Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized ran ....Stochastic modelling and analysis of spatio-temporal processes with fractal characteristics. Interest has grown in recent years on the derivation of fractal models to represent certain physical phenomena such as diffusion and transport in porous media, oceanic and atmospheric turbulence, climatology, etc. This project focuses on the phenomenon of diffusion on domains with multifractal geometry. Recent advances in harmonic analysis on fractals and our own development of fractional generalized random fields allow us to formulate a comprehensive program to tackle some key problems including modeling, processing and statistical estimation of fractional diffusion. Advances made in this program will in turn benefit the developments in related scientific fields.Read moreRead less
Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the ....Increasing the effectiveness of quantitative verification. The ability to analyse the performance of complex systems and protocols is a vital part of the development of large-scale computer applications. Methods that improve the effectiveness of the analysis task would increase the competitiveness of the software industry, and would attract future development work (in complex systems) to Australia. The results of this project will have a direct influence on currently available design tools; the fact that Australian institutions will be (in part) responsible for key theoretical results in this growing field will strengthen Australia's position worldwide as an international centre for computer science.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.
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.
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
Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also ....Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also applicable to microscopic systems. The expressions will determine the probability that finite sized systems will violate the Second Law for small periods of time and will therefore contribute to development of a fundamental understanding of microscopic systems and the development of nanotechnology.
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Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their appli ....Quantum many-body systems with long-range interactions. Integrable many-body systems with long-range interactions are the subject of intense research activity worldwide, because they involve powerful mathematics and have various physical applications ranging from condensed matter physics to high energy physics. This project involves intensive collaboration between leading mathematical physics groups in Japan and Australia on exciting new developments in the theory of such systems and their applications to physics. The expected outcomes are new progress in an area at the cutting edge of mathematical physics and the establishment of strong research links between Japan and Australia.Read moreRead less
Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their ....Quantized Algebraic (Super) Structures and Applications. Algebraic structures such as quantized superalgebras and affine Lie (super)algebras provide a universal common algebraic framework underlying applications in a wide range of physical systems, leading to a high level of research activity worldwide. The project involves intensive collaborations between leading mathematical physics groups in China and Australia on exciting new developments in the theory of these algebraic structures and their applications to condensed matter physics and quantum field theories. The expected outcomes are significant new progress in an area at the forefront of mathematical physics and the establishment of strong research links between China and Australia.Read moreRead less
Low-dimensional quantum systems. The theory of integrable systems of statistical mechanics and quantum field theory is currently one of most rapidly developing and fascinating subjects in theoretical physics and mathematics.
It allows to obtain an exact description of strongly-interacting quantum systems in one or two space dimensions and provides fundamental tools for understanding of critical phenomena and physics of small systems like quantum wires, carbon nanotubes and Josephson junctions ....Low-dimensional quantum systems. The theory of integrable systems of statistical mechanics and quantum field theory is currently one of most rapidly developing and fascinating subjects in theoretical physics and mathematics.
It allows to obtain an exact description of strongly-interacting quantum systems in one or two space dimensions and provides fundamental tools for understanding of critical phenomena and physics of small systems like quantum wires, carbon nanotubes and Josephson junctions. The project addresses two particular problems in this field: the three-dimensional lattice model with continuous spins and calculation of form factors in a two-dimensional massive field theory with a supersymmetry.
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