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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.15594 |
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| _version_ | 1866909427350634496 |
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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 |