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Main Authors: Du, Jianxing, Su, Xifeng
Format: Preprint
Published: 2020
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Online Access:https://arxiv.org/abs/2012.15594
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author Du, Jianxing
Su, Xifeng
author_facet Du, Jianxing
Su, Xifeng
contents This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals. We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number $θ$, we show that there are multiple equilibria with rotation number $θ$, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.
format Preprint
id arxiv_https___arxiv_org_abs_2012_15594
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle On the existence of solutions for Frenkel-Kontorova models on quasi-crystals
Du, Jianxing
Su, Xifeng
Dynamical Systems
This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals. We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number $θ$, we show that there are multiple equilibria with rotation number $θ$, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.
title On the existence of solutions for Frenkel-Kontorova models on quasi-crystals
topic Dynamical Systems
url https://arxiv.org/abs/2012.15594