Static and Dynamic Properties of Inhomogeneous Elastic Media on Disordered Substrate

TL;DR

This paper investigates the static and dynamic behaviors of inhomogeneous elastic media on disordered substrates, revealing their equivalence to higher-dimensional random manifold problems and exploring depinning transitions.

Contribution

It establishes a robust analogy between elastic media on disordered substrates and higher-dimensional random manifolds, applicable across various elastic media types.

Findings

Static and dynamic properties are equivalent to those of higher-dimensional random manifolds.

Depinning transition under constant force is equivalent to near-critical behavior under small velocity drive.

The analogy applies to amorphous and nearly-periodic elastic media with local or nonlocal elasticity.

Abstract

The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of a $D$-dimensional random manifold embedded in $(D+D)$-dimensions. The analogy is found to be very robust, applicable to a wide range of elastic media, including those which are amorphous or nearly-periodic, with local or nonlocal elasticity. Also demonstrated explicitly is the equivalence between the dynamic depinning transition obtained at a constant driving force, and the self-organized, near-critical behavior obtained by a (small) constant velocity drive.