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Minimal Foliations for the High-Dimensional Frenkel-Kontorova Model

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Abstract

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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Authors and Affiliations

  1. School of Sciences, Nantong University, Nantong, 226019, China

    Xueqing Miao  (缪雪晴) & Jianhua Ge  (葛建华)

  2. Department of Mathematics, Soochow University, Suzhou, 215006, China

    Wenxin Qin  (秦文新)

  3. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097, China

    Yanan Wang  (王亚南)

Authors
  1. Xueqing Miao  (缪雪晴)
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  2. Jianhua Ge  (葛建华)
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  3. Wenxin Qin  (秦文新)
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  4. Yanan Wang  (王亚南)
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Corresponding author

Correspondence to Xueqing Miao  (缪雪晴).

Additional information

The first author was supported by the National Natural Science Foundation of China (11701298).

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Miao, X., Ge, J., Qin, W. et al. Minimal Foliations for the High-Dimensional Frenkel-Kontorova Model. Acta Math Sci 43, 564–582 (2023). https://doi.org/10.1007/s10473-023-0207-3

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  • DOI: https://doi.org/10.1007/s10473-023-0207-3

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