带有小障碍物的平面量子波导中的离散和嵌入陷波模式:精确解法

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
P. Zhevandrov, A. Merzon, M. I. Romero Rodríguez, J. E. De la Paz Méndez
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引用次数: 0

摘要

以具有小刚性障碍物的平面量子波导的小参数幂级数的收敛形式,构造了描述其捕获模式的精确解。该级数的项通过描述无界流体流过膨胀障碍物的拉普拉斯方程的外诺伊曼问题的解来表示。所得到的精确解描述了问题在一定几何条件下的离散特征值,当障碍物是对称的时,这些解描述了嵌入特征值。对于相对于波导中心线对称的障碍物,即使没有小假设,也可以知道嵌入的捕获模式的存在(由于相应微分算子的域的分解技巧)。对于小障碍,我们用显式形式构造这些解。对于相对于垂直轴对称的障碍物,我们找到了障碍物特定垂直位移的嵌入捕获模式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Discrete and Embedded Trapped Modes in a Plane Quantum Waveguide with a Small Obstacle: Exact Solutions

Discrete and Embedded Trapped Modes in a Plane Quantum Waveguide with a Small Obstacle: Exact Solutions

Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of this series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the inflated obstacle. The exact solutions obtained describe discrete eigenvalues of the problem under certain geometric conditions, and, when the obstacle is symmetric, these solutions describe embedded eigenvalues. For obstacles symmetric with respect to the centerline of the waveguide, the existence of embedded trapped modes is known (due to the decomposition trick of the domain of the corresponding differential operator) even without the smallness assumption. We construct these solutions in an explicit form for small obstacles. For obstacles symmetric with respect to the vertical axis, we find embedded trapped modes for a specific vertical displacement of the obstacle.

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来源期刊
Acta Applicandae Mathematicae
Acta Applicandae Mathematicae 数学-应用数学
CiteScore
2.80
自引率
6.20%
发文量
77
审稿时长
16.2 months
期刊介绍: Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.
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