Edge Mode Amplification in Disordered Elastic Networks

TL;DR

This paper investigates how disordered elastic networks can support modes that exponentially amplify displacement fields, revealing potential for designing elastic amplifiers and molecular machines.

Contribution

It provides a theoretical and numerical analysis of edge mode amplification in disordered elastic materials, introducing an analytical distribution for Lyapounov exponents.

Findings

Some modes decay with inverse penetration depth.

Other modes exponentially amplify with rate |5|.

Isostatic materials can act as elastic amplifiers.

Abstract

We study theoretically and numerically the propagation of a displacement field imposed at the edge of a disordered elastic material. While some modes decay with some inverse penetration depth $\kappa$, other exponentially {\it amplify} with rate $|\kappa|$, where $\kappa$'s are Lyapounov exponents analogous to those governing electronic transport in a disordered conductors. We obtain an analytical approximation for the full distribution $g(\kappa)$, which decays exponentially for large $|\kappa|$ and is finite when $\kappa\rightarrow0$. Our analysis shows that isostatic materials generically act as levers with possibly very large gains, suggesting a novel principle to design molecular machines that behave as elastic amplifiers.