W. Quapp and J. M. Bofill

Newton Trajectories for the tilted Frenkel-Kontorova Model

submitted 13.08.2018 for Molecular Physics

abstract
Newton trajectories are used for the Frenkel-Kontorova model of a finite 
chain with free-end boundary conditions. We optimize stationary structures,
as well as barrier breakdown points for a critical tilting force were 
depinning of the chain happens. These special points can be obtained 
straight forwardly by the tool of Newton trajectories.
We explain the theory and add examples for a finite-length chain of a 
fixed number of 2, 3, 4, 5 and 23 particles.

keywords 
 Frenkel-Kontorova model, Tilting, Newton trajectory, 
 Barrier breakdown point, Twist map