The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the ....The canonical stratification of jet spaces. Singularities occur everywhere in nature, from the formation and collapse of stars to the morphology of living embryos. They appear whenever the geometry of surfaces or spaces undergoes a process of twisting, folding, or collapsing on itself. Singularity Theory is the study of such phenomena, an important branch of modern mathematics which has close connections with many other branches of mathematics and applied sciences. Singularity Theory lies at the crossroads of the paths connecting the most important areas of applications of mathematics with its most abstract parts. Analytic Singularity Theory is a central part of Singularity Theory. This project would lead to substantially new advancements in Analytic Singularity Theory.Read moreRead less
Orthogonal Sensing Strategies for Soft Sensors to Discern Multiple Stimuli . The project seeks to create new orthogonal sensing technologies that enable a single soft sensor to detect multiple mechanical and thermal stimuli, overcoming the challenge of cross-talk between stimuli. The project expects to generate new knowledge of orthogonal sensing mechanisms and the effects of microstructure designs. The expected outcomes include novel soft sensors capable of accurately detecting pressure, stretc ....Orthogonal Sensing Strategies for Soft Sensors to Discern Multiple Stimuli . The project seeks to create new orthogonal sensing technologies that enable a single soft sensor to detect multiple mechanical and thermal stimuli, overcoming the challenge of cross-talk between stimuli. The project expects to generate new knowledge of orthogonal sensing mechanisms and the effects of microstructure designs. The expected outcomes include novel soft sensors capable of accurately detecting pressure, stretch, shear, and temperature simultaneously. The new technologies are expected to support Australian companies in developing, producing and exporting sensors for soft robots and wearable devices for health monitoring, an area recognized as a key priority by the Federal Government’s Industry Growth Centres.Read moreRead less
Ceramic matrix nanocomposites. Using a novel process developed by the applicant, this project will create and study ceramic matrix nanocomposites of two types: (i) those in which the nanoparticles are homogeneously distributed in alumina and (ii) functionally-graded nanocomposites of controlled heterogeneity, that is, nanocomposites in which the nanoparticles are distributed heterogeneously in glass. Homogeneous nanocomposites of alumina are potentially of great importance to the mining industry ....Ceramic matrix nanocomposites. Using a novel process developed by the applicant, this project will create and study ceramic matrix nanocomposites of two types: (i) those in which the nanoparticles are homogeneously distributed in alumina and (ii) functionally-graded nanocomposites of controlled heterogeneity, that is, nanocomposites in which the nanoparticles are distributed heterogeneously in glass. Homogeneous nanocomposites of alumina are potentially of great importance to the mining industry as they can increase the toughness and wear resistance of mining components. Heterogeneous nanocomposities have the potential to revolutionise the dental restoration industry by combining greatly increased toughness with the aesthetic benefit of controllable translucency.Read moreRead less
Nano-toughening of Conductive Composites with High Electrical Ductility. This project aims to develop a new technology to effectively toughen conductive thin films including metals and conductive polymers with significantly improved mechanical robustness for next-generation stretchable electronics. This new technique will tackle the major limitation of stretchable electronics propensity to abrupt electrical failure caused by plastic deformation and long channel cracks in conductive thin films of ....Nano-toughening of Conductive Composites with High Electrical Ductility. This project aims to develop a new technology to effectively toughen conductive thin films including metals and conductive polymers with significantly improved mechanical robustness for next-generation stretchable electronics. This new technique will tackle the major limitation of stretchable electronics propensity to abrupt electrical failure caused by plastic deformation and long channel cracks in conductive thin films of low yield strain and ductility. By overcoming the bottleneck issue of low stretchability and ductility of existing conductive thin film materials, it will be possible to significantly expand the design space of flexible and stretchable electronic devices.Read moreRead less
Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manif ....Harmonic analysis of Laplacians in curved spaces. Harmonic Analysis is a branch of mathematics which is interrelated to other fields of mathematics like complex analysis, number theory and partial differential equations (pdes) with many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems at the frontier of harmonic analysis in understanding Laplacians in curved spaces. Such Laplacians control the propagation of heat and waves on manifolds and Lie groups, arising in mathematical physics and quantum mechanics. Expected outcomes are the solutions of dispersive equations and the framework of singular integrals in curved spaces; new ideas and techniques in harmonic analysis developed; and training of Australian future mathematicians.Read moreRead less
