Assier, Raphael and Peake, Nigel
(2012)
*Precise description of the different far fields encountered in the problem of diffraction of acoustic waves by a quarter-plane.*
IMA Journal of Applied Mathematics, 77 (5).
pp. 605-625.

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## Abstract

This paper provides a review of important results concerning the Geometrical Theory of Diffraction and Geometrical Optics. It also reviews the properties of the existing solution for the problem of diffraction of a time harmonic plane wave by a half-plane. New mathematical expressions are derived for the wave fields involved in the problem of diffraction of a time harmonic plane wave by a quarter-plane, including the secondary radiated waves. This leads to a precise representation of the diffraction coefficient describing the diffraction occurring at the corner of the quarter-plane. Our results for the secondary radiated waves are an important step towards finding a formula giving the corner diffraction coefficient everywhere.

Item Type: | Article |
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Additional Information: | This article is an invitation publication, following the award of the Lighthill-Thwaites prize, awarded for the 2012 Wave Motion paper. |

Uncontrolled Keywords: | geometrical theory of diffraction acoustic diffraction quarter-plane |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 30 Functions of a complex variable MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 43 Acoustics |

Depositing User: | Dr Raphael Assier |

Date Deposited: | 08 Dec 2014 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2207 |

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