Galkowski, Jeffrey;
Marchand, Pierre;
Wang, Jian;
Zworski, Maciej;
(2024)
The Scattering Phase: Seen at Last.
SIAM Journal on Applied Mathematics
, 84
(1)
pp. 246-261.
10.1137/23M1547147.
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Abstract
The scattering phase, defined as log detS(λ)/2πi where S(λ) is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn's spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.
| Type: | Article |
|---|---|
| Title: | The Scattering Phase: Seen at Last |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/23M1547147 |
| Publisher version: | https://doi.org/10.1137/23M1547147 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | scattering phase, obstacle scattering, finite element, Weyl law, trapping |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10181263 |
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