Spectral Patterns of Elastic Transmission Eigenfunctions: Boundary Localization, Surface Resonance, and Stress Concentration

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2023-12-05 DOI:10.1137/22m1538417

Yan Jiang, Hongyu Liu, Jiachuan Zhang, Kai Zhang

引用次数: 1

Abstract

SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2469-2498, December 2023.
Abstract. We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localization, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.

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弹性传输特征函数的谱图:边界局部化、表面共振和应力集中

应用数学学报，第83卷，第6期，第2469-2498页，2023年12月。摘要。我们全面研究了弹性透射本征函数谱图的新发现，包括边界局部化、表面共振和应力集中。在这种情况下，区域是径向的，基本参数是恒定的，我们给出了严格的理由，并得出了对那些有趣的几何和物理模式的透彻理解。我们还给出了数值例子来验证相同的结果适用于一般的几何和参数设置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.