I am always interested in recruiting excellent PhD students. Brief outlines of a couple of potential research projects can be found here.
Multi-scale structures for the control of elastic waves
This project involves the mathematical modelling and design of mechanical structures capable of controlling the propagation of surface and bulk waves in elastic solids. The project will employ both numerical and asymptotic analysis to study a combination of continuous and discrete structures in one-, two-, and three-dimensions. The research programme includes scattering, homogenisation, and spectral problems for finite and infinite systems and has a broad range of applications including, filtering of waves, lensing, and cloaking.
Defect states in discrete elastic systems
This project involves the analysis of finite and semi-infinite defects in elastic lattice systems. These defects may be dislocations or variations in inertial properties and, for finite defects, will have an associated spectrum of eigenstates. The focus of the research programme is on the analysis of these eigenstates and the fields in the vicinity of the defect sites; algorithms will be developed to study the solutions in various asymptotic regimes. The research programme will involve both analytical and numerical models. The project may also include the study of edge and interfacial waves in mechanical lattices.
The mathematics of vascular stents - waves and fluid/solid interaction
The project will be carried out within a collaborative framework involving Applied Mathematicians and Medical Practitioners who study fluid flows and deformation of solids and practice the installation of periodically reinforced stents into blood vessels. The successful candidate will have a strong background in the theory and numerical analysis of partial differential equations. The main focus will be made on modelling of dynamic fluid-solid interaction for stents channelling the blood flow, as well as on special regimes leading to stent failure or resonant blockages of the blood flow. The developed multiscale methodology will be applied to cellular interaction problems.
In collaboration with the Liverpool Centre for Mathematics in Healthcare.
Supervisory team: Prof A B Movchan, Dr D Colquitt, Prof N Movchan, Dr R Bearon, Dr A England