The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem
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| Format: | Preprint |
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2022
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| _version_ | 1866915676555313152 |
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| author | Shishkina, Ekaterina V. Gavrilov, Serge N. Mochalova, Yulia A. |
| author_facet | Shishkina, Ekaterina V. Gavrilov, Serge N. Mochalova, Yulia A. |
| contents | We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing of the non-localized propagating component of the wave-field in a neighbourhood of an inclusion. In other words, it is a tendency for non-stationary waves to propagate avoiding a neighbourhood of an inclusion. The anti-localization is caused by a destructive interference of the harmonics involved into the representation of the solution in the form of a Fourier integral. The anti-localization is associated with the waves from the pass-band, whereas the localization related with a trapped mode is due to poles inside the stop-band. In the framework of a simple illustrative problem considered in the paper, we have demonstrated that the anti-localization exists for all cases excepting the boundary of the domain in the parameter space where the wave localization occurs. Thus, the anti-localization can be observed in the absence of the localization as well as together with the localization. We also investigate the influence of the anti-localization on the wave-field in whole. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_06736 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem Shishkina, Ekaterina V. Gavrilov, Serge N. Mochalova, Yulia A. Classical Physics We introduce a new wave phenomenon, which can be observed in continuum and discrete systems, where a trapped mode exists under certain conditions, namely, the anti-localization of non-stationary linear waves. This is zeroing of the non-localized propagating component of the wave-field in a neighbourhood of an inclusion. In other words, it is a tendency for non-stationary waves to propagate avoiding a neighbourhood of an inclusion. The anti-localization is caused by a destructive interference of the harmonics involved into the representation of the solution in the form of a Fourier integral. The anti-localization is associated with the waves from the pass-band, whereas the localization related with a trapped mode is due to poles inside the stop-band. In the framework of a simple illustrative problem considered in the paper, we have demonstrated that the anti-localization exists for all cases excepting the boundary of the domain in the parameter space where the wave localization occurs. Thus, the anti-localization can be observed in the absence of the localization as well as together with the localization. We also investigate the influence of the anti-localization on the wave-field in whole. |
| title | The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2210.06736 |