On regular and singular perturbations of acoustic and quantum waveguides

Reverse Time Migration for Reconstructing Extended Obstacles in Planar Acoustic Waveguides

We propose a new reverse time migration method for reconstructing extended obstacles in the planar waveguide using acoustic waves at a fixed frequency. We prove the resolution of the reconstruction method in terms of the aperture and the thickness of the waveguide. The resolution analysis implies that the imaginary part of the cross-correlation imaging function is always positive and thus may have better stability properties. Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.

量子图论在超材料设计中的应用：声波导模式的负折射

Application of Quantum Graph Theory to Metamaterial Design: Negative Refraction of Acoustic Waveguide Modes

本研究将量子图论应用于声学超材料设计，通过含各向异性键长的模型表征空间卷曲结构的色散，构建超表面实现声学表面波非共振负折射，验证了该理论作为超材料设计新范式的有效性。

Initial length scale estimate for waveguides with some random singular potentials

In this work we consider three examples of random singular perturbations in multi-dimensional models of waveguides. These perturbations are described by a large potential supported on a set of a small measure, by a compactly supported fast oscillating potential, and by a delta-potential. In all cases we prove initial length scale estimate.

Klein-Gordon奇异波导的积分公式化

Integral formulation of Klein-Gordon singular waveguides

针对二维分隔绝缘相的奇异波导，本文建立积分公式并分析其性质，采用快速多极与扫描加速迭代法求解，数值验证快速收敛及散射效应。

Coupling in the singular limit of thin quantum waveguides

We analyze the problem of approximating a smooth quantum waveguide with a quantum graph. We consider a planar curve with compactly supported curvature and a strip of constant width around the curve. We rescale the curvature and the width in such a way that the strip can be approximated by a singular limit curve, consisting of one vertex and two infinite, straight edges, i.e. a broken line. We discuss the convergence of the Laplacian, with Dirichlet boundary conditions on the strip, in a suitable sense and we obtain two possible limits: the Laplacian on the line with Dirichlet boundary conditio…

On the spectrum of narrow Neumann waveguide with periodically distributed $δ'$ traps

We analyze a family of singular Schrödinger operators describing a Neumann waveguide with a periodic array of singular traps of a $δ'$ type. We show that in the limit when perpendicular size of the guide tends to zero and the $δ'$ interactions are appropriately scaled, the first spectral gap is determined exclusively by geometric properties of the traps.