Tao Gao PhD

Department of Mathematics

Imperial College London

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.

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.

**University College London**:**PhD**in Mathematics supervised by Prof. J.-M. Vanden-Broeck. Thesis: Nonlinear flexural-gravity free-surface flows and related gravity-capillary flows. Download PDF.**University College London**:**MSc**in Mathematical Modelling. Dissertation: Flows past sharp corners: the Brown-Michael Model Download PDF. Supervisor: Prof. R. Mcdonald. Final award:**Distinction**.**Imperial College London**:**MSc**in Applied Mathematics. Dissertation: Extreme eigenvalue problem of LUE Download PDF. Supervisor: Prof. Y. Chen. Final award:**Distinction**.**Université Pierre et Marie Curie**:**BSc**in Mathematics. Final award: très bien (equivalent to 1st honour degree).

- Gao, T., & Vanden-Broeck, J. M. 2014 Numerical studies of two-dimensional hydroelastic periodic and generalised solitary waves.
*Physics of Fluids*(1994-present),**26**(8), 087101. http://dx.doi.org/10.1063/1.4893677. - Gao, T., Wang, Z. & Vanden-Broeck, J. M. 2016 New hydroelastic solitary waves in deep
water and their dynamics,
*Journal of Fluid Mechanics***788**:469–491. http://dx.doi.org/10.1017/jfm.2015.695. - Gao, T., Wang, Z. & Vanden-Broeck, J. M. 2017. Investigation of symmetry breaking in
periodic gravity-capillary waves,
*Journal of Fluid Mechanics***811**:622-641. http://dx.doi.org/10.1017/jfm.2016.751. - Gao, T., Wang, Z. & Vanden-Broeck, J. M. 2016. On asymmetric generalized solitary gravity–capillary waves in finite depth,
*Proceedings of the Royal Society A*Vol. 472, No. 2194, p. 20160454 http://dx.doi.org/10.1098/rspa.2016.0454 - Alexandru, V. A., Gao, T., Hu, J. & Kim, E.-S. 2016. Numerical Optimisation for Actuarial Applications,
*North American Actuarial Journal*(submitted). Link. - Gao, T., Milewski, P. A., Papageorgiou, D. T. & Vanden-Broeck, J. M. 2017. Dynamics of fully nonlinear capillary-gravity solitary waves under normal electric fields, Journal of Engineering Mathematics, 1--16https://doi.org/10.1007/s10665-017-9912-z.
- Gao, T., Milewski, P. A., Papageorgiou, D. T., Vanden-Broeck, J.-M. 2017 Steady grey solitary waves on a conducting fluid under the effects of vertical electric fields (Preprint).Link.
- Gao, T. Wang, Z. & Vanden-Broeck, J.-M. 2017 Numerical computations of flexural-gravity waves on water of arbitrary depth, IMA J. Appl. Math. (Preprint). Link.

- 150th Anniversary Postdoctoral Mobility Grant by the London Mathematical Society, Tao Gao (PMG 16-17 17).
- Individual Grant (Dr A.V. Asimit, T. Gao, J. Hu) by the Society of Actuaries' Committee on Knowledge and Extension Research (CKER) and the Casualty Actuarial Society (CAS).
- The George Jessel Scholarship awarded by Department of Mathematics, University College London.
- The JJ Sylvester Scholarship, the Edwin Power Scholarship and the Corte Studentship awarded by Department of Mathematics, University College London.
- The Monica Hulse Scholarship awarded by Department of Mathematics, University College London.

Contact information:

>- UCL Mathematics Department
- Applied Mathematics Seminars List
- Postgraduate Seminars List
- Chalkdust: a magazine lauched by PhD students from Department of Mathematics of UCL

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