Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of ....Asymptotics of the exponentially small. Asymptotic analysis plays a vital role in studying the complex interfacial dynamics that are fundamental for practical problems in fluid mechanics such as the withdrawal of oil and gas from underground reservoirs and the optimal design of ship hulls to minimise wave drag. These applications exhibit extremely small physical effects that may be crucially important but cannot be described using classical asymptotic analysis. This project will develop state of the art mathematical techniques in exponential asymptotics to address this deficiency in the classical theory, and provide a deeper understanding of pattern formation, instabilities and wave propagation on the interface between two fluids.Read moreRead less
Image-based Multiscale Modelling of Transport Phenomena in Porous Media. This project aims to develop an innovative general framework to build multiphase porous media transport models directly from electron microscope images of the underlying microstructure. Leading edge experimental, computational and applied mathematical techniques are proposed to drive this novel approach of multiscale modelling, employable across numerous fields of science and engineering. The central project theme of develo ....Image-based Multiscale Modelling of Transport Phenomena in Porous Media. This project aims to develop an innovative general framework to build multiphase porous media transport models directly from electron microscope images of the underlying microstructure. Leading edge experimental, computational and applied mathematical techniques are proposed to drive this novel approach of multiscale modelling, employable across numerous fields of science and engineering. The central project theme of developing an efficient and accurate multiscale model for simulating transport in heterogeneous porous media is expected to find application in the drying, timber and crop industries, and governmental agencies managing pollution in groundwater resources. This insight is likely to be invaluable for designing new industrial technologies and optimising current operations.Read moreRead less