Newton trajectories for the tilted Frenkel–Kontorova model

ABSTRACT

Newton trajectories are used for the Frenkel–Kontorova model of a finite chain with free-end boundary conditions. We optimise 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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Frenkel–Kontorova model
• tilting
• newton trajectory
• barrier breakdown point
• twist map

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

W. Quapp http://orcid.org/0000-0002-0366-1408

J. M. Bofill http://orcid.org/0000-0002-0974-4618

Additional information

Funding

We acknowledge the financial support from the Spanish Ministerio de Economía y Competitividad, Project: CTQ2016-76423-P, and from the Generalitat de Catalunya, Departament d'Empresa i Coneixement, Project: 2017 SGR 348.