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Pulse propagation in chains with nonlinear interactions.

Alexandre Rosas1, Katja Lindenberg

  • 1Department of Chemistry and Biochemistry, and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
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Common pulse dispersion measures can be misleading in nonlinear arrays. Our study reveals these measures may reflect multiple narrow pulses, not a single pulse

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Pulse propagation in nonlinear arrays is crucial for understanding energy transfer with minimal dispersion.
  • Anharmonic systems present unique challenges in accurately characterizing pulse behavior.

Purpose of the Study:

  • To investigate the accuracy of common dispersion measures in nonlinear arrays.
  • To analyze pulse propagation in strongly anharmonic systems.
  • To develop analytic methods for predicting energy distribution and velocity in leading pulses.

Main Methods:

  • Analysis of pulse propagation dynamics in nonlinear arrays.
  • Development of analytic estimates for energy fraction in leading pulses.
  • Derivation of analytic predictions for leading pulse velocity.

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Main Results:

  • Common dispersion measures can be misleading in strongly anharmonic systems.
  • Dispersion may manifest as a succession of narrow pulses at decreasing velocities.
  • Analytic estimates quantify the energy fraction carried by leading pulses.
  • Analytic predictions for leading pulse velocity in Fermi-Pasta-Ulam beta chains were obtained.

Conclusions:

  • Standard dispersion measures require careful interpretation in nonlinear, anharmonic systems.
  • The study provides a more accurate framework for understanding pulse behavior and energy transfer.
  • Findings are applicable to theoretical models like the Fermi-Pasta-Ulam beta chain.