should provide ideal training in mathematical research.Read moreRead less
Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, a ....Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, another line of applications will be emphasized, and a new axis of international linkage formed.Read moreRead less