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Scattering anomalies in a resonator above the thresholds of the continuous spectrum. / Nazarov, S.A.

In: Sbornik Mathematics, No. 6, 2015, p. 782-813.

Research output: Contribution to journal › Article

Harvard

Nazarov, SA 2015, 'Scattering anomalies in a resonator above the thresholds of the continuous spectrum', Sbornik Mathematics, no. 6, pp. 782-813. https://doi.org/10.1070/SM2015v206n06ABEH004479

APA

Nazarov, S. A. (2015). Scattering anomalies in a resonator above the thresholds of the continuous spectrum. Sbornik Mathematics, (6), 782-813. https://doi.org/10.1070/SM2015v206n06ABEH004479

Vancouver

Nazarov SA. Scattering anomalies in a resonator above the thresholds of the continuous spectrum. Sbornik Mathematics. 2015;(6):782-813. https://doi.org/10.1070/SM2015v206n06ABEH004479

Author

Nazarov, S.A. / Scattering anomalies in a resonator above the thresholds of the continuous spectrum. In: Sbornik Mathematics. 2015 ; No. 6. pp. 782-813.

BibTeX

@article{eff39008cd884524a9436930aa04bac3,
title = "Scattering anomalies in a resonator above the thresholds of the continuous spectrum",
abstract = "{\textcopyright} 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.We consider the Dirichlet spectral problem for the Laplace operator in a multi-dimensional domain with a cylindrical outlet to infinity, a Helmholtz resonator. Using asymptotic analysis of the scattering matrix we demonstrate different types of reflection of high-amplitude near-threshold waves. One scattering type or another, unstable or stable with respect to variations of the resonator shapes, is determined by the presence or absence of stabilizing solutions at the threshold frequency, respectively. In a waveguide with two cylindrical outlets to infinity, we discover the effect of almost complete passage of the wave under 'fine tuning' of the resonator.",
author = "S.A. Nazarov",
year = "2015",
doi = "10.1070/SM2015v206n06ABEH004479",
language = "English",
pages = "782--813",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "6",

}

RIS

TY - JOUR

T1 - Scattering anomalies in a resonator above the thresholds of the continuous spectrum

AU - Nazarov, S.A.

PY - 2015

Y1 - 2015

N2 - © 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.We consider the Dirichlet spectral problem for the Laplace operator in a multi-dimensional domain with a cylindrical outlet to infinity, a Helmholtz resonator. Using asymptotic analysis of the scattering matrix we demonstrate different types of reflection of high-amplitude near-threshold waves. One scattering type or another, unstable or stable with respect to variations of the resonator shapes, is determined by the presence or absence of stabilizing solutions at the threshold frequency, respectively. In a waveguide with two cylindrical outlets to infinity, we discover the effect of almost complete passage of the wave under 'fine tuning' of the resonator.

AB - © 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.We consider the Dirichlet spectral problem for the Laplace operator in a multi-dimensional domain with a cylindrical outlet to infinity, a Helmholtz resonator. Using asymptotic analysis of the scattering matrix we demonstrate different types of reflection of high-amplitude near-threshold waves. One scattering type or another, unstable or stable with respect to variations of the resonator shapes, is determined by the presence or absence of stabilizing solutions at the threshold frequency, respectively. In a waveguide with two cylindrical outlets to infinity, we discover the effect of almost complete passage of the wave under 'fine tuning' of the resonator.

U2 - 10.1070/SM2015v206n06ABEH004479

DO - 10.1070/SM2015v206n06ABEH004479

M3 - Article

SP - 782

EP - 813

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 6

ER -

ID: 4011839