Cooper, S;
(2018)
Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media.
Calculus of Variations and Partial Differential Equations
, 57
, Article 76. 10.1007/s00526-018-1365-3.
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Abstract
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) twoscale 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.
| Type: | Article |
|---|---|
| Title: | Quasi-periodic two-scale homogenisation and effective spatial dispersion in high-contrast media |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00526-018-1365-3 |
| Publisher version: | https://doi.org/10.1007/s00526-018-1365-3 |
| Language: | English |
| Additional information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10120078 |
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