Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model

Ramaz Khomeriki, Stefano Lepri, and Stefano Ruffo
Phys. Rev. E 70, 066626 – Published 28 December 2004

Abstract

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other. The supratransmission regime occurs for driving frequencies above the upper band edge and originates from direct moving discrete breather creation. We derive approximate analytical estimates of the supratransmission threshold, which are in excellent agreement with numerics. When analyzing the long-time behavior, we discover that, below the supratransmission threshold, a conducting stationary state coexists with the insulating one. We explain the bistable nature of the energy flux in terms of the excitation of quasiharmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
1 More
  • Received 6 July 2004

DOI:https://doi.org/10.1103/PhysRevE.70.066626

©2004 American Physical Society

Authors & Affiliations

Ramaz Khomeriki1,*, Stefano Lepri2,†, and Stefano Ruffo3,4,2,‡

  • 1Tbilisi State University, 3 Chavchavadze Avenue, Tbilisi 380028, Republic of Georgia
  • 2Istituto Nazionale per la Fisica della Materia, Unità di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
  • 3Dipartimento di Energetica “S. Stecco” and CSDC, Universitá di Firenze, via S. Marta 3, I-50139 Firenze, Italy
  • 4Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy

  • *Electronic address: khomeriki@hotmail.com
  • Electronic address: stefano.lepri@unifi.it
  • Electronic address: ruffo@avanzi.de.unifi.it

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 70, Iss. 6 — December 2004

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×