Current research students

- Cheuk-Him Yeung, PhD 2017-2021
- James Haughton, PhD 2016-2020
- Georgia Lynott, PhD 2015-2019
- William Rowley, PhD 2014-2018
- Christian Berger, PhD 2013-2017
- Duncan Joyce, PhD 2012-2016

Past research students - click on titles to download theses.

- Dr Maria Thorpe, PhD 2011-2015. "Deformation and buckling of isolated and interacting thin shells in an elastic medium". Maria solved some really difficult problems associated with the buckling of thin shells embedded in other elastic materials. Very little work has been done in this realm. She first re-analysed the only existing work associated with a single shell. She introduced a new approximation, known as the "stiff, thin-shell approximation" appropriate for the parameter regime of interest to industrial collaborators (and more generally often of interest) when the shell stiffness is much higher than that of the host medium. Following this she did some very nice work studying the buckling of a pair of thin shells, located some distance away from each other. This is certainly the first work of its kind and is highly non-trivial! Maria now works for the Civil Service in Sheffield.

- Dr Ellis Barnwell, PhD 2010-2014. "One and two-dimensional propagation of waves in periodic heterogeneous media: transient effects and band-gap tuning". Ellis worked on transient problems solely initially. Very little work in this area has been done in heterogeneous media. He obtained some very nice results regarding how pulses travel out from the forcing point. In some cases the energy becomes trapped inside the structure, in this case a one dimensional array of point masses. After this work we decided to move into the area of configurable phononic media and Ellis developed some models of wave propagation in periodic media where phases are deformed nonlinearly. This generates a pre-stress and affects the wave propagation significantly, shifting band-gaps and in some cases annihilating them or opening them up. In order to study this phenomenon the so-called Plane Wave Expansion method had to be modified to include the case of phases with inhomogeneous material properties. Ellis subsequently worked on some short postdoc projects via Impact Acceleration funding with Thales. He now works for HVPD.

- Dr Vicki Andrew, PhD 2010-2014. "Efficient numerical evaluation of the scattering of acoustic waves by arrays of cylinders and bodies of revolution of arbitrary cross section". Vicki's project focussed on understanding how acoustic waves are transmitted into and reflected from a two dimensional array of scatterers with somewhat general shape, in this case bodies of revolution. The general shape necessitated a numerical approach and Vicki developed a boundary element method. This required some careful analysis of doubly periodic Green's functions. We also wanted to do elastodynamics but the acoustic case was hard enough! Some nice results followed in the acoustic case. Vicki worked for IBM for a while but now works for Qxbranch.

- Dr Ruth Voisey, PhD 2010-2014. "Multiple wave scattering by quasiperiodic structures". Ruth's PhD focussed on media that are not periodic but at the same time have more order to them than random structures. So-called quasiperiodic media are of importance in many applications. In particular quasicrystals are of great importance and their discoverers recently won the Nobel prize. We studied scalar (e.g. acoustic) wave propagation in such materials and developed models to understand the associated band-gap structure of these materials. Ruth did a six month internship with Dyson in 2013 which was very successful. As a result of this she was offered a job with Dyson at the end of her PhD. For some time she worked there as an applied mathematician in the acoustics research team until 2017 when she took on the broader role of Research Projects Manager.

- Dr Tom Shearer, PhD 2009-2013. "Waves in nonlinear elastic media with inhomogeneous pre-stress". Tom's PhD focused on canonical wave scattering problems in nonlinear elastic materials (such as rubber) that are subjected to some large pre-stress. In particular when such media have e.g. cavities inside them the stress fields that are set up around the cavities or inhomogeneities generate fields that waves scatter from. Such problems have never been studied before because the so-called incremental wave equation associated with such problems is very difficult to solve. Tom studied torsional waves in an annulus, antiplane shear wave scattering from a cylindrical cavity and the general problem of scattering from a sphere. In each case hydrostatic pressure is imposed to modify the medium that the wave sees as it propagates. Tom obtained an EPSRC Doctoral prize, 2013-14 in which he studied the mechanics of tendons and ligaments. He held a prestigious EPSRC Postdoctoral Fellowship at Manchester from April 2014-April 2017 and this has now blended into a permanent lectureship (joint between Mathematics and Materials Science) at Manchester.

- Dr Natasha Willoughby, PhD 2006-2012 (maternity leave 2008-2010). "Dynamic homogenization for the elastic properties of periodic and random composites". Natasha worked on models of inhomogeneous media of interest to Thales and in particular continued to develop a new integral equation method of homogenization that I originally worked on in my PhD. The method is rather nice because explicit expressions can be determined for the effective properties of composite media. She also worked on a so-called "Representative Volume Element" method with a periodic cell using asymptotic homogenization. She did this in 2D (fibre reinforced composites) and 3D (particulate composites) and this was also collaborative work with Andrew Hazel since we used finite element methods to solve the cell problem. Natasha now works from Thales in their theoretical acoustics group.

Current PDRAs

- Dr Mike Smith. Mike is working with me on my EPSRC Fellowship regarding theoretical modelling of syntactic foams.
- Dr Pu Zhang. Pu is working with me on my EPSRC Fellowship regarding tunable metamaterials.
- Dr Artur Gower. Art is working with me and David Abrahams, working on an EPSRC project concerning multiple scattering in dispersions.

Past PDRAs

- Dr Valentina Balbi. Valentina currently holds a Marie Curie Postdoctoral Fellowship at the University of Galway in Ireland.
- Dr Ellis Barnwell. Ellis worked on a two EPSRC Impact Acceleration grants, collaborating with Thales. He now works for HVPD.
- Dr Riccardo De Pascalis. Riccardo is currently a Postdoc in the Physics Lab at Universite Paris 7.
- Dr Tom Shearer. Tom is currently a Lecturer in Applied Mathematics and Materials Science, based in the School of Mathematics at Manchester.