The laminations of a crystal near an anti-continuum limit

Knibbeler, Vincent, Mramor, Blaz and Rink, Bob (2014) The laminations of a crystal near an anti-continuum limit. Nonlinearity, 27 (5). pp. 927-952. ISSN 0951-7715

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Abstract

The anti-continuum limit of a monotone variational recurrence relation consists of a lattice of uncoupled particles in a periodic background. This limit supports many trivial equilibrium states that persist as solutions of the model with small coupling. We investigate when a persisting solution generates a so-called lamination and prove that near the anti-continuum limit the collection of laminations of solutions is homeomorphic to the (N - 1)-dimensional simplex, with N the number of distinct local minima of the background potential. This generalizes a result by Baesens and MacKay on twist maps near an anti-integrable limit.

Item Type:	Article
Subjects:	F200 Materials Science
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Becky Skoyles
Date Deposited:	05 Jun 2014 10:13
Last Modified:	12 Oct 2019 19:20
URI:	http://nrl.northumbria.ac.uk/id/eprint/16517

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