New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to w ....New regularisation techniques in electromagnetic diffraction from cavities and related complex scatterers. Modern technology, such as radar and other imaging devices, exploits the information carried by electromagnetic waves. New technology depends centrally upon advances in the mathematics of waves to give precise, reliable and effective means of predicting how objects capture and re-radiate wave energy in the scattering environment. This project aims to develop a new mathematical approach to wave scattering by objects with complex scattering mechanisms, as typified by cavity structures. This new formulation is obtained by a process of analytical regularisation of the equations describing the scattering process. It generates algorithms more reliable and computationally accurate than current codes.
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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
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
Discrete integrable systems. Discrete integrable systems are a fundamental generalisation of traditional integrable systems. This project, combining 5 world experts from 3 countries and 2 early career researchers, will expand and systematise this new interdisciplinary field, and will place Australia at the forefront of this intensive international activity.
Random matrix products, loop equations and integrability. This project aims to research integrable structures inherent in random matrix products and loop equations. These are topics in random matrix theory, which is well known for its diverse appearances in mathematics and its applications. Integrable structures provide random matrix theory with quantitative predictions for use in these applications; link seemingly distinct theories; and are a unifying theme of fundamental and lasting importance ....Random matrix products, loop equations and integrability. This project aims to research integrable structures inherent in random matrix products and loop equations. These are topics in random matrix theory, which is well known for its diverse appearances in mathematics and its applications. Integrable structures provide random matrix theory with quantitative predictions for use in these applications; link seemingly distinct theories; and are a unifying theme of fundamental and lasting importance. This project will strengthen international collaborations, provide research training, and make the footprint of Australian mathematical science more visible.Read moreRead less
Higher Order Effects in Miniaturized Piezoelectric Devices. The national benefits of this project are: (a) We will provide opportunities to two postdoctoral researchers to pursue cutting edge research on electromagnetic radiation/scattering and self-heating phenomena in microelectronic devices involving ultrathin lossy electrodes. (b) We will provide industry-oriented research on coating and shielding problems in microelectronic devices to two postgraduate students. (c) We will team up with worl ....Higher Order Effects in Miniaturized Piezoelectric Devices. The national benefits of this project are: (a) We will provide opportunities to two postdoctoral researchers to pursue cutting edge research on electromagnetic radiation/scattering and self-heating phenomena in microelectronic devices involving ultrathin lossy electrodes. (b) We will provide industry-oriented research on coating and shielding problems in microelectronic devices to two postgraduate students. (c) We will team up with world leading industrial partners and transfer high-tech know-how to Australia. (d) The outcomes of our research will position Australia as the prime focal point for the design, modelling and simulation of microacoustic devices.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL120100094
Funder
Australian Research Council
Funding Amount
$3,184,657.00
Summary
Geometric construction of critical solutions of nonlinear systems. Whether we are looking at waves on a beach, the dispersal of herds of animals in a landscape, or the interaction of black holes, their patterns of movement rely on rules expressed by non-linear mathematical models. This project will aim to create new mathematical methods to describe the solutions of non-linear systems, which are ubiquitous in modern science.
Critical solutions of nonlinear systems. Whether we are looking at waves on a beach, the dispersal of herds of animals in a landscape, or the interaction of black holes, their patterns of movement rely on rules expressed by nonlinear mathematical models. This project aims to create new mathematical methods to describe critical solutions of nonlinear systems, which are ubiquitous in modern science.
Reflection Groups and Discrete Dynamical Systems. This project aims to solve long-standing problems in discrete dynamical systems that are of particular interest to physics, by using reflection groups to reveal unexpected geometric insights. Mathematics has the power to abstract crucial patterns from complex observations. Symmetries familiar in the real world, like the hexagonal patterns of honeycombs, arise inside convoluted structures in high-dimensional systems. By revealing the structure of ....Reflection Groups and Discrete Dynamical Systems. This project aims to solve long-standing problems in discrete dynamical systems that are of particular interest to physics, by using reflection groups to reveal unexpected geometric insights. Mathematics has the power to abstract crucial patterns from complex observations. Symmetries familiar in the real world, like the hexagonal patterns of honeycombs, arise inside convoluted structures in high-dimensional systems. By revealing the structure of space-filling polytopes in integrable systems, the project seeks to find sought-after reductions of high-dimensional discrete models to two dimensions. Expected outputs include new reductions to discrete Painlevé equations, new circle patterns useful for computer graphics and discrete holomorphic functions.Read moreRead less
Algebraic interpretations of discrete integrable equations. The important mathematical disciplines of discrete geometry on one hand, and structure in discrete non-linear dynamics known as integrability on the other, have an emerging and fruitful interrelation. This project will construct a new algebraic framework in order to better understand and exploit this point of intersection.