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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > A two-complex-variables approach to the right-angled no-contrast penetrable wedge diffraction problem

## A two-complex-variables approach to the right-angled no-contrast penetrable wedge diffraction problemAdd to your list(s) Download to your calendar using vCal - Valentin Kunz (University of Manchester)
- Friday 10 February 2023, 09:00-09:45
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. MWSW01 - Canonical scattering problems We study the two dimensional problem of diffraction of a time-harmonic plane wave incident on a right-angled no-contrast penetrable wedge by using a two-complex-variables approach. The idea behind our work dates back to 1964 when J. Radlow discovered a two-complex-variable Wiener-Hopf type equation for this problem. After outlining these historical aspects, we explain how successive applications of the classical, one-complex-variable, Wiener-Hopf technique leads to two novel equations which control the Wiener-Hopf equation’s unknown spectral functions’ behaviour, but do not yet allow for solving the problem [1]. Thereafter, we discuss the analyticity properties of the two-complex-variables spectral functions. The singularities of the spectral functions are unveiled and their local behaviour in the vicinity of the singular set is discussed, as presented in [2]. Finally, we briefly outline how we plan to combine this with the machinery developed by R. Assier, A. Shanin, and A. Korolkov to recover the far-field asymptotics of the physical problem, including a description of the diffracted and lateral waves. [1] V. Kunz and R. Assier (2022), Diffraction by a Right-Angled No-Contrast Penetrable Wedge Revisited: A Double Wiener-Hopf Approach. SIAM J . Appl. Math. 82(4), 1495-1519 [2] V.D. Kunz and R.C. Assier (2022), Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions. Preprint on ArXiv:2211.13307 This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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