Collision of One-Dimensional Nonlinear Chains

TL;DR

This paper studies how one-dimensional nonlinear chains collide with a wall, revealing that the coefficient of restitution varies with velocity and depends on the potential's nonlinearity, with theoretical derivations for low velocities.

Contribution

It introduces a velocity-dependent coefficient of restitution for nonlinear chains and derives its relationship with collision velocity using perturbation methods.

Findings

COR varies with collision velocity, showing a minimum at a certain point.

The velocity dependence of COR is linked to the nonlinearity exponent of the potential.

Theoretical derivation matches numerical observations at low velocities.

Abstract

We investigate one-dimensional collisions of unharmonic chains and a rigid wall. We find that the coefficient of restitution (COR) is strongly dependent on the velocity of colliding chains and has a minimum value at a certain velocity. The relationship between COR and collision velocity is derived for low-velocity collisions using perturbation methods. We found that the velocity dependence is characterized by the exponent of the lowest unharmonic term of interparticle potential energy.