Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force

TL;DR

This paper investigates how anharmonic convex interparticle potentials affect the dynamics of the driven overdamped Frenkel-Kontorova model, revealing asymmetries and mode-locking phenomena in particle motion.

Contribution

It introduces analysis of anharmonic convex potentials in the Frenkel-Kontorova model and uncovers new behaviors like asymmetry and mode-locking in both motion directions.

Findings

Mirror symmetry in amplitude dependence is not universal.

Strong interparticle forces lead to mode-locking in both directions.

Behavior differs from the standard model with harmonic potentials.

Abstract

The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model [Commun. Nonlinear Sci. Numer. Simul. 47, 100 (2017)] is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles' motion is presented.