声学空间卷曲元晶体建模

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2023-12-06 DOI:10.1137/22m1527131

Joar Zhou Hagström, Kim Pham, Agnés Maurel

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引用次数: 0

摘要

SIAM 应用数学杂志》，第 83 卷第 6 期，第 2499-2521 页，2023 年 12 月。摘要。我们提出了一种有效的 "空间卷曲元晶体 "模型，它由一个周期性的声刚性块阵列组成，其中的长槽被卷曲起来。块的周期性单元包含一个卷曲槽，其直线部分与波长尺度一致，这使得布拉格共振得以出现。这些共振会阻碍高传输，与整个槽的法布里-佩罗共振竞争，从而促进完美传输。这就导致了复杂的散射特性，而散射特性是由转折区域的特性驱动的，这些转折区域就像一维盘绕晶体中的原子。利用适当的缩放并结合二尺度均质化和匹配渐近技术，提出了这种元晶体的建模方法。通过与谐波和瞬态下的全波数值进行比较，验证了由此产生的模型。

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Modeling Acoustic Space-Coiled Metacrystals

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2499-2521, December 2023.
Abstract. We present an effective model of “space-coiled metacrystals” composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry–Pérot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.