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Edge mode amplification in disordered elastic networks.

Le Yan1, Jean-Philippe Bouchaud, Matthieu Wyart

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Summary
This summary is machine-generated.

Disordered isostatic materials amplify elastic signals like levers, with amplification scaling with system size. This contrasts with more connected materials where amplification is limited to surfaces.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Mechanical Engineering

Background:

  • Elastic wave propagation in crystalline lattices can be amplified by topologically-protected edge modes.
  • The role of these edge modes in disordered systems is not well understood.
  • Isostatic materials possess a minimal number of constraints, influencing their mechanical properties.

Purpose of the Study:

  • To develop a theoretical framework for understanding edge modes in disordered isostatic materials.
  • To compute the distribution of Lyapunov exponents characterizing edge mode penetration into the bulk.
  • To compare the amplification properties of disordered isostatic materials with more connected systems.

Main Methods:

  • Development of a theoretical model for edge modes in disordered isostatic lattices.
  • Computation of the Lyapunov exponent distribution using techniques from free random matrix theory.
  • Numerical simulations to validate theoretical predictions.

Main Results:

  • Disordered isostatic materials exhibit generic lever-like amplification of elastic signals, scaling as L^L with system size L.
  • More connected materials show amplification only near free surfaces.
  • The theory shows good agreement with numerical results.

Conclusions:

  • Disordered isostatic materials possess unique properties for elastic signal amplification.
  • The findings provide insights into the behavior of mechanical systems in disordered environments.
  • The study draws an analogy between elastic transport and electronic transport in disordered conductors.