Relative free energies from nonequilibrium simulations: algorithms for determination of binding affinities, conformational states and phase transitions. Leading edge research will enable state of the art techniques in statistical mechanics to be applied to practical problems. All processes in biological, chemical and physical systems are governed by their free energy landscape, often only accessible computationally. This project will lead to an advanced tool for free energy calculation. Advanc ....Relative free energies from nonequilibrium simulations: algorithms for determination of binding affinities, conformational states and phase transitions. Leading edge research will enable state of the art techniques in statistical mechanics to be applied to practical problems. All processes in biological, chemical and physical systems are governed by their free energy landscape, often only accessible computationally. This project will lead to an advanced tool for free energy calculation. Advancement of emerging technologies in nanoscience, porous materials, membrane transport and drug design will benefit from this capability. The project therefore addresses the Priority Goal 'Breakthrough science'. A PhD student and an Early Career Research will be trained in research, gaining a range of valuable skills in theory and simulation. Read moreRead less
Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
Dissipation and relaxation in statistical mechanics. This project studies the mathematical conditions for relaxation either to equilibrium or to steady states, which is important in predicting behaviour in diverse fields including climate modelling, materials science, nanotechnology and biology. Early career researchers will be involved in the project, gaining valuable skills in theory and simulation.
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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Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these dev ....Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these developments by: generalizing a theorem which relates transport coefficients to chaoticity; detailed studies of the influence of thermostatting mechanisms on nonequilibrium chaoticity and fluctuations, and by understanding the range of applicability of a nonequilibrium fluctuation theorem for non-isoenergetic systems.Read moreRead less
Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing sta ....Supersymmetry and supergravity: new approaches and applications. This project aims to advance our understanding of supersymmetric quantum field, gravity, and higher-spin theories. Supersymmetry and supergravity play crucial roles in modern developments in fundamental particle physics and cosmology. They also have rich connections with many branches of mathematical physics. Major conceptual questions in the description of general supergravity-matter couplings are still unsolved. By performing state of the art analysis in supergravity and holographic dualities, the project will advance our understanding of quantum gravity, black holes, and cosmology placing Australia at the forefront of these important research fields.Read moreRead less
Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Topological properties of exactly-solvable, two-dimensional quantum systems. Two-dimensional quantum systems have unique properties which are driving developments in the emerging generation of quantum-based technologies. This project will facilitate progress by elucidating the mathematics underlying these systems. The results will impact on downstream research and development in the area of superior information processing.
Mathematical models for disordered critical point theories. This project sets up a team to develop innovative techniques for fundamental advances in critical behaviour of disordered systems including the Nobel Prize winning integer quantum Hall effect. It will yield new mathematical models for disordered critical point theories, essential for the theoretical analysis of associated emerging technologies.
Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems des ....Towards logarithmic representation theory of W-algebras. Aims: To construct and analyse indecomposable representations of significance in conformal field theory.
Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems described by logarithmic conformal field theory.
Expected Outcomes: Novel representations of fundamental importance in logarithmic conformal field theory.
Benefit: Resolution of open problems in logarithmic conformal field theory, thus continuing the strong tradition in the field in Australia.
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