Edge Mode Amplification in Disordered Elastic Networks

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 $κ$, other exponentially {\it amplify} with rate $|κ|$, where $κ$'s are Lyapounov exponents analogous to those governing electronic transport in a disordered conductors. We obtain an analytical approximation for the full distribution $g(κ)$, which decays exponentially for large $|κ|$ and is finite when $κ\rightarrow0$. 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.

5 pages, 5 figures; Supplementary: 3 pages, 2 figures