Advanced numerical and analytical techniques for exact studies in combinatorics and statistical mechanics. Exactly solved models are of immense importance in all areas of the theoretical sciences and play important roles in our understanding of complex natural and social phenomena. This project aims to develop powerful new methods that will enable mathematicians and physicists to greatly expand the types of models for which we can find a solution.
Design, analysis and application of Monte Carlo algorithms in statistical mechanics. Monte Carlo methods provide a powerful computational tool with an enormous range of applications. However when applied in statistical mechanics they typically suffer from severe critical slowing-down, so that their computational efficiency tends rapidly to zero as a critical point is approached. We will develop novel, more efficient Monte Carlo algorithms, to simulate a range of models in statistical mechanics a ....Design, analysis and application of Monte Carlo algorithms in statistical mechanics. Monte Carlo methods provide a powerful computational tool with an enormous range of applications. However when applied in statistical mechanics they typically suffer from severe critical slowing-down, so that their computational efficiency tends rapidly to zero as a critical point is approached. We will develop novel, more efficient Monte Carlo algorithms, to simulate a range of models in statistical mechanics and back this up with rigorous mathematical analysis proving that their results can be trusted.Read moreRead less
Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as we ....Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as well as to viable paths towards the unknown theory that interpolates them. This project contributes to these developments by adapting and developing sophisticated technical tools and insights from integrable models to shed light on that unknown theory that transcends the gauge/string gap. Read moreRead less
Imaging surface topography using Lloyd's Mirror in photo-emission electron microscopy. The wide-ranging and innovative nature of the proposal will significantly raise Australia's international profile in condensed matter physics through high impact publications and invited presentations at major international conferences. Researchers will be trained in cutting-edge electron microscopy and synchrotron science. A spin-off company will be formed to commercialise software for reconstructing surface ....Imaging surface topography using Lloyd's Mirror in photo-emission electron microscopy. The wide-ranging and innovative nature of the proposal will significantly raise Australia's international profile in condensed matter physics through high impact publications and invited presentations at major international conferences. Researchers will be trained in cutting-edge electron microscopy and synchrotron science. A spin-off company will be formed to commercialise software for reconstructing surface topography and generating movies of dynamic events. The development of new synchrotron based electron microscopy techniques will establish the expertise for the future creation of a dedicated nanotechnology beamline equipped with photo-emission electron microscopy which will have far reaching national benefit in the physical sciences.Read moreRead less
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
Critical behaviour of lattice models of spin systems. A common feature of complex systems is that simple, short-range forces can produce long-range effects. Lattice spin systems are paradigms of this phenomenon, and this project proposes to solve a number of outstanding and significant problems in these systems. This will enhance our understanding of complex systems in general, and key models in particular.
Single atom defined nanostructures: atom-electronics beyond the miniaturization limit. The emerging era of atom-electronics promises to revolutionise microelectronics in the 21st century by going beyond the conventional miniaturization limit of microelectronics. Emerging atom level fabrication and control techniques offer the promise of building devices whose fundamental components are built atom-by-atom and function under completely new rules. This Discovery Project will apply critical new theo ....Single atom defined nanostructures: atom-electronics beyond the miniaturization limit. The emerging era of atom-electronics promises to revolutionise microelectronics in the 21st century by going beyond the conventional miniaturization limit of microelectronics. Emerging atom level fabrication and control techniques offer the promise of building devices whose fundamental components are built atom-by-atom and function under completely new rules. This Discovery Project will apply critical new theoretical tools, in partnership with leading experimental groups, to enable the exploration of this technology and the creation of new and innovative applications which will have far reaching implications in all areas of society and significant national benefit.Read moreRead less
Acoustics of the Didjeridu. We shall undertake a comprehensive experimental and theoretical study of the acoustics of the didjeridu-lips-vocal tract system. There is very little published technical literature on the dynamic acoustics of this important and uniquely Australian instrument, whose operation is surprisingly complex. A combination of stroboscopic measurements of lip motion, acoustic and vocal tract impedance measurements, MRI imaging of the vocal tract and computer modeling will be use ....Acoustics of the Didjeridu. We shall undertake a comprehensive experimental and theoretical study of the acoustics of the didjeridu-lips-vocal tract system. There is very little published technical literature on the dynamic acoustics of this important and uniquely Australian instrument, whose operation is surprisingly complex. A combination of stroboscopic measurements of lip motion, acoustic and vocal tract impedance measurements, MRI imaging of the vocal tract and computer modeling will be used to synthesize all components of the acoustic system into one quantitative model. The expected outcome will be an understanding of this instrument of unparalleled detail.Read moreRead less
Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptua ....Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptual questions in string theory, new types of extra dimensions, and new methods to compute quantum corrections in string theory. This should provide significant benefits, such as interdisciplinary collaborations at the national and international level and a strengthening of string theory in Australia.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