Commensurate sliding on a multiple-well substrate potential

Abstract

In the context of microscopic solid friction phenomena, we study the underdamped dynamics of a Frenkel–Kontorova (FK) chain subject to an external dc force and a substrate potential defined by the sum of two sinusoidal functions with different periodicities. Particularly, focusing on mutually commensurate choices for the three inherent length scales of the system allows us to consider the formation of commensurate structures during sliding over the multiple-well on-site potential. These structures characterize the dynamical states observed during the chain motion at different strengths of the imposed driving. We comment on the nature of the particle dynamics in the vicinity of the pinning–depinning transition point and investigate the role played by the coverage variable on the depinning mechanism. The dependence of the minimal force required to initiate the chain motion ( static friction) on the ratio of the model interaction strengths is analyzed and compared to the well-known case of the Frenkel–Kontorova model.