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Breath Collection from Children for Disease Biomarker Discovery
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Published on: February 14, 2019

Dark breathers in granular crystals.

C Chong1, P G Kevrekidis, G Theocharis

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-9305, USA. chong@math.umass.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

Researchers studied dark breathers in bead chains, finding large amplitude solutions and novel nonlinear instability. These localized vibrations can be detected experimentally through signal interference.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Wave phenomena

Background:

  • Dark breathers are localized nonlinear waves.
  • Understanding their behavior in discrete systems is crucial.
  • Previous studies often focused on specific models like the Fermi-Pasta-Ulam lattice.

Purpose of the Study:

  • Investigate the existence, stability, and bifurcation of dark breathers.
  • Analyze behavior in a 1D chain of spherical beads under static load.
  • Explore emergent large amplitude solutions and novel instabilities.

Main Methods:

  • Derivation of a defocusing nonlinear Schrödinger equation (NLS).
  • Construction of initial conditions for numerical computations.
  • Analysis of stability and bifurcation structures.

Main Results:

  • Existence of large amplitude dark breather solutions beyond NLS predictions.
  • Observation of a novel nonlinear instability not seen in classical lattices.
  • Demonstration of experimental detectability via actuating bead chain ends and inducing destructive interference.

Conclusions:

  • The study reveals complex dynamics of dark breathers in a granular chain.
  • A new type of nonlinear instability is identified.
  • Experimental detection is feasible, offering insights into nonlinear wave propagation.