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.
Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstra ....Inference in partially non-stationary time series models. Economic theories typically specify the long-run relationship between economic variables. However, researchers usually examine the long-run features of the data by fitting a restrictive class of models using criteria that have only proven useful for short-term forecasting. In this project we consider alternative models and modelling strategies that are appropriate for the study of the long-run. We also develop computer intensive (bootstrap) methods, which will provide a much-needed improvement over the existing (asymptotic) methods for making inference about the long-run. Our research will lead to more reliable models for long-term planning in business, industry and government.Read moreRead less
Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The ....Vector ARMA Models and Macroeconomic Modelling: Some New Methodology and Algorithms. Economic variables are strongly related to each other, as well as being strongly related to their recent history. As a result, good dynamic multivariate models are crucial for effective policy making and forecasting in areas of vital national importance such as monetary and fiscal policy, environmental policy and tourism. Our project advances the frontiers of knowledge in multivariate time series modelling. The outcome of this project will be immediately useful for macroeconomic policy makers such as the Reserve Bank of Australia and the Treasury, and for industry bodies such as Tourism Australia. Read moreRead less
Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the re ....Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the relationship between Tutte's work on dichromatic polynomials and matrix models, the outstanding problem of calculating the order parameters of the chiral Potts model, and the eigenvalue spectra of the transfer matrices that occur in integrable models.
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Algebraic invariants in mathematics and physics. This project is at the leading edge of fundamental mathematics and will result in important scientific advances that will keep Australia at the forefront internationally in this field of research. The topics under investigation are having high impact worldwide so there is an emphasis on international networking and on research training, particularly of research students. Australians would normally need to go to leading international centres such a ....Algebraic invariants in mathematics and physics. This project is at the leading edge of fundamental mathematics and will result in important scientific advances that will keep Australia at the forefront internationally in this field of research. The topics under investigation are having high impact worldwide so there is an emphasis on international networking and on research training, particularly of research students. Australians would normally need to go to leading international centres such as Paris to partake in projects of this nature. That high profile research of this kind can be done in Australia will enhance our capacity to retain scientific talent.Read moreRead less
The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less
Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study ....Solvable models and pattern formation: quantum spin ladders, combinatorics and stromatolite morphogenesis. The aim of this project is to develop new applications of exactly solved models in statistical mechanics. These include the study of quantum spin ladders of great interest in condensed matter physics. The physical properties of new and existing models will be derived to provide valuable benchmarks and predictions for future theoretical and experimental work. We will also undertake the study and development of a set of remarkable conjectures relating the properties of a solvable model to an established area of combinatorics. Another aspect of this project involves the investigation of the origins, growth and form of ancient stromatolites.
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Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the ....Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the building block of quantum information technologies, and so could realise quantum algorithms and quantum computations.Read moreRead less
Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an i ....Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an important contribution towards building a strong local knowledge base by addressing the problem of understanding the glassy state. The knowledge base can then serve as a springboard for possible high tech applications in materials science and engineering.Read moreRead less
Algebraic and computational approaches for classical and quantum systems. This project aims to use a combination of algebraic, analytic and numerical techniques to develop computational algorithms to address a range of notoriously challenging problems in the mathematical sciences. These problems involve predicting the large-scale behaviour of strongly interacting classical and quantum spin systems originating in condensed matter physics, including models of relevance to proposals for topological ....Algebraic and computational approaches for classical and quantum systems. This project aims to use a combination of algebraic, analytic and numerical techniques to develop computational algorithms to address a range of notoriously challenging problems in the mathematical sciences. These problems involve predicting the large-scale behaviour of strongly interacting classical and quantum spin systems originating in condensed matter physics, including models of relevance to proposals for topological quantum computation and the latest progress using field theory. The project outcomes will involve advances in understanding these systems from new exact results and high precision numerical estimates.Read moreRead less