Minimal Foliations for the High-Dimensional Frenkel-Kontorova Model

被引：0
|
作者：
Xueqing Miao
Jianhua Ge
Wenxin Qin
Yanan Wang
机构：
[1] Nantong University,School of Sciences
[2] Soochow University,Department of Mathematics
[3] Nanjing Normal University,School of Mathematical Sciences
来源：
Acta Mathematica Scientia | 2023年 / 43卷
关键词：
Aubry-Mather theory; Frenkel-Kontorova model; minimal foliation; depinning force; gradient flow; 37C65; 37K60; 82C22;
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摘要：
For the high-dimensional Frenkel-Kontorova (FK) model on lattices, we study the existence of minimal foliations by depinning force. We introduce the tilted gradient flow and define the depinning force as the critical value of the external force under which the average velocity of the system is zero. Then, the depinning force can be used as the criterion for the existence of minimal foliations for the FK model on a ℤd lattice for d > 1.
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页码：564 / 582
页数：18
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