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
A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fracti ....A unifying framework for generalised distributed-order fractional models. This project aims to develop a unifying theoretical framework for generalised fractional models using measure theory and a new class of distributed-order nonlocal operators to simulate anomalous transport processes in heterogeneous and anisotropic porous media. The project expects to generate a mathematical foundation for fractional modelling and clarity on the role of, and relationship between, the many variants of fractional operators used in modern practice and how to impose boundary conditions on finite domains. Expected outcomes of the project include an evaluation of dimensionality and/or complexity reduction of the governing equations in fractional transport models with a focus on groundwater applications.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
Advanced mathematical modelling and computation of fractional sub-diffusion problems in complex domains. Over the past few decades, researchers have observed numerous biological, physical and financial systems in which some key underlying random motion fails to conform to the classical model of diffusion. The project will extend current macroscopic models describing such anomalous sub-diffusion by correctly incorporating the confounding effects of nonlinear reactions, forcing and irregular geome ....Advanced mathematical modelling and computation of fractional sub-diffusion problems in complex domains. Over the past few decades, researchers have observed numerous biological, physical and financial systems in which some key underlying random motion fails to conform to the classical model of diffusion. The project will extend current macroscopic models describing such anomalous sub-diffusion by correctly incorporating the confounding effects of nonlinear reactions, forcing and irregular geometry. A key aspect of the project is the design of new algorithms that will fundamentally improve the accuracy and efficiency of direct numerical simulations of sub-diffusion in challenging applications. Read moreRead less