Undergraduate & Postgraduate Taught projects

I am always keen to supervise good undergraduate and MSc students. However, due to my other commitments, I will not normally supervise more than two projects per academic year so, if you are interested in undertaking a project under my supervision, it is best to get in touch early.

Below are a couple of sample projects that would be suitable for, either an MSc dissertation (MATH552 or MATH554) or, an undergraduate project (MATH490 or MATH499). If you are an MSc student, you may also wish to take a look at the research projects with which I am involved, as part of this work could also form the basis of an MSc dissertation. However, the list of projects here and at research projects are not exhaustive and I am happy to discuss the possibility of developing bespoke projects.

A surface wave

Surface wave control

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.

Further reading

Skelton EA, Craster RV, Colombi A, Colquitt DJ. 2018 The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion.New J Phys, 20, 053017. (doi: 10.1088/1367-2630/aabecf)

Carta G, Colquitt DJ, Movchan NV, Movchan AB, Jones IS. 2020 A new class of chiral flexural waves in structured plates: directional localisation and control.J Mech Phys Solids, 137, 103866 (doi: 10.1016/j.jmps.2020.103866).

Colquitt DJ, Colombi A, Craster RV, Roux P, Guenneau SRL. 2017 Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction. J Mech Phys Solids, 99, 379-393. (doi: 10.1016/j.jmps.2016.12.004)

Maling BJ, Colquitt DJ, Craster RV. 2017 The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on gratings. Wave Motion, 69, 35-49. (doi: 10.1016/j.wavemoti.2016.11.003)

A surface wave

Discrete defects

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.

Further reading

Colquitt DJ, Nieves MJ, Jones IS, Movchan AB, Movchan NV. 2013 Localisation for a line defect in an infinite square lattice. Proc. R Soc. A 469 : 20120579. (doi: 10.1098/rspa.2012.0579)

Colquitt DJ, Nieves MJ, Jones IS, Movchan NV, Movchan AB. 2012 Trapping of a crack advancing through an elastic lattice. Int J Eng Sci 61, 129–141. (doi: 10.1016/j.ijengsci.2012.06.016)

Madine KH, Colquitt DJ. 2021 Dynamic Green's functions in discrete flexural systems. Q J Mech Appl Math, hbab006. (doi: 10.1093/qjmam/hbab006)