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
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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Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscal ....Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel methodology will explore this stumbling block, and promises to radically change the modeling, exploration and understanding of multiscale complex system behaviour.Read moreRead less
Modelling of Adsorption Dynamics in Microporous Adsorbents Using Fractional Order Diffusion Equations. This project investigates the use of fractional order diffusion equations in modelling adsorption dynamics in microporous carbons. The long tail behaviour of adsorption processes cannot be readily explained by the classical second order Fickian model, and makes adsorption a candidate for the use of fractional order diffusion equations that have the potential to model such features. In the pre ....Modelling of Adsorption Dynamics in Microporous Adsorbents Using Fractional Order Diffusion Equations. This project investigates the use of fractional order diffusion equations in modelling adsorption dynamics in microporous carbons. The long tail behaviour of adsorption processes cannot be readily explained by the classical second order Fickian model, and makes adsorption a candidate for the use of fractional order diffusion equations that have the potential to model such features. In the present project we shall develop suitable numerical techniques for solving the fractional order diffusion model, and apply these to the interpretation of experimental kinetic data. The outcome will be an improved model of adsorption dynamics considering the fractal nature of the solid.Read moreRead less
Determination of Conductivity Values for Anisotropic Tissue. Well established mathematical models governing the electrical potential in biological tissue can be combined with measurements of the electric potential on the surface of the tissue to provide insight into subsurface tissue damage. However, before such observations can be convincingly accepted, reliable values for the tissue conductivity must be obtained. The aim of this project is to develop mathematical techniques to calculate the co ....Determination of Conductivity Values for Anisotropic Tissue. Well established mathematical models governing the electrical potential in biological tissue can be combined with measurements of the electric potential on the surface of the tissue to provide insight into subsurface tissue damage. However, before such observations can be convincingly accepted, reliable values for the tissue conductivity must be obtained. The aim of this project is to develop mathematical techniques to calculate the conductivity values so that one can apply the equations to solve problems of potential distribution and proceed to accurately simulate electrical potential distributions in damaged tissue. More accurate and reliable conductivity values will allow a better understanding of the way electric current moves through the heart which, in turn, will result in more efficient defibrillators and better diagnosis of abnormal function.Read moreRead less
Modelling of multiscale systems in engineering and science supports large-scale equation-free simulations and analysis. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are known, but the closures to translate microscale ....Modelling of multiscale systems in engineering and science supports large-scale equation-free simulations and analysis. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel, equation free, computational methodologies will circumvent this stumbling block, and promises to radically change the modeling, exploration and understanding of complex system behavior. We continue to develop this powerful computational methodology. Read moreRead less
A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can ....A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can be used by engineers in Australia and France to simulate transport phenomena in porous media, which have significant environmental impact. The research will lead to publications in scientific journals and communications at national/international conferences. Research training of postdocs and PhD students is another excellent outcome of the project.Read moreRead less
Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficie ....Yield strength and plastic flow of heterogeneous materials: Designing optimal composites and porous materials. A major goal of materials science is to design materials with improved functionality at lower weight, cost and size. It is important to guide this expensive and time-consuming process with sophisticated computer modelling. In this project we aim to model how and why composite and porous materials fail when they are placed under stress. Our results will make materials design more efficient by providing a valuable experimental interpretive tool and a theoretical map for material optimization. Our models will also provide crucial information needed for modelling the behavior of composites in applications.Read moreRead less