Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents ....Operations research without convexity. Operations Research (OR) is one of the most applicable areas of mathematics and of importance for the future of technologically advanced Australia. However, applications of OR often require convexity. This is a serious limitation. A new approach, monotonic analysis, which is applicable to a broad class of nonconvex problems, was given birth by the CI. Promising results have been obtained and leading researchers around the world (including the Presidents of the Canadian Mathematical and French Applied Mathematics Societies) are keen to work with the CI developing this topic. This project both cements and extends world leadership in this field.Read moreRead less
Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by t ....Integrable structures in models of complex systems. The CI is in the happy circumstance of having almost completed (now in the proof reading stage) a large monograph on random matrices commissioned by Princeton University Press. This gives great international profile to the CI, and more generally Australian mathematical sciences in the subject matter of the proposal. To build on this base it is essential that significant new results, impacting on the work of others, continue to be obtained by the CI. All indications are that the new ideas relating integrable structures and random matrices underpinning this proposal will fulfil this goal. For the postdoctral researcher involved the stimulating atmosphere of discovery should provide ideal training in mathematical research.Read moreRead less
Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, a ....Random matrix theory and high dimensional inference. The topic of high dimensional inference and random matrix theory is one of present international prominence, as evidenced by the number of special programs on this theme of late. This is due both to recent advances in random matrix theory, and the fact that there are applications to areas such as econometrics, meteorology and engineering. With the CI being an expert in random matrix theory, and Professor Bassler an expert in complex systems, another line of applications will be emphasized, and a new axis of international linkage formed.Read moreRead less
Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
Conformal invariance and stationary states. Universal properties in nonequilibrium processes, such as scaling of space and time, suggest the existence of a fundamental, model independent theory describing such phenomena. An analogous theory for equilibrium phenomena exists, namely conformal field theory, and is extremely important for our understanding. Using recent insights this project aims at formulating such a theory for universal nonequilibrium behaviour.
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
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
Fractional Integration, Power Laws and Econometric Models: Some Methodological and Theoretical Developments. The fundamental objectives of this project are to: (i) Extend
current econometric practice and consider the use of power laws as
a basis for the construction of a more flexible and realistic
class of models for the analysis of economic and financial time
series. (ii) To develop inferential techniques appropriate for the
modelling of dynamic econometric systems that incorporate
struc ....Fractional Integration, Power Laws and Econometric Models: Some Methodological and Theoretical Developments. The fundamental objectives of this project are to: (i) Extend
current econometric practice and consider the use of power laws as
a basis for the construction of a more flexible and realistic
class of models for the analysis of economic and financial time
series. (ii) To develop inferential techniques appropriate for the
modelling of dynamic econometric systems that incorporate
structure characterized by power laws. This will be achieved by
building upon the class of fractionally integrated processes. New
econometric models and methodologies for the analysis of
non-stationarity series will be developed, along with the
associated theoretical results.Read moreRead less