Spherical Sommerfeld Integrals

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• Valentin Kunz (University of Cambridge)
• Thursday 04 July 2024, 14:30-15:00
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

This talk is dedicated to the diffraction problem resulting from the interaction of a monochromatic plane-wave with a quarter-plane (flat cone) in three spatial dimensions.  One of the key-quantities involved in this problem is the diffraction coefficient, which describes the amplitude of the spherical wave diffracted by the quarter-plane’s vertex. This coefficient can be described in terms of the problem’s (edge) Green’s functions. By generalising Sommerfeld’s method of images from the (complexified) circle to the (complexified) sphere, we find a spherical plane-wave decomposition of these Green’s functions, in the sense explained in A. Shanin’s talk https://www.newton.ac.uk/seminar/42186/. This generalisation is achieved by analytically continuing wave-fields from the real sphere to the complexified sphere, in the spirit of [1]. Our corresponding ‘spherical Sommerfeld integral’ involves some unknown directivities (the spectral functions), which depend only on a single(!) complex variable. Here, we will give an overview of our theory. All of this work is done in collaboration with Raphael C. Assier and Andrey V. Shanin. References:[1] Assier, R.C. and Shanin, A.V. (2021) Analytical continuation of two-dimensional wave fields Proc. Roy. Soc. A, 477:2020081

This talk is part of the Isaac Newton Institute Seminar Series series.

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