The homepage of Tao Gao

The homepage of Tao Gao

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Tao Gao PhD
Department of Mathematics
Imperial College London

Research interest

My research interest is on nonlinear waves. The problem is concerned with a two-dimensional irrotational flow of inviscid and incompressible fluid. The upper free boundary of the fluid, which is also called the free-surface, is deformed by a train of waves. The problem of gravity-capillary waves and flexural-gravity waves are both considered. Gravity and surface tension are present in the former case while surface tension is replaced by the pressure exerted by an elastic sheet in the latter case. Flexural-gravity waves have many applications in the presence of ice sheets in polar regions, e.g. road design, ice breaking and etc. A simple schematic is sketched as below. The major objective is to investigate the shapes and the properties of these waves. Several different numerical methods are used to solve full Euler equations which describe the fluid motion. The problem of the dynamics and the stability can also be worked out. Recently I focus on solving Euler equations for non-symmetric waves. This can be achieved by studying the symmetry-breaking problem. So far all the non-symmetric waves have been found to be bifurcated from the symmetric waves.

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Currently I am in corporation with Dr Alexandu Vali Asimit and Junlei Hu on empirical reinsurance.
From a mathematical point of view, the main difficulty of this project to solve a nonlinear and non-convex optimisation problem. We choose the Interior Point Method as the algorithm for the optimiser. A multi-start technique is being introduced for global search.



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