Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Sc ....Propagation of singularities for the Schrodinger equation. The time-dependent Schrodinger equation governs the evolution of quantum particles. In this project we aim to use new techniques from mathematical scattering theory to analyse solutions of the Schrodinger equation and obtain sharp bounds on their singularities. Controlling such singularities will allow us to deduce quantitative bounds on the number of eigenvalues in certain situations, and provide new techniques for studying nonlinear Schrodinger equations. Read moreRead less
The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have impl ....The impact of crime on the mental wellbeing of communities. Considering not only the direct impact of crime on the victims but also the indirect consequences of living in a community with a higher crime rate may in fact lead to a more accurate analysis of the size of the consequences of criminal activities on the society. Further, it may also be the case that the negative externality of crime on non-victims is much larger for some crimes than for others. If this were the case, it could have implications for the way in which police resources are presently distributed across different crimes. Better understanding the total societal cost of crime - to both victims and non-victims - could therefore help improve public policy. Read moreRead less
Hardy spaces of differential forms and applications. Hardy spaces on Euclidean spaces were developed in the 1970's following the fundamental work of Stein, Weiss and Fefferman. These spaces play an important role in harmonic analysis, as they are the natural spaces on which to consider singular integral operators. They arise in many contexts, such as when using Jacobians in non-linear partial differential equations. Recently the French participants and the Australian participants have have obt ....Hardy spaces of differential forms and applications. Hardy spaces on Euclidean spaces were developed in the 1970's following the fundamental work of Stein, Weiss and Fefferman. These spaces play an important role in harmonic analysis, as they are the natural spaces on which to consider singular integral operators. They arise in many contexts, such as when using Jacobians in non-linear partial differential equations. Recently the French participants and the Australian participants have have obtained different but related results concerning Hardy spaces of exact differential forms. The time is now ripe to construct a unified theory.
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Boron nitride nanotubes for tunable conductivity. The proposed research in nanotubes falls into the national research priority areas of advanced materials and breakthrough science. This ANU research group has a leading role in Boron Nitride (BN) nanotube research internationally. The proposed collaborative research will enhance this position and further improve the nation's research profile in nanotechnology. New intellectual properties will be generated if the project is successful, which wi ....Boron nitride nanotubes for tunable conductivity. The proposed research in nanotubes falls into the national research priority areas of advanced materials and breakthrough science. This ANU research group has a leading role in Boron Nitride (BN) nanotube research internationally. The proposed collaborative research will enhance this position and further improve the nation's research profile in nanotechnology. New intellectual properties will be generated if the project is successful, which will benefit the commercialization activity of BN nanotubes at ANU. New PhD and undergraduate students will be trained by the proposed cutting edge research project.Read moreRead less
Structure-property correlation in metal-oxide aerogels. Aerogels are truly remarkable materials with unique physical properties including extraordinary thermal insulation capabilities. The influence of mechanical deformation on these nanoscale materials is only poorly understood, despite key technological interest. This project aims to measure the response of a variety of aerogels samples to forces applied by nanoindentation and, using advanced electron microscopy and ion-beam analysis techniqu ....Structure-property correlation in metal-oxide aerogels. Aerogels are truly remarkable materials with unique physical properties including extraordinary thermal insulation capabilities. The influence of mechanical deformation on these nanoscale materials is only poorly understood, despite key technological interest. This project aims to measure the response of a variety of aerogels samples to forces applied by nanoindentation and, using advanced electron microscopy and ion-beam analysis techniques, to directly identify the atomic-level deformation mechanisms.Read moreRead less
Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, ....Asymptotic Geometric Analysis and Machine Learning. Phenomena in large dimensions appear in a number of domains of Mathematics and adjacent domains of science (e.g. Computer Science), dealing with functions of infinitely growing number of parameters. Here, we focus on several questions naturally linked to Asymptotic Geometric Analysis which have natural applications to Statistical Learning Theory. We intend to use geometric, probabilistic and combinatorial methods to investigate these problems, with an emphasis on modern tools in Empirical Processes Theory and the theory of Random Matrices.Read moreRead less
International linkages between financial and real economy cycles. This project will develop empirical multivariate models of business cycles for different countries, and will study how they are linked via international financial markets. The significance of the project is that the models will integrate previous work done on financial-real economy links in single country settings, and it will explicitly study the effects of disequilibrium in international financial markets (such as overvaluation ....International linkages between financial and real economy cycles. This project will develop empirical multivariate models of business cycles for different countries, and will study how they are linked via international financial markets. The significance of the project is that the models will integrate previous work done on financial-real economy links in single country settings, and it will explicitly study the effects of disequilibrium in international financial markets (such as overvaluation of foreign currency) on individual economies. The project will determine the appropriate domestic monetary policy response to such shocks, and the potential for forecasting both the advent of such shocks and their impact on individual economies.Read moreRead less
What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effec ....What are the determinants and effects of school choice? An international comparison between Australia and the UK. The project will provide a clearer picture of the determinants of school choice, most notably the impact of economic phenomena on that choice. For Australia, this will mean we have a better understanding of the competing explanations of the growth of students at private schools over the past three decades: the role of government subsidies; the role of demographic changes; the effects of increased income inequality; and the role of changes in preferences towards private schools. This information will provide a better evidence base for future policy development in this area.Read moreRead less
Correlation between surface force and morphology of self-assembled monolayer. As a most potential solid support for biological molecules without denaturing their functions, gold thiol self-assembled monolayers (SAMs) have been studied extensively for surface fabrication. In this project we will prepare functional monolayers using newly synthesized thiol derivatives, evaluate correlation between surface force and surface morphology of the SAMs using the surface forces apparatus, and optimize the ....Correlation between surface force and morphology of self-assembled monolayer. As a most potential solid support for biological molecules without denaturing their functions, gold thiol self-assembled monolayers (SAMs) have been studied extensively for surface fabrication. In this project we will prepare functional monolayers using newly synthesized thiol derivatives, evaluate correlation between surface force and surface morphology of the SAMs using the surface forces apparatus, and optimize the condition to fabricate biological devices such as immune sensors.Read moreRead less
Positron processes - From Basic to Applied Science. Australian scientists are at the forefront of international activities in atomic and molecular physics and materials science research. This program will expand the level of expertise in an emerging field that has importance in both these areas - the use of positron beams. Australia is developing a new and exciting capacity for positron research through the National Positron Beamline Facility. Scientists in this collaboration will work with o ....Positron processes - From Basic to Applied Science. Australian scientists are at the forefront of international activities in atomic and molecular physics and materials science research. This program will expand the level of expertise in an emerging field that has importance in both these areas - the use of positron beams. Australia is developing a new and exciting capacity for positron research through the National Positron Beamline Facility. Scientists in this collaboration will work with other outstanding, international research groups in the field of positron studies to stimulate new directions for their research. The international links, and the novel capabilities of the new Australian Facility, will enable our researchers to fully exploit this new field of research.Read moreRead less