The stability of unsteady fluid flows in channels and pipes. The main benefit from this project will be a better theoretical understanding of the stability properties of unsteady fluid flows. The theoretical results obtained would help guide future experimental
investigations into the paths to turbulence in unsteady flows and would be a basis for future research in the increasingly important area of flow stability control. The project will also provide advanced training and skills transfer in a ....The stability of unsteady fluid flows in channels and pipes. The main benefit from this project will be a better theoretical understanding of the stability properties of unsteady fluid flows. The theoretical results obtained would help guide future experimental
investigations into the paths to turbulence in unsteady flows and would be a basis for future research in the increasingly important area of flow stability control. The project will also provide advanced training and skills transfer in an important area of fluid mechanics research.
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Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficie ....Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficient by providing a valuable experimental interpretive tool and a theoretical map for material optimization. Our models will also provide crucial information needed for modelling the behavior of composites in applications.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 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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Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less
Quantum decoherence: A game-theoretic perspective. Algorithms based on quantum computation have the ability to significantly speed up information processing compared to standard computers. The increase in computational power can have enormous impact on humankind and this project will help maintain Australia's position in the global forefront of this effort.This project focuses on the thoeretical foundations of quantum computation and complements the efforts of several groups in Australia collabo ....Quantum decoherence: A game-theoretic perspective. Algorithms based on quantum computation have the ability to significantly speed up information processing compared to standard computers. The increase in computational power can have enormous impact on humankind and this project will help maintain Australia's position in the global forefront of this effort.This project focuses on the thoeretical foundations of quantum computation and complements the efforts of several groups in Australia collaborating on the experimental design of quantum computers. The project will increase the fundamental understanding of how quantum information is processed in the presence of noise, which is necessary for the successful operation of quantum computers. 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.
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
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