论文标题
多尺度近距离触发夹杂物之间的现场浓度的最佳估计值3-D Helmholtz系统
Optimal estimate of field concentration between multiscale nearly-touching inclusions for 3-D Helmholtz system
论文作者
论文摘要
我们关注的是具有高对比度材料参数的两个几乎触觉的包含物之间的田间浓度，这是复合材料理论中的一个核心主题。浓度程度的特征在于基础场梯度的爆炸速率。在本文中，我们得出了准静态状态中3-D Helmholtz系统的波的最佳梯度估计。我们的结果有两个显着特征，这些特征是文献的新功能。首先，我们涵盖了所有可能的方案，即包含物的大小在渐近距离参数$ε$方面处于不同的尺度，可用于表征夹杂物形状对场浓度的曲率效应。其次，我们的估计不仅可以在静态情况下恢复文献中已知的结果，而且还可以揭示对场浓度的有趣频率影响。实际上，一种新的现象表明，即使静态部分消失，由于（低）频率效应，野外爆炸仍然会发生。
We are concerned with the field concentration between two nearly-touching inclusions with high-contrast material parameters, which is a central topic in the theory of composite materials. The degree of concentration is characterised by the blowup rate of the gradient of the underlying field. In this paper, we derive optimal gradient estimates for the wave filed of the 3-D Helmholtz system in the quasi-static regime. There are two salient features of our results that are new to the literature. First, we cover all the possible scenarios that the size of the inclusions are in different scales in terms of the asymptotic distance parameter $ε$, which can be used to characterise the curvature effects of the shape of the inclusions on the field concentration. Second, our estimates can not only recover the known results in the literature for the static case, but can also reveal the interesting frequency effect on the field concentration. In fact, a novel phenomena is shown that even if the static part vanishes, field blowup can still occur due to the (low) frequency effect.
