Frenkel—Kontorova模型论文：二维Frenkel-Kontorova模型中相变和整流的研究.doc

FrenkelKontorova模型论文：二维Frenkel-Kontorova模型中相变和整流的研究【中文摘要】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FrnenkelKontorova 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FrnenkelKontorova (FK)模型技在摩擦学应用方面的研究。采用二维frFrnenkelKontorova fFK)模型讨论了具有TF方形对称的特殊材料的lockedtosli(=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、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FrenkelKontorovafFK)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。【英文摘要】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, 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 heightj0. In the steps, rectifications in the transverse direction occur though there is no netdc force in the transverse direction.【关键词】FrenkelKontorova模型 相变 整理流【英文关键词】Frenkel-Kontorova model Phase transition Rectification【目录】二维Frenkel-Kontorova模型中相变和整流的研究摘要4-5Abstract5第一章 绪论7-111.1 Frenke1-Kontorova模型的CI相变7-101.2 研究目标和意义10-11第二章 Frnenke1-Kontorova模型及在摩擦学中的应用11-242.1 研究背景及现实意义112.2 二维Frenke1-Kontorova模型11-132.3 模拟结果13-232.4 结论23-24第三章 二维Fren