论文标题
关于在准晶体上的Frenkel-Kontorova模型存在的解决方案
On the existence of solutions for Frenkel-Kontorova models on quasi-crystals
论文作者
论文摘要
本文重点介绍了对frenkel-kontorova模型平衡的最新研究，该模型受到准晶体产生的电势。我们提出了一个特定的一维模型，该模型具有由斐波那契准晶体驱动的明确电势。对于给定的正数$θ$，我们表明有多个旋转号$θ$的均衡，例如，最小的配置和非最小平衡配置。提供了一些验证这种平衡存在的数值实验。
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.
