My undergraduate degree was in Mathematics from the University of Warwick, specialising in applied maths and numerical methods. During the summer preceding my final year I completed a URSS summer research project affiliated with HetSys on new adaptive grid methods designed to decrease the CPU time required to solve thin-film fluid flow initial value problems with highly-local control terms. My final year research project was on the hybrid modelling of droplet ejecta after drop impact on a surface. It focussed on developing a hydrodynamic description of the expanding droplet cloud and methods to couple this to direct numerical simulations of the initial impact and particle trajectory models at greater distances.
Over the next 4 years my research will focus on developing a new methodology for hierarchical modelling of complex physical systems in a control-theoretic setting, specifically thin-film fluid flow down inclined planes. The full description of these strongly nonlinear waves is too complex to be analytically tractable and so it is prohibitively computationally expensive to adequately develop controls for the full system. However, if we simplify the model down to either weakly nonlinear models or more advanced reduced-order models, it becomes possible to design optimal feedback controls to force the system towards certain states. The aim is to create a framework to couple the rapid numerical calculations from the lower order models with the highly accurate solutions of the full model.
MMath Mathematics, University of Warwick