Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or la ....Complex Multiscale Systems: Modeling, Analysis and Scientific Computation. This project aims to develop and implement a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. The wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or partial differential equations or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, this approach is expected to empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing.Read moreRead less
Fuzzy modelling and design of complex networked systems. This project aims to develop analysis and synthesis approaches for non-linear networked control systems, including modelling, stability analysis and design problems. The non-linear effects and analysis of networked control systems have received considerable attention because of the universal existence of nonlinearities in practice. Network-based non-linear systems are widely used but face problems from non-linearities and networks. This pr ....Fuzzy modelling and design of complex networked systems. This project aims to develop analysis and synthesis approaches for non-linear networked control systems, including modelling, stability analysis and design problems. The non-linear effects and analysis of networked control systems have received considerable attention because of the universal existence of nonlinearities in practice. Network-based non-linear systems are widely used but face problems from non-linearities and networks. This project will establish a software-based nonlinear networked control system platform to test the presented algorithms and strengthen the scenarios in applications. This project is expected to increase Australian excellence in cyber-security and advanced manufacturing.Read moreRead less
A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of ....A Novel Geometric Approach to Shocks in Reaction-Nonlinear Diffusion Models. Reaction-nonlinear diffusion models play a vital role in the study of cell migration and population dynamics. However, the presence of aggregation, or backward diffusion, leads to the formation of shock waves - distinct, sharp interfaces between different populations of densities of cells - and the breakdown of the model. This project will develop new geometric methods to explain the formation and temporal evolution of these shock waves, while simultaneously unifying existing regularisation techniques under a single, geometric banner. It will devise innovative tools in singular perturbation theory and stability analysis that will identify key parameters in the creation of shock waves, as well as their dynamic behaviour.Read moreRead less
Accurate modelling of large multiscale dynamical systems for engineering and scientific simulation and analysis. In current modelling the underlying microscopic mechanisms are known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available. The project's computational methodologies will circumvent this stumbling block to radically change the modelling, exploration and understanding of complex systems.
Construction of near optimal oscillatory regimes in singularly perturbed control systems via solutions of Hamilton-Jacobi-Bellman inequalities. Problems of optimal control of systems evolving in multiple time scales arise in a great variety of applications (from diet to environmental modelling). This project addresses the challenge of analytically and numerically constructing rapidly oscillating controls that would 'near optimally coordinate' the slow and fast dynamics.
Multiscale modelling of systems with complex microscale detail. In modern science and engineering many complex systems are described by distinctly different microscale physical models within different regions of space. This project is to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling and computation of such systems for application in industrial research and development. Our sparse simulations, justified with mathematical analysis, use ....Multiscale modelling of systems with complex microscale detail. In modern science and engineering many complex systems are described by distinctly different microscale physical models within different regions of space. This project is to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling and computation of such systems for application in industrial research and development. Our sparse simulations, justified with mathematical analysis, use small bursts of particle/agent simulations, PDEs, or difference equations, to efficiently evaluate macroscale system-level behaviour. The objective is to accurately interface between disparate microscale models and establish provable predictions on how the microscale parameter spaces resolve at the macroscale.Read moreRead less
Multiscale modelling of systems with complex microscale detail. This project aims to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling of systems with microscopic irregular details. The methodology, justified with mathematical analysis and computation, uses small bursts of particle/agent simulations, partial differential equation (PDEs), or difference equations, to efficiently predict macroscale behaviour. This project’s mathematical meth ....Multiscale modelling of systems with complex microscale detail. This project aims to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling of systems with microscopic irregular details. The methodology, justified with mathematical analysis and computation, uses small bursts of particle/agent simulations, partial differential equation (PDEs), or difference equations, to efficiently predict macroscale behaviour. This project’s mathematical methodology aims to efficiently and accurately extract and simulate the collective dynamics which emerge on macroscales, leading to improved prediction and understanding of the significant features of these complex systems at the scale relevant to engineers and scientists.Read moreRead less
Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be com ....Flow structures and transport: predictability and control. Moving flow structures (the boundary of an eddy, the flow interface between two fluids) are crucial in fluid mixing and in the transport of heat, pollutants and nutrients. This project will analyse their roles in improving predictions of spreading extents and rates for geophysical-scale problems, and in controlling transport at the micro-scale. Inaccuracies in currently available numerical diagnostics for transport prediction will be comprehensively evaluated via comparison with recent exact models. Analytical methods for quantifying transport under unsteady flow protocols will be developed, and used to answer questions on controlling transport in microfluidic applications in conjunction with experimentalists.Read moreRead less
Modeling, Mathematical Analysis, and Computation of Multiscale Systems. This project develops and implements a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. Our wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or PDE or lattice equations). Comprehensively a ....Modeling, Mathematical Analysis, and Computation of Multiscale Systems. This project develops and implements a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. Our wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or PDE or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, our approach will empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing. Read moreRead less
Occupational measures, perturbations and complex deterministic systems. When tackling complex problems, scientists and engineers seek methods that judiciously exploit stochasticity and perturbations as antidotes to unpredictability of outputs that the latter can induce if they inadvertently influence their models. The project proposes for this study vaccine-like perspective of stochasticity and singular perturbations.