Elastic String in a Random Medium

TL;DR

This paper studies the nonlinear dynamics of an elastic string driven through a disordered medium, highlighting how anisotropy and boundary conditions influence depinning behavior and nonlinear effects.

Contribution

It introduces a model incorporating longitudinal fluctuations and boundary conditions, revealing their impact on nonlinear behavior near the depinning transition.

Findings

Nonlinear effects depend on medium anisotropy.

Nonlinear terms diverge at the depinning transition.

Longitudinal fluctuations influence string dynamics.

Abstract

We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We present evidence that the consideration of longitudinal fluctuations leads to nonlinear behavior in the equation of motion which is {\it kinematically} generated by the motion of the string. The strength of the nonlinear effects depends on the anisotropy of the medium and the distance from the depinning transition. On the other hand the consideration of restricted solid on solid conditions imposed to the growth of the string leads to a nonlinear term in the equation of motion with a {\it diverging} coefficient at the depinning transition.