The Scattering Phase: Seen at Last

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-02-12 DOI:10.1137/23m1547147

Jeffrey Galkowski, Pierre Marchand, Jian Wang, Maciej Zworski

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 246-261, February 2024.
Abstract. The scattering phase, defined as [math] where [math] is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn’s spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.

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散射阶段终于看到了

SIAM 应用数学杂志》第 84 卷第 1 期第 246-261 页，2024 年 2 月。摘要。散射相定义为[math]，其中[math]为（单元）散射矩阵，是处理外部域时特征值计数函数的类似物，与 Kreĭn 的谱移函数密切相关。我们重温了散射相位渐近的经典结果，并指出在波的强捕获情况下，散射相位从来不是单调的。也许更重要的是，我们首次对非径向散射体的散射相位进行了数值计算。结果表明，即使在低频下，渐近韦尔定律也是准确的，并揭示了陷波的影响，如缺乏单调性。这是通过使用最新的高级多物理场有限元软件 FreeFEM 实现的。

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.