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Nonlinear waves in disordered diatomic granular chains.

Laurent Ponson1, Nicholas Boechler, Yi Ming Lai

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Summary
This summary is machine-generated.

Highly nonlinear waves in disordered diatomic granular chains exhibit two propagation regimes. Low disorder shows exponential decay, while high disorder leads to power-law decay, revealing a critical transition point.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Disordered granular chains with diatomic units exhibit complex wave propagation phenomena.
  • Hertzian contact interactions govern the behavior of these granular systems.
  • Statistical mechanics provides a framework for modeling granular chains as spin chains.

Purpose of the Study:

  • To investigate the propagation and scattering of highly nonlinear waves in disordered diatomic granular chains.
  • To identify and characterize different wave propagation regimes based on disorder levels.
  • To develop a theoretical interpretation for the transition between these regimes.

Main Methods:

  • Experimental investigation of wave propagation.
  • Numerical simulations of nonlinear wave dynamics.
  • Application of statistical mechanics principles to model granular units as spins.

Main Results:

  • Two distinct wave propagation mechanisms were observed: exponential decay in low-disorder chains and power-law decay beyond a critical disorder level.
  • Wave transmission becomes insensitive to disorder in the high-disorder regime.
  • The spatiotemporal structure of the wave was characterized for both propagation regimes.

Conclusions:

  • A critical transition in wave propagation behavior occurs with increasing disorder in diatomic granular chains.
  • An elastic spin chain model effectively represents heterogeneities influencing highly nonlinear wave propagation.
  • This study offers insights into the role of disorder in wave dynamics within complex material systems.