English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this note we investigate spectral properties of a periodic waveguide$\Omega^\varepsilon$ ($\varepsilon$ is a small parameter) obtained from astraight strip by attaching an array of $\varepsilon$-periodically distributedidentical protuberances having "room-and-passage" geometry. In the current workwe consider the operator$\mathcal{A}^\varepsilon=-\rho^\varepsilon\Delta_{\Omega^\varepsilon}$, where$\Delta_{\Omega^\varepsilon}$ is the Neumann Laplacian in $\Omega^\varepsilon$,the weight $\rho^\varepsilon$ is equal to $1$ everywhere except the union ofthe "rooms". We will prove that the spectrum of $\mathcal{A}^\varepsilon$ hasat least one gap as $\varepsilon$ is small enough provided certain conditionson the weight $\rho^\varepsilon$ and the sizes of attached protuberances hold.  (Dedicated to Pavel Exner's 70th birthday)

Example of periodic Neumann waveguide with gap in spectrum