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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ARC Centre for Complex Dynamic Systems & Control. Complex dynamic systems are an inescapable feature of the world we live in. Modelling, analysing and optimizing complex behaviour is crucial for environment, process industry, biomedical, energy distribution, transportation and other applications. The Centre for Complex Dynamic Systems and Control will become an international authority in the analysis, design and optimization of complex dynamic systems, pursuing both outstanding fundamental and c ....ARC Centre for Complex Dynamic Systems & Control. Complex dynamic systems are an inescapable feature of the world we live in. Modelling, analysing and optimizing complex behaviour is crucial for environment, process industry, biomedical, energy distribution, transportation and other applications. The Centre for Complex Dynamic Systems and Control will become an international authority in the analysis, design and optimization of complex dynamic systems, pursuing both outstanding fundamental and cutting edge applied research outcomes. These outcomes will be of specific benefit to partner organizations including minerals, process, metal forming, and automotive industries.Read moreRead less
The prediction of sleep/wake behaviour based on physiological and social factors. The prevalence of shiftwork has increased in Australia over the last few decades. Shiftworkers obtain less sleep, have greater difficulty maintaining good relationships, have poorer health, and are more likely to be injured at work than others. Using the largest dataset of its kind, we will substantially contribute to understanding the relationships between work hours, sleep, performance and safety. Ultimately, the ....The prediction of sleep/wake behaviour based on physiological and social factors. The prevalence of shiftwork has increased in Australia over the last few decades. Shiftworkers obtain less sleep, have greater difficulty maintaining good relationships, have poorer health, and are more likely to be injured at work than others. Using the largest dataset of its kind, we will substantially contribute to understanding the relationships between work hours, sleep, performance and safety. Ultimately, the project will answer a question critical to workplace safety - how much time off between shifts is needed to be alert and safe at work? The project will also produce tools to help industry design fatigue-friendly rosters, improving the safety, productivity and general well-being of shiftworkers in Australia and overseas.Read moreRead less
Improved Monte Carlo Methods for Estimation, Optimisation and Counting. The project will benefit the Australian society by building the theoretical and methodological foundations for the next generation of Monte Carlo techniques. The advancement of the knowledge in this area will provide important tools for solving complex estimation, optimisation and counting problems in engineering, statistics, computer science, mathematics and the physical and life sciences. As a result it will generate a com ....Improved Monte Carlo Methods for Estimation, Optimisation and Counting. The project will benefit the Australian society by building the theoretical and methodological foundations for the next generation of Monte Carlo techniques. The advancement of the knowledge in this area will provide important tools for solving complex estimation, optimisation and counting problems in engineering, statistics, computer science, mathematics and the physical and life sciences. As a result it will generate a competitive advantage for various sections of the Australian industry, including telecommunications, biotechnology and finance. The project will enable Australian researchers to continue to work at the forefront of this fast moving and exciting area of international research.Read moreRead less
Special Research Initiatives - Grant ID: SR0354793
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
A Neural Network: Understanding Brain Function. This proposal focuses on the mechanisms that regulate brain function, particularly those underpinning the changes in circuitry (plasticity) caused by altered inputs. As such, its core goal is to create an interface between researchers in the neurosciences, computational modelling, robotics and cognitive sciences in order to facilitate optimum collaborative interactions, identify key research questions and promote training opportunities across a mul ....A Neural Network: Understanding Brain Function. This proposal focuses on the mechanisms that regulate brain function, particularly those underpinning the changes in circuitry (plasticity) caused by altered inputs. As such, its core goal is to create an interface between researchers in the neurosciences, computational modelling, robotics and cognitive sciences in order to facilitate optimum collaborative interactions, identify key research questions and promote training opportunities across a multidisciplinary spectrum. This will drive an integrated and accelerated program of discovery and technological development, enhancing Australia's leadership in this crucial field and helping to highlight new biotechnology opportunities and capture social and economic benefits for the nation. Read moreRead less
Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground fo ....Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground for Higher Degree Students with interests in pure mathematics as well as computer
algebra and symbolic computation.Read moreRead less
Discovery Indigenous Researchers Development - Grant ID: DI0453648
Funder
Australian Research Council
Funding Amount
$144,184.00
Summary
Modelling of coupled heat and water flow through layered soils with an extension to heat flow through granulated soils. The main aim of this project is to develop a mathematical model to simulate coupled heat and water flow through layered soils. The coupling of the two processes will allow us to examine the interaction between heat and water flow. The project also aims to extend the heat component of the flow model to granulated heterogeneous soils by developing a model that encapsulates heat e ....Modelling of coupled heat and water flow through layered soils with an extension to heat flow through granulated soils. The main aim of this project is to develop a mathematical model to simulate coupled heat and water flow through layered soils. The coupling of the two processes will allow us to examine the interaction between heat and water flow. The project also aims to extend the heat component of the flow model to granulated heterogeneous soils by developing a model that encapsulates heat effects at the microscopic and macroscopic level. The model will be applied to two problems 1) hydraulic barriers in cover liner designs for landfills and 2) assessing the ability of heat sensors to measure various soil properties under field conditions.Read moreRead less
Stochastic Modelling of Genetic Regulatory Networks: Subtitle - Genetic Regulation is a Noisy Business. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in ....Stochastic Modelling of Genetic Regulatory Networks: Subtitle - Genetic Regulation is a Noisy Business. The completion of the human genome marked the culmination of one hundred years of reductionist science in cell biology. Although further bioinformatics analysis will continue, the focus is shifting towards synthesis and understanding how the regulatory genetic components dynamically interact to form functional phenotypes. The key to this is the understanding of the roles of stochasticity in cellular processes. This project will explore these roles and will develop an integrated complex systems modelling, simulation and visualisation framework. This will be used on an exemplar application for lineage commitment in haematopoiesis and for exploring and validating genetic regulatory models in general.Read moreRead less