Loughborough University
Tel: +44 (0) 1509 22 2861
Fax: +44 (0) 1509 22 3969
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School of Mathematics Loughborough University Tel: +44 (0) 1509 22 2861 Fax: +44 (0) 1509 22 3969 |
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| December 2008 |
ResearchI am a member of the Loughborough linear and nonlinear waves research group.I have a number of research interests, mostly concerned with linear wave diffraction theory. I am particularly interested in analytic or semi-analytic solution methods such as matched eigenfunction expansions, multipole expansions, integral equations and Weiner-Hopf type methods. Mathematical methods for wave interaction with large arrays. With Phil McIver and Ian Thompson, I am developing efficient methods of solution for large array problems based on techniques which take advantage of simpler solutions to infinite array problems, and formulating novel extended homogenization techniques which can capture the band-gap phenomena associated with periodic arrays. This work was supported by EPSRC grant EP/C510941/1. Associated with large array scattering are problems formulated on semi-infinite arrays, ie arrays with just one end or edge. Semi-infinite arrays of isotropic point scatterers. A unified approach. Multiple scattering theory in acoustics: trees, dispersions, and rough surfaces. I am working on these problems with Keith Attenborough from the Univeristy of Hull, and Paul Martin from Colorado School of Mines. This work was supported by EPSRC grant GR/S35585/01. Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber. Reflection of sound from random distributions of semi-cylinders on a smooth hard surface: models and data. Effects of porous covering on sound attenuation by periodic arrays of cylinders. Multiple scattering by multiple spheres: A new proof of the Lloyd-Berry formula for the effective wavenumber. The efficient computation of series. The derivation of new analytic representations for certain slowly-convergent series that arise in diffraction theory, which are suitable for numerical computation. One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation. Schlomilch series that arise in diffraction theory and their efficient computation. Efficient computation of Schlomilch-type series. Edge waves and trapped modes. I am interested in methods for the evaluation of frequencies at which these phenomena occur and also the implications for the uniqueness of certain hydrodynamic and acoustic problems. Work in this area was supported by EPSRC grant GR/M30937. Recent publications include work with PhD student Keith Ratcliffe on bound states in coupled quantum waveguides: Bound states in coupled guides. I. Two dimensions. Bound states in coupled guides. II. Three dimensions. Water-wave/sea-ice interaction. This is collaborative research with Hyuck Chung in Auckland, New Zealand. Reflection and transmission at the ocean/sea-ice boundary. Reflection and transmission across a finite gap in an infinite elastic plate on water. Wave scattering in two-layer fluids. Water-wave scattering is usually considered under the assumption that the fluid has constant density. With PhD student Jon Cadby, I have examined the case of a fluid with a layer of fresh water on top of a deep body of sea water. Scattering of oblique waves in a two-layer fluid. Trapped modes in a two-layer fluid. |