MathsNet: Research Student Directory

Name Brewer, Cerian S
Group Industrial and Applied Mathematics
Room B15, Math Sci
Telephone +44 (0) 115 82 32127 [direct dial]
Thesis Title Wave propagation and complexity - a transfer operator approach
Thesis Abstract Modelling wave propagating inside complex enclosures is important for a variety of physical and engineering applications. In the electromagnetic world, wireless communication within buildings, or characterising electromagnetic interference within devices, is a formidable challenge. Likewise, modelling noise and vibration in a car, airplane or train is a hard problem. It is often said that engineers can model every aspect of car on the computer these days, except how it will sound! These problems are most efficiently solved by splitting the whole structure into substructures, determining the solutions for each sub-structure and then coupling these local solutions. The sub-system solutions can be determined on the boundary (such as the building walls) rather than on the higher-dimensional interior. This project aims to investigate the use of boundary-based calculations to provide an analytical tool to develop approaches such as ray-based propagation. The main idea will be to provide an explicit relationship between the wave arriving at a boundary and the wave leaving it in terms of a so-called transfer operator. This transfer operator characterises the effect of passage through the interior of the cavity to give the wave arriving at the boundary at one part in terms of the wave leaving it elsewhere. It is related to the numerical boundary-based approaches such as the Boundary Element Method but better suited to developing analytical approximations.
School contact information School of Mathematical Sciences
University of Nottingham
University Park
Nottingham, NG7 2RD
Tel: +44 (0) 115 951 4949
Fax: +44 (0) 115 951 4951