论文标题
非平稳线性波的抗本地化及其与定位的关系。最简单的说明性问题
The anti-localization of non-stationary linear waves and its relation to the localization. The simplest illustrative problem
论文作者
论文摘要
我们引入了一种新的波浪现象，可以在连续和离散系统中观察到，其中在某些条件下存在捕获模式，即非平稳线性波的抗位置。这是在包含邻里的波场非定位的传播成分的归零。换句话说，这是非平稳波传播避免包容邻里的趋势。抗本地化是由谐波以傅立叶积分形式涉及的谐波的破坏性干扰引起的。抗本地化与传球带的波相关，而与陷阱模式相关的定位是由于止损带内的极点。在本文中考虑的简单说明性问题的框架中，我们已经证明了所有情况下存在的反区域化，除了在发生波浪定位的参数空间中域的边界。因此，在没有定位以及与定位的情况下，可以观察到抗本地化。我们还研究了抗本地化对波场整体的影响。
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.
