A model for a driven Frenkel–Kontorova chain

We study a Frenkel–Kontorova (FK) model of a finite chain with free-end boundary conditions. The model has two competing potentials. Newton trajectories are an ideal tool to understand the circumstances under a driving of an FK chain by external forces. To reach the insights we calculate some stationary structures for a chain with 23 particles. We search the lowest energy saddle points for a complete minimum energy path of the chain for a movement over the full period of the on-site potential, a sliding. If an additional tilting is set, then one is interested in barrier breakdown points (BBPs) on the potential energy surface for a critical tilting force named the static frictional force. In symmetric cases, such BBPs are often valley-ridge inflection points of the potential energy surface. We explain the theory and demonstrate it with an example. We propose a model for a DC drive, as well as an AC drive, of the chain using special directional vectors of the external force.