The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem

Ekaterina V. Shishkina; Serge N. Gavrilov; Yulia A. Mochalova

doi:10.1016/j.jsv.2023.117673

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arXiv · 2210.06736

The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem

Ekaterina V. Shishkina·Serge N. Gavrilov·Yulia A. Mochalova

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Abstract

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.

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Ekaterina V. Shishkina, Serge N. Gavrilov, Yulia A. Mochalova. 2022-10-13. The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem. https://doi.org/10.1016/j.jsv.2023.117673

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