Phase Transition And Rectification In Two Dimensional Frenkel-Kontorova Model

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.