Microwave Antennas based on Metamaterials. This project concerns one of the most exciting and dynamic areas of research at present. Metamaterials have tremendous potential, with the promise of multitudinous applications in microwave, optical and optoelectronic fields. This project will contribute towards the ARC priority goal on advanced materials and frontier technologies by (a) developing new synthesized materials which have special properties not found in nature, and (b) developing new techn ....Microwave Antennas based on Metamaterials. This project concerns one of the most exciting and dynamic areas of research at present. Metamaterials have tremendous potential, with the promise of multitudinous applications in microwave, optical and optoelectronic fields. This project will contribute towards the ARC priority goal on advanced materials and frontier technologies by (a) developing new synthesized materials which have special properties not found in nature, and (b) developing new technologies to deliver practical benefits for communication systems users by exploiting these materials. Other benefits for Australia include intellectual property and patent outcomes, which may help Australia to become a leader in metamaterial-based technologies.Read moreRead less
Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical an ....Generalised conformal mappings. A conformal mapping preserves shape, at least at very small scale, circles are mapped to circles. The more recently introduced quasi-conformal mappings nearly preserves shape, at least at a very small scale, circles are mapped to regions which are similar to circles. This project will allow different directions to be scaled differently, and will consider mappings that send circles to ellipses of arbitrary eccentricity. The theory to be developed is mathematical and it will provide a unified approach to important results in several areas, including Lie groups and functions of several complex variables. Read moreRead less
Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
Discovery Early Career Researcher Award - Grant ID: DE140100223
Funder
Australian Research Council
Funding Amount
$385,735.00
Summary
Diophantine approximation, transcendence, and related structures. Sequences produced by low-complexity structures are objects of importance to mathematics, linguistics and theoretical computer science. In the 1960s, Chomsky and Schützenberger formalised and popularised a hierarchy of such objects. In the 1920s, Mahler provided a corresponding analytic framework, which has proven extremely useful for analysing the algebraic character of low-complexity real numbers. This project will further devel ....Diophantine approximation, transcendence, and related structures. Sequences produced by low-complexity structures are objects of importance to mathematics, linguistics and theoretical computer science. In the 1960s, Chomsky and Schützenberger formalised and popularised a hierarchy of such objects. In the 1920s, Mahler provided a corresponding analytic framework, which has proven extremely useful for analysing the algebraic character of low-complexity real numbers. This project will further develop Mahler's method in order to investigate the connection between the algebraic and arithmetic properties of real numbers and the various Chomskian complexity measures of those numbers. The results of this proposal will advance our knowledge of the nature of "randomness" in low-complexity arithmetic sequences.Read moreRead less
Development of Deformation-Mechanism Based Parameters for Improved Design of Hard Coatings. The use of thin hard abrasion-resistant coatings is an important method for significantly improving the operational lifetime of components in a wide range of mechanical, biomedical and sensory applications. The optimal design of these coatings is however severely restricted by a lack of detailed knowledge of their material deformation mechanisms. The proposed project will use novel nano-indentation and el ....Development of Deformation-Mechanism Based Parameters for Improved Design of Hard Coatings. The use of thin hard abrasion-resistant coatings is an important method for significantly improving the operational lifetime of components in a wide range of mechanical, biomedical and sensory applications. The optimal design of these coatings is however severely restricted by a lack of detailed knowledge of their material deformation mechanisms. The proposed project will use novel nano-indentation and electron microscope techniques to create a basis for mechanism-based deformation models. These models will then be used to develop new coating architectures with improved operational lifetimes as well as predicting coating lifetimes and developing simple tools for coating assessment.Read moreRead less