THE STABILITY OF GLASS-FORMING ALLOYS: SIMULATION STUDIES. Many of the properties that make common glass so valuable as a material can also be achieved in amorphous metals. The 'trick' is to avoid crystallization as the molten state is cooled. Recently, novel combinations of metals have been found to slow down crystallization enough to produce stable amorphous alloys. Developing these new materials depends on an accurate atomic level understanding of how crystallization is frustrated in glass-fo ....THE STABILITY OF GLASS-FORMING ALLOYS: SIMULATION STUDIES. Many of the properties that make common glass so valuable as a material can also be achieved in amorphous metals. The 'trick' is to avoid crystallization as the molten state is cooled. Recently, novel combinations of metals have been found to slow down crystallization enough to produce stable amorphous alloys. Developing these new materials depends on an accurate atomic level understanding of how crystallization is frustrated in glass-forming alloys. This project's aim is to use computer simulations to provide the first microscopic picture of the atomic order that stabilzes the amorphous alloys with regards to both crystallization and mechanical stress.Read moreRead less
Soft modes in glasses: chemical control of relaxation and mechanical response. The unusual dynamical and mechanical properties of viscous liquids and glasses underpins many existing and emerging technologies, from lubrication to the strength and fragility of bulk metallic glasses. An improved understanding of how macroscopic properties such as viscous flow, ductility and fracture emerge from the microscopic interactions between atoms and molecules will provide the enabling scientific knowledge f ....Soft modes in glasses: chemical control of relaxation and mechanical response. The unusual dynamical and mechanical properties of viscous liquids and glasses underpins many existing and emerging technologies, from lubrication to the strength and fragility of bulk metallic glasses. An improved understanding of how macroscopic properties such as viscous flow, ductility and fracture emerge from the microscopic interactions between atoms and molecules will provide the enabling scientific knowledge for exploiting the properties of such materials on the nanoscale. National expertise in this area will help establish and strengthen international collaboration with leading research institutes in the field.Read moreRead less
Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will signif ....Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will significantly advance the theory of quantum cryptography and knowledge of the fundamental resource of secret keys. It is expected to have immediate application for the classical security of existing (non-quantum) communication devices, and benefit security, military, government, industry, individuals, and the community.Read moreRead less
Quantum effects in zero-error communication. This project will establish a systematic quantum zero-error information theory to build highly reliable quantum communications networks. This innovative, breakthrough technology will advance research into the physical realisation of quantum communication. It has global implications and will promote Australia's position in this new research field.
A mathematical foundation and novel solutions for highly secure communications. This project will deliver novel solutions to security and privacy in communication networks by exploring the power of quantum information with mathematical tools from operator stuctures. It will significantly advance our knowledge about quantum communication, with expected benefits on Australian social, economic and even military security.
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
Geometric analysis of nonlinear systems. Modern science derives its power from mathematics. The project aims to capture, identify and describe pivotal, transcendental solutions of nonlinear systems that are universal in science, in the sense that they always arise as mathematical models under certain physical limits. The project expects to produce new mathematical methods to describe such functions by using a newly discovered geometric framework. Expected outcomes include the description of elus ....Geometric analysis of nonlinear systems. Modern science derives its power from mathematics. The project aims to capture, identify and describe pivotal, transcendental solutions of nonlinear systems that are universal in science, in the sense that they always arise as mathematical models under certain physical limits. The project expects to produce new mathematical methods to describe such functions by using a newly discovered geometric framework. Expected outcomes include the description of elusive solutions of discrete and higher-dimensional nonlinear systems. This should provide significant benefits, such as new mathematical knowledge, innovative techniques, enhanced scientific capacity in Australia.Read moreRead less
Classical and affine W-algebras. The project aims to address major mathematical problems on representations of the families of quantum groups and vertex algebras associated with Lie algebras. It aims to create new connections between representation theory and mathematical physics. The theory of quantum groups originated from solvable lattice models in statistical mechanics and has turned out to have important connections with and applications to a wide range of subjects in mathematics and physic ....Classical and affine W-algebras. The project aims to address major mathematical problems on representations of the families of quantum groups and vertex algebras associated with Lie algebras. It aims to create new connections between representation theory and mathematical physics. The theory of quantum groups originated from solvable lattice models in statistical mechanics and has turned out to have important connections with and applications to a wide range of subjects in mathematics and physics. The project aims to rely on these connections to extend and develop explicit theory of both the classical and quantum versions of the vertex algebras which are of great importance to conformal field theory and soliton spin chain models.Read moreRead less