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My research interests are mostly in the applications of differential equations to real-world problems. I have particular interests in free and moving boundary problems and applications of complex variable methods in continuum mechanics, and in the mathematics of finance.
There are very many free and moving boundary problems in materials science and fluid dynamics. One of the simplest is the Hele-Shaw problem which is also a model for groundwater flows. It is a special case of the Stefan model for melting or solidification of a pure material, which is of enormous practical and theoretical importance, and I have devoted considerable effort to it in the belief that it encapsulates the essential features of the more complex situation. I have also worked on the Stefan model itself and on the related alloy solidification problem.
I am involved with other free boundary problems from materials science; of particular current interest are the macroscopic modelling of dislocation arrays in materials, and models of superconductivity. The former area is basic to our understanding of plasticity, and the latter has become a major world-wide research area as a result of the recent discovery of high-Tc superconductors.
More generally, work with industry has included problems in lubrication theory, circuit device analysis (thermistors), ship hydrodynamics, analysis of thin layer flows and paints, and the mathematics of colour vision.
There are very many free and moving boundary problems in materials science and fluid dynamics. One of the simplest is the Hele-Shaw problem which is also a model for groundwater flows. It is a special case of the Stefan model for melting or solidification of a pure material, which is of enormous practical and theoretical importance, and I have devoted considerable effort to it in the belief that it encapsulates the essential features of the more complex situation. I have also worked on the Stefan model itself and on the related alloy solidification problem.
I am involved with other free boundary problems from materials science; of particular current interest are the macroscopic modelling of dislocation arrays in materials, and models of superconductivity. The former area is basic to our understanding of plasticity, and the latter has become a major world-wide research area as a result of the recent discovery of high-Tc superconductors.
More generally, work with industry has included problems in lubrication theory, circuit device analysis (thermistors), ship hydrodynamics, analysis of thin layer flows and paints, and the mathematics of colour vision.
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CoRR (2023)
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Social Science Research Network (2022)
arxiv(2021)
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Emerging applications in free boundary problemspp.13-23, (2020)
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