Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing internat ....Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing international research experience for early career researchers. As a result, this proposal will enhance Australia's distinguished reputation in analysis and further link the UQ group with a number of mathematical institutes in USA and China.Read moreRead less
Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with ....Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with applications in physics and and other sciences. Specialist training will be provided for Australia's next generation of mathematicians. This project will enable Australian researchers to stay at the forefront of research in this area, strengthening links with a number of world-leading mathematicians.Read moreRead less
Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE110100023
Funder
Australian Research Council
Funding Amount
$500,000.00
Summary
Integrated command and control facility for large-scale critical infrastructure management. This is a test bed facility for achieving sustainable operation of Australia's critical infrastructure, particularly at airports. The facility will enable an integrated and coordinated strategy to increase operational resilience while not losing sight of the complex nature and dynamic requirements of critical infrastructure management.
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0882357
Funder
Australian Research Council
Funding Amount
$500,000.00
Summary
A Computational Facility for Multi-scale Modelling in Bio and Nanotechnology. Bio- and nanotechnology have the potential to transform Australian industry and research, and to bring significant benefits for consumers. The scope will include materials for energy storage, medical diagnostics and cellular imaging, bioengineering, drug and gene delivery, improved foods by molecular design, novel materials for electronics, improved techniques for particle processing, and molecular sieves for filtering ....A Computational Facility for Multi-scale Modelling in Bio and Nanotechnology. Bio- and nanotechnology have the potential to transform Australian industry and research, and to bring significant benefits for consumers. The scope will include materials for energy storage, medical diagnostics and cellular imaging, bioengineering, drug and gene delivery, improved foods by molecular design, novel materials for electronics, improved techniques for particle processing, and molecular sieves for filtering/purifying water and gases. The dedicated computing facility will enable a fast interactive cycle between simulation and experiment in these areas, accelerating the pace of research and applications.Read moreRead less
Investigating the Effects of Network-Induced Delays on Networked Control Systems. Networked control is the current trend for industrial automation. The results of this project will be the first in the world to contribute directly to a deeper understanding of both negative and positive effects of network-induced delays on networked control systems. It will firmly place Australia at the forefront of this research by developing cutting edge technology for reliability and efficiency of industrial ne ....Investigating the Effects of Network-Induced Delays on Networked Control Systems. Networked control is the current trend for industrial automation. The results of this project will be the first in the world to contribute directly to a deeper understanding of both negative and positive effects of network-induced delays on networked control systems. It will firmly place Australia at the forefront of this research by developing cutting edge technology for reliability and efficiency of industrial networked-based control systems. This novel frontier technology will result in cost-saving and improved productivity for Australian industries, e.g. manufacturing industries, power stations, processing industries, automotive industries, vehicular networks and locomotives.Read moreRead less
Variable Structure Control Systems in Networked Environments. This project will be the first in the world to lay the foundation for a new theory for understanding and designing new variable structure control systems in the networked environments, which is in great need due to increasing use of shared communication networks in modern industrial systems. It will firmly place Australia at the forefront of this research by developing a cutting edge technology for improving reliability and efficiency ....Variable Structure Control Systems in Networked Environments. This project will be the first in the world to lay the foundation for a new theory for understanding and designing new variable structure control systems in the networked environments, which is in great need due to increasing use of shared communication networks in modern industrial systems. It will firmly place Australia at the forefront of this research by developing a cutting edge technology for improving reliability and efficiency of industrial variable structure control systems in the networked environments, hence resulting in cost-saving and improved productivity for industry. It will provide training for new leading researchers specialised in this new theory and technology.Read moreRead less
Climate change: adaptation and resilience in the face of uncertainty. Climate change poses a wide range of challenges to Australia's agricultural sector and for the management of natural ecosystems. These challenges are recognised in the National Research Priorities 1, An Environmentally Sustainable Australia, and 4, Safeguarding Australia. The potential economic costs of climate change to vital national assets such as the Murray-Darling Basin and the Great Barrier Reef, amount to billions of do ....Climate change: adaptation and resilience in the face of uncertainty. Climate change poses a wide range of challenges to Australia's agricultural sector and for the management of natural ecosystems. These challenges are recognised in the National Research Priorities 1, An Environmentally Sustainable Australia, and 4, Safeguarding Australia. The potential economic costs of climate change to vital national assets such as the Murray-Darling Basin and the Great Barrier Reef, amount to billions of dollars per year, and ecological costs are even more significant. Uncertainty about the rate at which climate change will take place and about effects in different regions is central to the problem. This project will explore adaptive management strategies that promote resilience in the face of uncertainty.
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Optimum location of FACTS devices with advanced control scheme for improving the security of complex power grid. Prevention of blackouts is one of the highest priorities of the electricity industry. One of the fundamental reasons for the recent blackouts in long transmission network is inter-area oscillations. Queensland's long transmission network is a vital part of the Australian electricity grid and is vulnerable to inter-area oscillations. There is a need for a comprehensive approach to inve ....Optimum location of FACTS devices with advanced control scheme for improving the security of complex power grid. Prevention of blackouts is one of the highest priorities of the electricity industry. One of the fundamental reasons for the recent blackouts in long transmission network is inter-area oscillations. Queensland's long transmission network is a vital part of the Australian electricity grid and is vulnerable to inter-area oscillations. There is a need for a comprehensive approach to investigate the effect of inter-area oscillation that contributes to blackouts. Focussing the Queensland network, this project will provide a complete assessment tool for the optimum location of FACTS devices with modern and advanced control schemes in improving the security of complex interconnected power-grid. Read moreRead less