随机激励下Frenkel-Kontorova模型的纳米摩擦现象  

Nano-friction phenomena in driven Frenkel-Kontorova model with stochastic excitation

作　　者：李毅伟 雷佑铭[2] 杨勇歌 Li Yi-Wei;Lei You-Ming;Yang Yong-Ge(Department of Mathematics,Shanxi Agricultural University,Jinzhong 030801,China;Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710129,China;School of Applied Mathematics,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]山西农业大学数学系,晋中030801 [2]西北工业大学应用数学系,西安710129 [3]广东工业大学应用数学学院,广州510520

出　　处：《物理学报》2021年第9期220-225,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11902081);山西省高等学校科技创新基金(批准号:2020L0172);山西农业大学青年科技创新基金(批准号:2020QC04)资助的课题。

摘　　要：基于一维Frenkel-Kontorova (FK)模型,借助随机龙格库塔方法,在非公度(incommensurate)和公度(commensurate)两种情形下,分别研究了高斯白噪声激励下,随机FK模型的纳米摩擦现象(滞回和超滑)随噪声强度的变化而变化的规律.两种情形表明随着噪声强度的增大,对减小系统滞回,产生超滑有积极的影响.另一方面,当系统机动性能(chain mobility)未达到饱和状态(B=1)时,噪声的引入,能加速原子的运动,使得原子更易脱离基底势的束缚而做运动,但是当系统达到饱和状态后,系统机动性能并不受噪声的影响.另外,两种情形的区别是,公度情形下,由于原子受到基底势更强烈的耦合作用,所以噪声对公度情形影响更为明显.In this paper,the effects of a Gaussian white noise excitation on the one-dimensional Frenkel-Kontorova(FK)model are studied by the stochastic Runge-Kutta method under two different types of substrate cases,i.e.incommensurate case and commensurate case.The noise excitation is considered through the inclusion of a stochastic force via a Langevin molecular dynamics approach,and we uncover the mechanism of nano-friction phenomenon in the FK model driven by the stochastic force.The relationship between the noise intensity and the nano-friction phenomenon,such as hysteresis,maximum static friction force,and the super-lubricity,is investigated by using the stochastic Runge-Kutta algorithm.It is shown that with the increase of noise intensity,the area of the hysteresis becomes smaller and the maximum static friction force tends to decrease,which can promote the generation of super-lubricity.Similar results are obtained from the two cases,in which the ratios of the atomic distance to the period of the substrate potential field are incommensurate and commensurate,respectively.In particular,a suitable noise density gives rise to super-lubricity where the maximum static friction force vanishes.Hence,the noise excitation in this sense is beneficial to the decrease of the hysteresis and the maximum static friction force.Meanwhile,with the appropriate external driving force,the introduction of a noise excitation can accelerate the motion of the system,making the atoms escape from the substrate potential well more easily.But when the chain mobility reaches a saturation state(B=1),it is no longer affected by the stochastic excitation.Furthermore,the difference between the two circumstances lies in the fact that for the commensurate interface,the influence of the noise is much stronger and more beneficial to triggering the motion of the FK model than for the incommensurate interface since the atoms in the former case are coupled and entrapped more strongly by the substrate potential.

关 键 词：FRENKEL-KONTOROVA模型 高斯白噪声 滞回 超滑 

分 类 号：TH117.1[机械工程—机械设计及理论]