中国物理B ›› 2022, Vol. 31 ›› Issue (5): 50501-050501.doi: 10.1088/1674-1056/ac439d

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Nano-friction phenomenon of Frenkel—Kontorova model under Gaussian colored noise

Yi-Wei Li(李毅伟)1, Peng-Fei Xu(许鹏飞)1,†, and Yong-Ge Yang(杨勇歌)2   

  1. 1 Department of Mathematics, Shanxi Agricultural University, Jinzhong 030801, China;
    2 School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • 收稿日期:2021-09-04 修回日期:2021-12-04 发布日期:2022-04-18
  • 通讯作者: Peng-Fei Xu,E-mail:xpf019@163.com E-mail:xpf019@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No.11902081),the Science and Technology Innovation Foundation of Higher Education Institutions of Shanxi Province,China (Grant No.2020L0172),the Natural Science Foundation for Young Scientists of Shanxi Agricultural University,China (Grant No.2020QC04),and the Research Fund of Shanxi Agriculture University,China (Grant No.2021BQ12).

Nano-friction phenomenon of Frenkel—Kontorova model under Gaussian colored noise

Yi-Wei Li(李毅伟)1, Peng-Fei Xu(许鹏飞)1,†, and Yong-Ge Yang(杨勇歌)2   

  1. 1 Department of Mathematics, Shanxi Agricultural University, Jinzhong 030801, China;
    2 School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2021-09-04 Revised:2021-12-04 Published:2022-04-18
  • Contact: Peng-Fei Xu,E-mail:xpf019@163.com E-mail:xpf019@163.com
  • About author:2021-12-16
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No.11902081),the Science and Technology Innovation Foundation of Higher Education Institutions of Shanxi Province,China (Grant No.2020L0172),the Natural Science Foundation for Young Scientists of Shanxi Agricultural University,China (Grant No.2020QC04),and the Research Fund of Shanxi Agriculture University,China (Grant No.2021BQ12).

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摘要： The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova (FK) model under Gaussian colored noise is investigated by using the molecular dynamic simulation method. The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method. Via the stochastic Runge-Kutta algorithm, the relationship between different parameter values of the Gaussian colored noise (the noise intensity and the correlation time) and the nano-friction phenomena such as hysteresis, the maximum static friction force is separately studied here. Similar results are obtained from the two geometrically opposed ideal cases: incommensurate and commensurate interfaces. It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force, the introduction of noise can accelerate the motion of the system, making the atoms escape from the substrate potential well more easily. Interestingly, suitable correlation time and noise intensity give rise to super-lubricity. It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.

关键词: Frenkel-Kontorova model, Gaussian colored noise, hysteresis, super-lubricity

Abstract: The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova (FK) model under Gaussian colored noise is investigated by using the molecular dynamic simulation method. The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method. Via the stochastic Runge-Kutta algorithm, the relationship between different parameter values of the Gaussian colored noise (the noise intensity and the correlation time) and the nano-friction phenomena such as hysteresis, the maximum static friction force is separately studied here. Similar results are obtained from the two geometrically opposed ideal cases: incommensurate and commensurate interfaces. It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force, the introduction of noise can accelerate the motion of the system, making the atoms escape from the substrate potential well more easily. Interestingly, suitable correlation time and noise intensity give rise to super-lubricity. It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.

Key words: Frenkel-Kontorova model, Gaussian colored noise, hysteresis, super-lubricity

中图分类号:  (Stochastic analysis methods)

  • 05.10.Gg
68.35.Af (Atomic scale friction) 81.40.Pq (Friction, lubrication, and wear) 83.10.Rs (Computer simulation of molecular and particle dynamics)