Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media
Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media
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高对比度介质中的准周期二尺度均质化和有效空间色散
DOI：
10.1007/s00526-018-1365-3
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发表时间：
2017
影响因子：
2.1
通讯作者：
S. Cooper
中科院分区：
文献类型：
--
作者：
S. Cooper
双孔隙度模型的谱收敛是通过双尺度收敛来实现的。在这些作品中的一个重要假设是，身体的刚性组件形成一个连接的集合。我们表明，根据放松这一假设的（周期性）两个尺度的限制的运营商是不足以捕捉高对比度周期性介质的完整的渐近谱特性。渐近地，波的所有周期（或准动量）的持续和适当的扩展的概念，两个尺度收敛。其结果是，齐次极限方程与非平凡的准动量的依赖被发现作为原运营商家庭的预解极限。这将导致渐近谱行为与丰富的依赖准动量。
The convergence of spectra via two-scale convergence for double-porosity models is well known. A crucial assumption in these works is that the stiff component of the body forms a connected set. We show that under a relaxation of this assumption the (periodic) two-scale limit of the operator is insufficient to capture the full asymptotic spectral properties of high-contrast periodic media. Asymptotically, waves of all periods (or quasi-momenta) are shown to persist and an appropriate extension of the notion of two-scale convergence is introduced. As a result, homogenised limit equations with none trivial quasi-momentum dependence are found as resolvent limits of the original operator family. This results in asymptotic spectral behaviour with a rich dependence on quasimomenta.
具有周期系数的一维高对比度椭圆问题的谱分析
影响因子：
1.6
作者：
Cherednichenko K
通讯作者：
Cherednichenko K