Phonon based condensed matter imaging. This project will exploit observations of phonon-based chemical contrast in the SHeM to determine the physics that underpins the imaging mechanism and use them to probe vibrational processes in condensed matter imaging. Imaging is an essential tool for the discovery, application and fabrication of new materials, structures and devices. However, many delicate structures are irrevocably degraded and changed when imaged using conventional microscopy. This team ....Phonon based condensed matter imaging. This project will exploit observations of phonon-based chemical contrast in the SHeM to determine the physics that underpins the imaging mechanism and use them to probe vibrational processes in condensed matter imaging. Imaging is an essential tool for the discovery, application and fabrication of new materials, structures and devices. However, many delicate structures are irrevocably degraded and changed when imaged using conventional microscopy. This team recently invented the scanning helium atom microscope (SHeM), which can image surfaces non-destructively with nanoscale resolution. They will use the SHeM to determine the new fundamental physics that underpins the imaging mechanism. Outcomes include turning SHeM into a tool that materials and biological scientists can use in laboratories worldwide.Read moreRead less
Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project ....Structure and states of operator-algebraic dynamical systems. This project is in the general area of functional analysis, and more specifically operator theory, an area in which the University of Wollongong has an active research group and a strong international reputation. The investigators will study dynamical systems arising in combinatorial and number-theoretic situations, where the analogue of the "dynamics'' is provided by an action of the real line on an operator algebra. Thus the project will involve ideas and techniques from a wide range of mathematical disciplines, and will help to broaden Australia's expertise across these disciplines.Read moreRead less
Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theor ....Endomorphisms, transfer operators and Hilbert modules. This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theory. It is hoped that the results will give new understanding of the algebraic and analytic structure underlying the multi-resolution analyses used in approximation theory and Fourier analysis. This project will help ensure that Australia has a strong foundation in mathematics which will foster innovation.Read moreRead less
Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of ....Operator algebras associated to semigroups and graphs. This project aims to unify ideas from two highly topical areas of mathematics in which one studies discrete objects by representing them as families of linear transformations. In the first area, one represents the semigroups which model irreversible dynamics as isometries (that is, distance-preserving transformations); in the second, one represents networks by families of partially defined isometries in a way which reflects the behaviour of paths in the network. The link will be achieved by viewing the operator algebras they generate as semidirect products which have been twisted by a noncommutative cocycle.Read moreRead less
Operator algebras associated to groupoids. Australian researchers have a strong reputation for excellence and innovation in the field of operator algebras. Operator algebras associated to groupoids have been immensely influential in recent decades, both within mathematics and via applications to theoretical physics. This project will develop an innovative approach to groupoid algebras, and will help to maintain the high standing of Australian researchers in this important field.
Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in cont ....Co-universal operator algebras. Australian researchers have established themselves at the very forefront of research into operator algebras associated to graphs. The proposed research will make an important impact, at a fundamental level, on the way that researchers around the world view these operator algebras. This will help to further strengthen Australia's reputation in this field. The proposed program will also train two PhD students in a very active area of mathematics and put them in contact with a vibrant research community. This will help contribute to the strong future of pure mathematics in Australia.Read moreRead less
New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary val ....New Directions in Noncommutative Geometry. A. Connes' noncommutative geometry has recently become important in topology, geometry and physics. The central geometric objects in noncommutative geometry are called spectral triples. Spectral triples also provide the framework for studying some important classes of equations. This project will extend the definitions of spectral triples to cover additional important examples. This extension will provide the tools to study a broad class of boundary value problems in the theory of equations. Such problems occur in several areas of modern physics. In addition, results obtained will be useful for studying the structure of the most important spectral triples, called noncommutative manifolds.Read moreRead less
High performance complex oxide heterostructures for nanoelectronic devices. This project aims to develop a material with ultrahigh electron mobility and conductivity well above today’s materials at room temperature to enable next generation nanoelectronics. The demand for higher performance and lower power consumption in electronic systems drives the creation of materials for devices in nanometre scale. The success of these materials depends on enhancement in carrier mobility and conductivity. T ....High performance complex oxide heterostructures for nanoelectronic devices. This project aims to develop a material with ultrahigh electron mobility and conductivity well above today’s materials at room temperature to enable next generation nanoelectronics. The demand for higher performance and lower power consumption in electronic systems drives the creation of materials for devices in nanometre scale. The success of these materials depends on enhancement in carrier mobility and conductivity. This project will spatially separate the electron generation layer from the conduction layer by individually engineering the atomically sharp complex oxide heterointerfaces to enhance the electron mobility and density. This is expected to develop new materials and nanoelectronic technologies.Read moreRead less
Development of new methods to measure in vivo properties of human body tissues. This project will develop new methods of noninvasively measuring the viscoelastic properties of soft tissues in live humans, using a novel magnetic resonance elastography technique. These methods will be applied to study the operation of the human muscle-tendon system, differences in neck muscle properties with age and gender and to measure the properties of the human brain, kidney and liver in vivo. These techniques ....Development of new methods to measure in vivo properties of human body tissues. This project will develop new methods of noninvasively measuring the viscoelastic properties of soft tissues in live humans, using a novel magnetic resonance elastography technique. These methods will be applied to study the operation of the human muscle-tendon system, differences in neck muscle properties with age and gender and to measure the properties of the human brain, kidney and liver in vivo. These techniques may be useful in diagnosing soft tissue disease or injury which are currently difficult to detect using standard imaging techniques. It will also explain how the muscle-tendon unit moves during normal motion in live humans.Read moreRead less
3D integrated crystalline UV optical lens-fiber couplers for astronomy. This project aims to create micro-optics for astronomical and bio medical applications by 3D sculpturing them out of crystals by ultra-short pulse lasers. This project will introduce a new 3D fabrication approach of optical probes which have self-aligned micro-optical elements and optical fibres for a wide spectral range and with high quality optical surfaces. Expected outcomes of this project include building new capabiliti ....3D integrated crystalline UV optical lens-fiber couplers for astronomy. This project aims to create micro-optics for astronomical and bio medical applications by 3D sculpturing them out of crystals by ultra-short pulse lasers. This project will introduce a new 3D fabrication approach of optical probes which have self-aligned micro-optical elements and optical fibres for a wide spectral range and with high quality optical surfaces. Expected outcomes of this project include building new capabilities in micro-optical probes for industrial environments, establishing new solutions for international astronomy partners, and developing new techniques to image through optical fibres. This should provide significant benefits by improving astronomical instrumentation and also lead to less invasive endoscopy.Read moreRead less