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Edge Mode Amplification in Disordered Elastic Networks

Abstract

Understanding how mechanical systems can be designed to transport efficiently elastic information is important in a variety of fields, including in material science and biology. Recently, it was discovered that certain crystalline lattices present ``topologically-protected'' edge modes that can amplify elastic signals. Several observations suggest that edge modes are important in disordered systems as well, an effect not well understood presently. Here we build a theory of edge modes in disordered isostatic materials and compute the distribution $g(\kappa)$ of Lyapunov exponents $\kappa$ characterizing how modes penetrate in the bulk and find good agreement with numerical results. We show that disordered isostatic materials generically act as levers with amplification of order $L^L$ where $L$ is the system size, whereas more connected materials amplify signals only close to free surfaces. Our approach, which is based on recent results in ``free'' random matrix theory, makes an analogy with electronic transport in a disordered conductor.

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Publication details

The article was received on 07 Mar 2017, accepted on 24 Jul 2017 and first published on 28 Jul 2017


Article type: Paper
DOI: 10.1039/C7SM00475C
Citation: Soft Matter, 2017, Accepted Manuscript
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    Edge Mode Amplification in Disordered Elastic Networks

    L. Yan, J. Bouchaud and M. Wyart, Soft Matter, 2017, Accepted Manuscript , DOI: 10.1039/C7SM00475C

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