The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to com ....The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to computational mathematics, particularly elliptic curve cryptosystems; - a huge boost to the development of number theory Australia-wide.
Read moreRead less
THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is antici ....THE DEVELOPMENT OF MECHANISTIC MODELS FOR BUBBLY FLOWS WITH HEAT AND MASS TRANSFER. Commercially available CFD computer codes are currently widely used in many Australian industrial sectors. It is clearly recognised that the state-of-the-art models for dealing with complex bubbly flows with/without heat and mass transfer in these computer codes require further developments and improvements. This research project will address the prevalent deficiency in many of these computer codes. It is anticipated that through this major development of new models capable of predicting a wide range of industrial bubbly flow problems and implementation thereafter in these computer codes, industries will experience significant benefits especially reduce time and costs in their design and production.Read moreRead less
Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of ....Experimental and Numerical Modelling of Gas-Liquid Flows. Multiphase flow systems are encountered in many process industries such as chemical, petroleum, mining, energy, food and pharmaceutical, which are fundamental to the Australian economy. Commercially available computer codes for simulating such systems are currently widely used in many Australian industrial sectors. This research project will address the prevalent deficiency in many of these computer codes and develop new models capable of predicting a wide range of industrial bubbly flow problems. The resultant improved computer codes will provide industries with significant benefits - especially reduced times and costs in their design and production.Read moreRead less
Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress ....Algorithms and computation in four-dimensional topology. This project will establish Australia as a world leader in computational topology, particularly in the all-important areas of topology in three and four dimensions. In four dimensions this work will be truly groundbreaking; until now the field has seen little development due to the complexity of the algorithms and computations required, and the applicant is in the unique position of having the necessary tools to make significant progress in a feasible time frame. In three dimensions this project will strengthen the distinguished computational topology community in Melbourne, led by pioneers such as Rubinstein, Goodman, Hodgson as well as the applicant himself.Read moreRead less
Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading the ....Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading theoretical groups, which will greatly aid research student education. There are direct applications to experiments on molecule formation with ultra-cold fermions in the ARC Centre of Excellence for Quantum-Atom Optics.Read moreRead less
Improving Upper and Lower Bounds on the Order of Large Graphs under Degree and Distance Constraints. Networks govern all aspects of society, including transportation networks, communication networks, computer networks and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs. This project will provide new theoretical results which will improve our knowledge of network topologi ....Improving Upper and Lower Bounds on the Order of Large Graphs under Degree and Distance Constraints. Networks govern all aspects of society, including transportation networks, communication networks, computer networks and networks for the distribution of goods etc. - and the theoretical analysis of such networks has become a subject of fundamental importance. Networks can be modelled by graphs. This project will provide new theoretical results which will improve our knowledge of network topologies. The new knowledge will then be utilised in the construction of large graphs with respect to given maximum degree and distance constraints.Read moreRead less
Using global optimization technique to determine the most efficient use of building/floor space to accommodate a given office design. The commercial property market is one of the largest business markets, both in Australia and globally. Businesses of all kinds use commercial office space, which represents many billions of investment dollars. A better understanding of what constitutes efficient and effective office space would produce enormous commercial benefits for this country. Historically, ....Using global optimization technique to determine the most efficient use of building/floor space to accommodate a given office design. The commercial property market is one of the largest business markets, both in Australia and globally. Businesses of all kinds use commercial office space, which represents many billions of investment dollars. A better understanding of what constitutes efficient and effective office space would produce enormous commercial benefits for this country. Historically, very little (if any) consideration has been given to the efficiency of office space design. The measurement of efficiency has now become an essential component of 'site selection'. To date, the application of optimization methodologies have not been applied to the architectural industry, making the development of tools to address this problem a significant and innovative move.Read moreRead less
Evolutionary multi-objective algorithms for Global Grids. This research investigates alternative software technologies for Grid-based evolutionary multi-objective decision algorithms. By employing the latest adaptive techniques and taking advantage of the low cost Grid infrastructure, new parallel evolutionary systems will be developed that can rapidly supply robust solutions to complex problems. This project will further develop an understanding of scaling issues in parallel evolutionary syste ....Evolutionary multi-objective algorithms for Global Grids. This research investigates alternative software technologies for Grid-based evolutionary multi-objective decision algorithms. By employing the latest adaptive techniques and taking advantage of the low cost Grid infrastructure, new parallel evolutionary systems will be developed that can rapidly supply robust solutions to complex problems. This project will further develop an understanding of scaling issues in parallel evolutionary systems and pave the way for even more widespread application of evolutionary techniques for large scale, data-intensive applications in science and industry.Read moreRead less
Advanced Computational and Analytic Studies in Lattice Statistical Mechanics and Applications. Lattice Statistical Mechanics is one of the current success stories of Australian Science with a significant international presence. The applicants represent a centre of excellence, particularly in the area of combining computational and analytic studies for maximum scientific benefit. The programme of research maximises Australia's investment in this human resource by focussing on an integrated set of ....Advanced Computational and Analytic Studies in Lattice Statistical Mechanics and Applications. Lattice Statistical Mechanics is one of the current success stories of Australian Science with a significant international presence. The applicants represent a centre of excellence, particularly in the area of combining computational and analytic studies for maximum scientific benefit. The programme of research maximises Australia's investment in this human resource by focussing on an integrated set of projects comprising a diverse and innovative group of applications in areas such as polymer science, DNA denaturation, combinatorics and the study of traffic flows. The underlying theme is always the utility of lattice statistical mechanics in 21st century science.Read moreRead less
Key combinatorial problems in lattice statistical mechanics. The enumeration of lattice animals is a famous open problem in combinatorics. These discrete structures also underpin our understanding of many physical phenomena, including polymer collapse and percolation in random media, through the integral part they play in many models in statistical mechanics and theoretical chemistry.
The project aims to answer some key open problems in this area using exact and numerical techniques. We expe ....Key combinatorial problems in lattice statistical mechanics. The enumeration of lattice animals is a famous open problem in combinatorics. These discrete structures also underpin our understanding of many physical phenomena, including polymer collapse and percolation in random media, through the integral part they play in many models in statistical mechanics and theoretical chemistry.
The project aims to answer some key open problems in this area using exact and numerical techniques. We expect that this will lead to proofs of the insolvability of certain problems, new exact solutions of others, and a greater understanding of the effect of topology and geometry on the behaviour of these models.Read moreRead less