Can I read Quasi-periodic Two-scale Homogenisation and Effective Spatial Dispersion in High-contrast Media on EtoBox?

Quasi-periodic Two-scale Homogenisation and Effective Spatial Dispersion in High-contrast Media by Cooper, Shane is a scholarly article available to read on EtoBox.

What is Quasi-periodic Two-scale Homogenisation and Effective Spatial Dispersion in High-contrast Media about?

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 quasimomentum dependence are found as resolvent limits of the original operator family, resulting in limiting spectral behaviour with a rich dependence on quasimomenta.

Author

Cooper, Shane

Published

2017

Language

EN