Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/2288
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Plamenevskii, B.A. | - |
dc.contributor.author | Poretskii, A.S. | - |
dc.contributor.author | Sarafanov, O.V. | - |
dc.date.accessioned | 2016-05-27T14:58:10Z | - |
dc.date.available | 2016-05-27T14:58:10Z | - |
dc.date.issued | 2015-01 | - |
dc.identifier.citation | St. Petersburg Math. J. 26 (2015), 91-116 | - |
dc.identifier.issn | 1061-0022 | - |
dc.identifier.uri | http://hdl.handle.net/11701/2288 | - |
dc.description.abstract | A waveguide occupies a domain $ G$ in $ \mathbb{R}^{n+1}$, $ n\geq 1$, having several cylindrical outlets to infinity. The waveguide is described by the Dirichlet problem for the Helmholtz equation. The scattering matrix $ S(\mu )$ with spectral parameter $ \mu $ changes its size when $ \mu $ crosses a threshold. To calculate $ S(\mu )$ in a neighborhood of a threshold, an ``augmented'' scattering matrix $ \mathcal {S} (\mu )$ is introduced, which keeps its size near the threshold and is analytic in $ \mu $ there. A minimizer of a quadratic functional $ J^R(\,\cdot \,, \mu )$ serves as an approximation to a row of the matrix $ \mathcal {S}(\mu )$. To construct such a functional, an auxiliary boundary-value problem is solved in the bounded domain obtained by cutting off the waveguide outlets to infinity at a distance $ R$. As $ R\to \infty $, the minimizer $ a (R, \mu )$ tends exponentially to the corresponding row of $ \mathcal {S}(\mu )$ uniformly with respect to $ \mu $ in a neighborhood of the threshold. The neighborhood may contain some waveguide eigenvalues corresponding to eigenfunctions exponentially decaying at infinity. Finally, the elements of the ``ordinary'' scattering matrix $ S(\mu )$ are expressed in terms of those of the augmented matrix $ \mathcal {S}(\mu )$. If an interval $ [\mu _1, \mu _2]$ of the continuous spectrum contains no thresholds, the corresponding functional $ J^R(\,\cdot \,, \mu )$ should be defined for the usual matrix $ S(\mu )$ and, as $ R\to \infty $, its minimizer $ a (R, \mu )$ tends to the row of the scattering matrix at exponential rate uniformly with respect to $ \mu \in [\mu _1, \mu _2]$. | en_GB |
dc.language.iso | en | en_GB |
dc.title | Method for computing waveguide scattering matrices in the vicinity of thresholds | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Articles |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
PPSeng (2).pdf | 445,05 kB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.