具有高阶跳跃条件的薄表面的光谱目标特征

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
F. Cakoni, Heejin Lee, P. Monk, Yangwen Zhang
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引用次数: 1

摘要

在本文中,我们考虑了从散射数据中确定\ begin{document}${\mathbb R}^m$\ end{document},\ begin{document}$m=2,3$\ end}中薄各向异性和耗散不均匀性的结构性质的反问题。在厚度为零时的渐近极限中,薄的不均匀性由开\ begin{document}$m-1$\ end{document}维流形(此处称为屏幕)建模,内部的场由涉及二阶表面微分算子的总场上的跳跃条件代替。我们证明了所有的表面系数(可能是矩阵值和复数)都是由固定频率下无限多个入射平面波引起的散射场的远场模式唯一确定的。然后,我们引入了一个由新的特征值问题表征的目标签名,使得特征值可以从测量的散射数据中确定,适用于[20]中的方法。测量的特征值的变化用于识别系数的变化,而不使用对健康屏幕建模的控制方程。在我们的调查中,屏幕的形状是已知的,因为它代表了被评估的对象。我们给出了一些初步的数值结果,表明了我们反演方法的有效性
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A spectral target signature for thin surfaces with higher order jump conditions

In this paper we consider the inverse problem of determining structural properties of a thin anisotropic and dissipative inhomogeneity in \begin{document}$ {\mathbb R}^m $\end{document}, \begin{document}$ m = 2, 3 $\end{document} from scattering data. In the asymptotic limit as the thickness goes to zero, the thin inhomogeneity is modeled by an open \begin{document}$ m-1 $\end{document} dimensional manifold (here referred to as screen), and the field inside is replaced by jump conditions on the total field involving a second order surface differential operator. We show that all the surface coefficients (possibly matrix valued and complex) are uniquely determined from far field patterns of the scattered fields due to infinitely many incident plane waves at a fixed frequency. Then we introduce a target signature characterized by a novel eigenvalue problem such that the eigenvalues can be determined from measured scattering data, adapting the approach in [20]. Changes in the measured eigenvalues are used to identified changes in the coefficients without making use of the governing equations that model the healthy screen. In our investigation the shape of the screen is known, since it represents the object being evaluated. We present some preliminary numerical results indicating the validity of our inversion approach

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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