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 $\kappa$, 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 $\kappa \to 0$. 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

References in corpus (8)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Fractal free energy landscapes in structural glasses
• Combinatorial Design of Textured Mechanical Metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Inhomogeneous elastic response of silica glass
• Architecture and Co-Evolution of Allosteric Materials
• Evidence for marginal stability in emulsions
• Phonons and elasticity in critically coordinated lattices

Cited by in corpus (5)

• Architecture and Co-Evolution of Allosteric Materials
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Principles for optimal cooperativity in allosteric materials
• Stress Response of Granular Systems
• Controlling the Deformation of Metamaterials: Corner Modes via Topology