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Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. / Nazarov, S. A.

In: Siberian Mathematical Journal, Vol. 59, No. 1, 2018, p. 85-101.

Research output: Contribution to journal › Article › peer-review

Harvard

Nazarov, SA 2018, 'Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide', Siberian Mathematical Journal, vol. 59, no. 1, pp. 85-101. https://doi.org/10.1134/S003744661801010X

APA

Nazarov, S. A. (2018). Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. Siberian Mathematical Journal, 59(1), 85-101. https://doi.org/10.1134/S003744661801010X

Vancouver

Nazarov SA. Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. Siberian Mathematical Journal. 2018;59(1):85-101. https://doi.org/10.1134/S003744661801010X

Author

Nazarov, S. A. / Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. In: Siberian Mathematical Journal. 2018 ; Vol. 59, No. 1. pp. 85-101.

BibTeX

@article{0dd74217f4014d048958653e0b225a25,
title = "Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide",
abstract = "We study wave diffraction at near-threshold frequencies in an acoustic waveguide with a cross-wall that has a small aperture of diameter ε > 0. We describe the effects of almost complete reflection or transmission of waves related to the classical Vainstein anomaly and the presence of almost standing waves for the threshold value Λk of the spectral parameter λ in continuous spectrum. The greatest attention is paid to analyzing the range λε = Λk + ε2μ2 of the spectral parameter with μ ≤ μ0, which generates scattering coefficients depending on μ > 0 and presents the greatest difficulties in constructing and justifying the asymptotics. Almost complete reflection and transmission correspond to the cases of going away from the threshold (as μ → +∞) and approaching it (as μ → +0) characterized by simpler asymptotics.",
keywords = "acoustic waveguide, almost complete transmission and reflection of waves, cross-wall, scattering, small aperture",
author = "Nazarov, {S. A.}",
note = "Nazarov, S.A. Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. Sib Math J 59, 85–101 (2018). https://doi.org/10.1134/S003744661801010X",
year = "2018",
doi = "10.1134/S003744661801010X",
language = "English",
volume = "59",
pages = "85--101",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide

AU - Nazarov, S. A.

N1 - Nazarov, S.A. Transmission of Waves Through a Small Aperture in the Cross-Wall in an Acoustic Waveguide. Sib Math J 59, 85–101 (2018). https://doi.org/10.1134/S003744661801010X

PY - 2018

Y1 - 2018

N2 - We study wave diffraction at near-threshold frequencies in an acoustic waveguide with a cross-wall that has a small aperture of diameter ε > 0. We describe the effects of almost complete reflection or transmission of waves related to the classical Vainstein anomaly and the presence of almost standing waves for the threshold value Λk of the spectral parameter λ in continuous spectrum. The greatest attention is paid to analyzing the range λε = Λk + ε2μ2 of the spectral parameter with μ ≤ μ0, which generates scattering coefficients depending on μ > 0 and presents the greatest difficulties in constructing and justifying the asymptotics. Almost complete reflection and transmission correspond to the cases of going away from the threshold (as μ → +∞) and approaching it (as μ → +0) characterized by simpler asymptotics.

AB - We study wave diffraction at near-threshold frequencies in an acoustic waveguide with a cross-wall that has a small aperture of diameter ε > 0. We describe the effects of almost complete reflection or transmission of waves related to the classical Vainstein anomaly and the presence of almost standing waves for the threshold value Λk of the spectral parameter λ in continuous spectrum. The greatest attention is paid to analyzing the range λε = Λk + ε2μ2 of the spectral parameter with μ ≤ μ0, which generates scattering coefficients depending on μ > 0 and presents the greatest difficulties in constructing and justifying the asymptotics. Almost complete reflection and transmission correspond to the cases of going away from the threshold (as μ → +∞) and approaching it (as μ → +0) characterized by simpler asymptotics.

KW - acoustic waveguide

KW - almost complete transmission and reflection of waves

KW - cross-wall

KW - scattering

KW - small aperture

UR - http://www.scopus.com/inward/record.url?scp=85043512129&partnerID=8YFLogxK

U2 - 10.1134/S003744661801010X

DO - 10.1134/S003744661801010X

M3 - Article

AN - SCOPUS:85043512129

VL - 59

SP - 85

EP - 101

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -

ID: 40973988