二维Frenkel-Kontorova模型中相变和整流的研究
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摘要
本文通过分子动力学方法，对非平衡统计物理的Langevin方程进行分析和计算，研究了二维Frnenkel—Kontorova fFK)模型存摩擦学领域和些过阴尼系统中的应用。土要研究内容可以概括为以下两个部分：
1.引入具有TF方形对称的一维FK模型，介绍Frnenkel—Kontorova (FK)模型技在摩擦学应用方面的研究。采用二维frFrnenkel—Kontorova fFK)模型讨论了具有TF方形对称的特殊材料的locked—to—sli(=1ing相变过程，随着外驱动力的逐渐增大，系统由锁态向涓动态转换的过程巾，发现系统的运动方向与外力的方向小同。进一步增加外力达到某一临界值时，系统运动的方向与外力方Jn'致。文巾讨论了这两个临界力随系统参数(外驱动力Faxt。错合角θ、耦台系数K和基底势振幅，)变化的影响，以及系统的参数对系统状态的影响，并在相变过程巾发现了分形的存在。
2介绍具有六角结构对称的过阴尼二维FK模型巾的整流和相锁。为更好地理解微摩擦机制以技生命科学巾的些输运行为，我们采用二维六角角结构对称的Frenkel—KontorovafFK)模型，研究个在恒定和交变外力作用下的过阻尼系统存运动过程中出现的整流现象。横向速度为台阶状态，UX-JVO(H为整数)，j为奇数时，系统在纵方向出现整流。
By using the classical molecular dynamics simulations, we study the driven two-dimensional Frenkel-Kontorova (FK) model and apply it in the field of tribology in thisthesis. The paper is organized as follows:
1. Locked-to-sliding phase transition has been studied in the driven two-dimensionalFrenkel-Kontorova model with the square symmetric substrate potential. It is found thatas the driving force increases, the system transfers from the locked state to the slidingstate where the motion of particles is in the direction di?erent from that of driving force.With the further increase in driving force, at some critical value, the particles start tomove in the direction of driving force. These two critical forces, the static friction ordepinning force, and the kinetic friction force for which particles move in the direction ofdriving force have been analyzed for di?erent system parameters (Fext,θ, K, f).
2. To better understand the micro-friction mechanism and some of the life sci-ences transport behavior, we use two dimensional Frenkel-Kontorova model system withcommensurate structure under the ac and dc driven external forces. As a function oflongitudinal dc amplitude, the longitudinal velocity increases in a series of steps of heightjν0. In the steps, rectifications in the transverse direction occur though there is no netdc force in the transverse direction.
1.引入具有TF方形对称的一维FK模型，介绍Frnenkel—Kontorova (FK)模型技在摩擦学应用方面的研究。采用二维frFrnenkel—Kontorova fFK)模型讨论了具有TF方形对称的特殊材料的locked—to—sli(=1ing相变过程，随着外驱动力的逐渐增大，系统由锁态向涓动态转换的过程巾，发现系统的运动方向与外力的方向小同。进一步增加外力达到某一临界值时，系统运动的方向与外力方Jn'致。文巾讨论了这两个临界力随系统参数(外驱动力Faxt。错合角θ、耦台系数K和基底势振幅，)变化的影响，以及系统的参数对系统状态的影响，并在相变过程巾发现了分形的存在。
2介绍具有六角结构对称的过阴尼二维FK模型巾的整流和相锁。为更好地理解微摩擦机制以技生命科学巾的些输运行为，我们采用二维六角角结构对称的Frenkel—KontorovafFK)模型，研究个在恒定和交变外力作用下的过阻尼系统存运动过程中出现的整流现象。横向速度为台阶状态，UX-JVO(H为整数)，j为奇数时，系统在纵方向出现整流。
By using the classical molecular dynamics simulations, we study the driven two-dimensional Frenkel-Kontorova (FK) model and apply it in the field of tribology in thisthesis. The paper is organized as follows:
1. Locked-to-sliding phase transition has been studied in the driven two-dimensionalFrenkel-Kontorova model with the square symmetric substrate potential. It is found thatas the driving force increases, the system transfers from the locked state to the slidingstate where the motion of particles is in the direction di?erent from that of driving force.With the further increase in driving force, at some critical value, the particles start tomove in the direction of driving force. These two critical forces, the static friction ordepinning force, and the kinetic friction force for which particles move in the direction ofdriving force have been analyzed for di?erent system parameters (Fext,θ, K, f).
2. To better understand the micro-friction mechanism and some of the life sci-ences transport behavior, we use two dimensional Frenkel-Kontorova model system withcommensurate structure under the ac and dc driven external forces. As a function oflongitudinal dc amplitude, the longitudinal velocity increases in a series of steps of heightjν0. In the steps, rectifications in the transverse direction occur though there is no netdc force in the transverse direction.
引文
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[61] C. H. Chen and S-W. Cheong 1996 Phys.Rev.Lett. 76 4042.
[62] J. Hu and R. M. Westervelt 1997 Phys.Rev.B 55 771.
[63] S. Little and A. Zangwill 1992 Phys.Rev.B 46 7981.
[64] Haibo Xu§Aiguo Xu§Guangrui Wang and Shigang Chen 2000 ModenPhys.Lett. B 14 725; 2000 Chin.Phys.Lett. 17 255; 2000 Chin.Phys. 942.
[65] C. S. O. Yokoi§L. H. Tangand, W. Chou 1998 Phys.Rev.B 37 2173.
[66] F. Axel and S. Aubry 1987 J.Phys.A 20 4873.
[67] S. C. Erwin§A. A. Baski§L. J. Whitman et al. 1999 Phys.Rev.Lett. 831818.
[68] Haibo Xu§Guangrui Wang§and Shigang Chen 2000 Chin.Phys.Lett.17 689.
[69] F. F. Abraham§W. E. Rudge§D. Auerbach§et al. 1984 Phys.Rev.Lett.52 445.
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