The Frenkel-Kontorova model is a
harmonic chain (mimic a soft layer of atoms)
contected to a rigid upper plate via leaf springs.
The chain feels a spatially periodic potential (mimic the substrate).
The upper plate is driven by a constant
velocity. The chain is damped
by a velocity-proportional damping forces
(emitting waves into the substrate and into the upper plate).
The equations of motion: