Soft quantum waveguides with an explicit cut-locus

Criteria for the Absence and Existence of Bounded Solutions at the Threshold Frequency in a Junction of Quantum Waveguides

In the junction $Ω$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[λ_\dagger, +\infty)$ with a positive cut-off value $λ_\dagger$. We give two different criteria for the threshold resonance generated by nontrivial bounded solutions to the Dirichlet problem for the Helmholtz equation $-Δu=λ_\dagger u$ in $Ω$. The first criterion is quite simple and is convenient to disprove the existence of bounded solutions. The second criterion is rather involved but can help to detect concrete shapes supporting the resonance. Moreove…

多层开放式同轴波导的色散建模与分析

Dispersion modeling and analysis for multilayered open coaxial waveguides

针对超长电力电缆波传播建模与机理理解需求，提出基于分层递推与磁环激励的多层开放式同轴波导电磁模型，可分析色散特性与模式贡献，为相关定量研究提供工具。

小窗口周期系统耦合波导中的带隙开口和分裂带边

Gap opening and split band edges in waveguides coupled by a periodic system of small windows

在两个耦合波导的例子中，我们构造了一个周期性的二阶微分算子，它作用在欧几里得整环中，并且具有严格在布里渊区内达到边缘的谱隙。在两个不同宽度的无限长的带，有一个共同的内部边界的拉普拉斯算子的波导建模。在这个共同的边界上，我们施加诺依曼边界条件，但削减了一个周期性的系统的小孔，而其余的外部边界上，我们施加狄利克雷边界条件。它示出，通过改变带的宽度和孔之间的距离，可以控制的带函数的极值的位置以及开放的间隙的数量。我们计算了间隙长度和极值位置的渐近性中的首项。