Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent ....Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent research breakthroughs, including novel datasets derived from satellite and field observations. The outcomes are expected to quantify sea ice retreat due to ocean waves for the first time, with potentially major implications for coupled wave–sea ice modelling in climate studies.Read moreRead less
Advanced algorithms for statistical mechanical models. Polymer science, percolation theory and models of magnetism are at the forefront of lattice statistical mechanics and condensed matter theory. Numerical techniques to determine the behaviour of model systems in these areas are predominantly Monte Carlo methods, series generation and analysis, or based on partition function zeroes. New algorithms have been developed for all three methods that are vastly more efficient than their predecessors. ....Advanced algorithms for statistical mechanical models. Polymer science, percolation theory and models of magnetism are at the forefront of lattice statistical mechanics and condensed matter theory. Numerical techniques to determine the behaviour of model systems in these areas are predominantly Monte Carlo methods, series generation and analysis, or based on partition function zeroes. New algorithms have been developed for all three methods that are vastly more efficient than their predecessors. Coupled with the availability of dramatically increased computer power, this project takes advantage of a unique position to make dramatic advances in the afore-mentioned research areas. Furthermore, the methods have wider applicability than those mentioned.Read moreRead less
Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamil ....Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.Read moreRead less
Study of mathematical models of evolution using the theory of quantum games - strengthening the theoretical foundation of quantum computation. The fields of nanotechnology, quantum technology and quantum information processing are rapidly converging. This project aims to provide a novel approach in the fundamental understanding of quantum computation/information by using methods inspired by mathematics of evolutionary competition. The project will contribute towards the theoretical foundations o ....Study of mathematical models of evolution using the theory of quantum games - strengthening the theoretical foundation of quantum computation. The fields of nanotechnology, quantum technology and quantum information processing are rapidly converging. This project aims to provide a novel approach in the fundamental understanding of quantum computation/information by using methods inspired by mathematics of evolutionary competition. The project will contribute towards the theoretical foundations of quantum computation by complementing efforts of several groups in Australia collaborating on the experimental design of quantum computers. The outcome of this project will contribute towards the successful operation of quantum computers and will help maintain Australia's position in the global forefront of quantum computation/information.
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The geometry of impossible, or contradictory objects and its applications to computing and cognition. The principal aim is pure research, the increase of knowledge within the Theory of Inconsistency and particularly its mathematical aspects, to be available to the national and world community. Additionally, a new stock of hitherto-unseen images (still, moving and three-dimensional) will be constructed in a virtual reality environment. In addition to enhancing Australia's strong reputation in log ....The geometry of impossible, or contradictory objects and its applications to computing and cognition. The principal aim is pure research, the increase of knowledge within the Theory of Inconsistency and particularly its mathematical aspects, to be available to the national and world community. Additionally, a new stock of hitherto-unseen images (still, moving and three-dimensional) will be constructed in a virtual reality environment. In addition to enhancing Australia's strong reputation in logic, there are spin-offs for mathematics, cognitive science, computer studies, and the arts and entertainment industries.Read moreRead less
Monopoles, instantons and metrics. This Project is pure basic research in the general area of differential geometry or the study of manifolds. Manifolds are higher dimensional analogues of surfaces such as the surface of the sphere or the surface of a doughnut. This Project studies monopoles and instantons which are solutions of partial differential equations arising in physics. These solutions and the so-called moduli spaces of all solutions have been used in the last two decades by the worlds ....Monopoles, instantons and metrics. This Project is pure basic research in the general area of differential geometry or the study of manifolds. Manifolds are higher dimensional analogues of surfaces such as the surface of the sphere or the surface of a doughnut. This Project studies monopoles and instantons which are solutions of partial differential equations arising in physics. These solutions and the so-called moduli spaces of all solutions have been used in the last two decades by the worlds leading mathematicians to revolutionize the study of three and four dimensional manifolds.Read moreRead less
Characterizing and classifying ovoids, flocks and generalized quadrangles. This project lies within the framework of the classification and characterization of fundamental structures in finite geometry. This research area is the site of much international activity, in which the proposed research team plays a central role. The aim of the project is to pursue twin goals: the classification of ovoids in three dimensional projective space, a famous long-standing problem; and the classification of ce ....Characterizing and classifying ovoids, flocks and generalized quadrangles. This project lies within the framework of the classification and characterization of fundamental structures in finite geometry. This research area is the site of much international activity, in which the proposed research team plays a central role. The aim of the project is to pursue twin goals: the classification of ovoids in three dimensional projective space, a famous long-standing problem; and the classification of certain generalized quadrangles. Our approach is novel as it utilises recently discovered links between these areas. The expected outcomes are significant progress towards these goals, as well as the development of new techniques in finite geometry.Read moreRead less
Three-dimensional magnetotelluric and controlled-source electromagnetic modelling and inversion in isotropic and anisotropic media with Gaussian Quadrature Grids. Electromagnetic methods are widely used by geophysicists in many applications, including mineral, petroleum and geothermal exploration, environmental and groundwater characterisation, and in imaging of Earth and other planets. Large data-sets are routinely collected, but to interpret these carefully we need efficient computer modellin ....Three-dimensional magnetotelluric and controlled-source electromagnetic modelling and inversion in isotropic and anisotropic media with Gaussian Quadrature Grids. Electromagnetic methods are widely used by geophysicists in many applications, including mineral, petroleum and geothermal exploration, environmental and groundwater characterisation, and in imaging of Earth and other planets. Large data-sets are routinely collected, but to interpret these carefully we need efficient computer modelling tools that incorporate the complexity of the subsurface. We will develop a new computer algorithm that uses an innovative approach to model the Earth in three dimensions. Computer codes will be available through the national AuScope infrastructure facilities, so that researchers will have free access to algorithms, largely for the first time, to better interpret their data.Read moreRead less
Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially impor ....Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially important results in applications.Read moreRead less
Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the clas ....Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the classification of topological phases in strongly interacting systems. This project involves postgraduate training as a crucial tool in achieving its aims and enhances Australia's position at the forefront of international research.Read moreRead less