Modal approximation for time-domain elastic scattering from metamaterial quasiparticles

Chen, Bochao; Gao, Yixian; Liu, Hongyu

doi:10.1016/j.matpur.2022.07.007

Cited by 5 publications

(5 citation statements)

References 52 publications

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“…where 𝑝 1𝑛 and 𝑝 2𝑛 are defined in (63). During the simplification, we have used the recursion formulas given in (28). Then, we can obtain the following lemma.…”

Section: Lemma 3 Let 𝑆 𝑘mentioning

confidence: 99%

“…19, 26, 27 for the Maxwell system, and Refs. 3, 5, 28–31 for the Lamé system. Most of the existing studies in the literature are concerned with the static or quasistatic cases (cf.…”

Section: Introductionmentioning

confidence: 99%

“…Remark 6. With the help of the recursion formulas in(28), the single-layer potentials 𝐒 𝜔 𝑘 𝑠 |𝐱|) and 𝐏 𝑜 𝑛 (𝑘 𝑝 |𝐱|) are radiating solutions to the equation ( 𝜆,𝜇 + 𝜔 2 )𝐮 = 0 in 𝐱 ∈ ℝ2 ∖𝐵 𝑅 . The function 𝐐 𝑜 𝑛 (𝑘 𝑠 |𝐱|) belongs to the s-wave and the function 𝐏 𝑜 𝑛 (𝑘 𝑝 |𝐱|) belongs to the p-wave.…”

mentioning

confidence: 99%

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Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Liu

Zou

2023

Stud Appl Math

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Given the flexibility of choosing negative elastic parameters, we construct material structures that can induce two resonance phenomena, referred to as the elastodynamical resonances. They mimic the emerging plasmon/polariton resonance and anomalous localized resonance in optics for subwavelength particles. However, we study the peculiar resonance phenomena for linear elasticity beyond the subwavelength regime. It is shown that the resonance behaviors possess distinct characters, with some similar to the subwavelength resonances, but some sharply different due to the frequency effect. It is particularly noted that we construct a core–shell material structure that can induce anomalous localized resonance as well as cloaking phenomena beyond the quasistatic limit. The study is boiled down to analyzing the so‐called elastic Neumann–Poincaré (N‐P) operator in the frequency regime. We provide an in‐depth analysis of the spectral properties of the N‐P operator on a circular domain beyond the quasistatic approximation, and these results are of independent interest to the spectral theory of layer potential operators.

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“…where 𝑝 1𝑛 and 𝑝 2𝑛 are defined in (63). During the simplification, we have used the recursion formulas given in (28). Then, we can obtain the following lemma.…”

Section: Lemma 3 Let 𝑆 𝑘mentioning

confidence: 99%

“…19, 26, 27 for the Maxwell system, and Refs. 3, 5, 28–31 for the Lamé system. Most of the existing studies in the literature are concerned with the static or quasistatic cases (cf.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Liu

Zou

2023

Stud Appl Math

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“…Gao and Li study the electromagnetic scattering problem of time-domain Maxwells equations in an unbounded structure [22] and study a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings [21]. In [9], the author is devoted to the mathematical analysis of the elastic wave scattering due to negative metamaterial structures under wide-band signals in the time domain. The analysis can be found in [15,57] for the time-domain acoustic and electromagnetic obstacle scattering problems, we refer to [38] for the analysis of the time-dependent electromagnetic scattering from an three-dimensional open cavity.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Electroseismic Conversion in an Unbounded Rough Surface

ZHANG

2022

Preprint

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Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock due to the electrokinetic phenomenon. This paper concerns the time-domain analysis of such an electroseismic conversion problem in an unbounded structure in three dimensions. Using an exact transparent boundary condition and suitable interface conditions, we study an initial- boundary value problem for the coupling of Maxwell’s equations and the Biot’s equations. The well-posedness and stability are established for the reduced problem. Our proof is based on the method of energy, the Lax-Milgram theorem, and the inversion theorem of the Laplace transform. Moreover, a priori estimates with explicit dependence on the time are achieved for the quantities of electric filed and solid-fluid fields by taking special test functions for the time-domain variational problem.

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“…Introduction. The inverse scattering problems to determine the obstacle/scatterer from the time-harmonic acoustic, elastic, or electromagnetic waves have received mounting attention due to their wide applications in nondestructive testing, bio-medical imaging, underwater object identification, and many other scenarios [4,7,14,18]. In contrast, the inverse cavity scattering problems in an infinitely thin elastic plate, which is governed by the biharmonic wave equation, is much less investigated.…”

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confidence: 99%

An optimization method for the inverse scattering problem of the biharmonic wave

Chang¹,

Guo²

2023

CAC

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We consider an inverse scattering problem of reconstructing the shape of a cavity in an infinitely thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. We first approximate the out-of-plane displacement of the plate by potentials over an auxiliary circle and then reformulate the inverse problem into an optimization problem. The convergence properties are established to show that when the regularization parameter tends to zero, the minimizer of the optimization problem tends to a solution of the inverse scattering problem. Numerical experiments are designed to verify the performance of the proposed method.

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Modal approximation for time-domain elastic scattering from metamaterial quasiparticles

Cited by 5 publications

References 52 publications

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Elastodynamical resonances and cloaking of negative material structures beyond quasistatic approximation

Analysis of Electroseismic Conversion in an Unbounded Rough Surface

An optimization method for the inverse scattering problem of the biharmonic wave

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