Special Research Initiatives - Grant ID: SR0354553
Funder
Australian Research Council
Funding Amount
$30,000.00
Summary
Network on Control, Dynamics and Systems (NCDS). Control systems theory provides principles and methods for design of complex engineering systems that automatically maintain desired performance despite changes in their environment (e.g. autopilot in an aircraft). This field is facing many new exciting challenges at the dawn of new millenium, such as design of complex engineering systems in possibly networked, asynchronous and distributed environments. The network will play a major role in addres ....Network on Control, Dynamics and Systems (NCDS). Control systems theory provides principles and methods for design of complex engineering systems that automatically maintain desired performance despite changes in their environment (e.g. autopilot in an aircraft). This field is facing many new exciting challenges at the dawn of new millenium, such as design of complex engineering systems in possibly networked, asynchronous and distributed environments. The network will play a major role in addressing these challenges by providing a national research focus, facilitating collaboration and the sharing of people and ideas. By delivering a National Graduate School, the network will enhance learning conditions for graduate students. Moreover, it will provide an important catalyst between Australian universities and industry. This initiative will be essential in assessing the present state of control research in Australia and drafting a detailed plan for the network's leading research role in the future. Read moreRead less
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
Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics a ....Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics and its applications.Read moreRead less
Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high spee ....Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high speed telecommunication networks. It will suggest new more profitable approaches to known problems such as effective bandwidth problem, analysis and design of computer networks, optimal control of dams, and anticipate not ordinary results and solutions. It will contribute to the mathematical culture in Australia and worldwide. 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
Nonlinear elliptic partial differential equations and applications. Many fundamental advances in modern technology, science and economics are driven by the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been increasing use in applications of partial differential equations of elliptic type with major discoveries made and longstanding problems resolved by the two Chief Investigators, who have in return received many international accolades ....Nonlinear elliptic partial differential equations and applications. Many fundamental advances in modern technology, science and economics are driven by the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been increasing use in applications of partial differential equations of elliptic type with major discoveries made and longstanding problems resolved by the two Chief Investigators, who have in return received many international accolades. This project provides for the continuation of Australian leadership in key strategic areas of international science, such as optimal transportation, as well as the continued building of related expertise and training.Read moreRead less
Nonlinear elliptic equations and applications. Many fundamental advances in modern technology, science and economics are driven through the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been an explosion in applications of partial differential equations of elliptic type with major discoveries in underlying theory being made by the two Chief Investigators. This project provides for the continuation of Australian leadership in key st ....Nonlinear elliptic equations and applications. Many fundamental advances in modern technology, science and economics are driven through the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been an explosion in applications of partial differential equations of elliptic type with major discoveries in underlying theory being made by the two Chief Investigators. This project provides for the continuation of Australian leadership in key strategic areas of international science, such as optimal transportation, as well as the continued building of related expertise and training.Read moreRead less
Variational problems of Monge-Ampere type. Nonlinear models dominate the frontline of modern theoretical and applied mathematics. This project concerns contemporary variational problems with analysis linked strongly to the Monge-Ampere equation, which is a fully nonlinear partial differential equation. Its study in recent years has generated complex and deep theoretical issues along with a diverse range of applications. The proposal is divided into two themes, affine maximal surfaces (involving ....Variational problems of Monge-Ampere type. Nonlinear models dominate the frontline of modern theoretical and applied mathematics. This project concerns contemporary variational problems with analysis linked strongly to the Monge-Ampere equation, which is a fully nonlinear partial differential equation. Its study in recent years has generated complex and deep theoretical issues along with a diverse range of applications. The proposal is divided into two themes, affine maximal surfaces (involving fourth order partial differential equations of Monge-Ampere type) and optimal transportation (where Monge-Ampere theory has been applied successfully in recent years). Each of these builds upon major recent research breakthroughs of the proposers.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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Complexity-manageable methodologies and efficient computational tools for analysis and design of large-scale systems. The tools to be developed in this project have impact on a broad range of disciplines, including system analysis, feedback control technology, signal processing, communication network, and information theory. Practically, the success of this project will create cutting edge technologies applicable to design and management of important infrastructures of the modern society such as ....Complexity-manageable methodologies and efficient computational tools for analysis and design of large-scale systems. The tools to be developed in this project have impact on a broad range of disciplines, including system analysis, feedback control technology, signal processing, communication network, and information theory. Practically, the success of this project will create cutting edge technologies applicable to design and management of important infrastructures of the modern society such as communication networks, transportation systems, electrical power grids, and collaborative intelligent machines, and water distribution networks. Success of this project will bring novel methodologies and computational tools which help engineers to systematically design and validate the performance of their engineering systems.Read moreRead less