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 $\mathbb{Z}^d$ lattice for $d>1$.
Xueqing Miao
,
Jianhua Ge
,
Wenxin Qin
,
Yanan Wang
. MINIMAL FOLIATIONS FOR THE HIGH-DIMENSIONAL FRENKEL-KONTOROVA MODEL*[J]. Acta mathematica scientia, Series B, 2023
, 43(2)
: 564
-582
.
DOI: 10.1007/s10473-023-0207-3
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