High-frequency limit of the transport cross section in scattering by an obstacle with impedance boundary conditions

Aleksenko, Alena; Cruz, João Pedro; Lakshtanov, Evgeny

doi:10.1088/1751-8113/41/25/255203

Cited by 2 publications

(3 citation statements)

References 10 publications

(12 reference statements)

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“…In case of constant value of γ(r) the first statement was proven in [7]. The 2 nd inequality is a consequence of the well known representation:…”

Section: Scattering Of a Plane Wave By Obstacle With Impedance Boundamentioning

confidence: 91%

Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Lakshtanov¹

2010

J. Phys. A: Math. Theor.

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We prove that the Dirichlet-to-Neumann operator (DtN) has no spectrum in the lower half of the complex plane. We find several application of this fact in scattering by obstacles with impedance boundary conditions. In particular, we find an upper bound for the gradient of the scattering amplitude and for the total cross section. We justify numerical approximations by providing bounds on difference between theoretical and approximated solutions without using any a priory unknown constants.

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“…In case of constant value of γ(r) the first statement was proven in [7]. The 2 nd inequality is a consequence of the well known representation:…”

Section: Scattering Of a Plane Wave By Obstacle With Impedance Boundamentioning

confidence: 91%

Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Lakshtanov¹

2010

J. Phys. A: Math. Theor.

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“…These general results are applied to a scattering problem for an obstacle coating by a springy layer. Some other results related to topics discussed below can be found in [3,11].…”

Section: Introductionmentioning

confidence: 99%

“…Let v ∞ = v ∞ (θ, α) be the scattering amplitude of this solution. It is defined by (3) with v instead of u and −ik instead of k. Then, for each α,…”

mentioning

confidence: 99%

Resonance regimes of scattering by small bodies with impedance boundary conditions

Lakshtanov¹,

Vainberg²

2010

J. Phys. A: Math. Theor.

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The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumannto-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when k = 0 is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position.Mathematics subject classifications: 35P25, 35Qxx,78A45

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High-frequency limit of the transport cross section in scattering by an obstacle with impedance boundary conditions

Cited by 2 publications

References 10 publications

Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Spectral properties of the Dirichlet-to-Neumann operator for the exterior Helmholtz problem and its applications to scattering theory

Resonance regimes of scattering by small bodies with impedance boundary conditions

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