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

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 analysing 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 quasi-harmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.

8 pages, 9 figures. Phys. Rev. E (accepted)

References in corpus (9)

• Thermal conduction in classical low-dimensional lattices
• Energy transmission in the forbidden bandgap of a nonlinear chain
• Nonlinear Supratransmission
• Nonlinear Band Gap Transmission in Optical Waveguide Arrays
• Nonlinear supratransmission as a fundamental instability
• Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
• Pattern formation and localization in the forced-damped FPU lattice
• Interaction of a Kink-Soliton with a Breather in a Fermi-Pasta-Ulam Chain
• Nonlinear absorption in discrete systems

Cited by in corpus (26)

• Phononic Frequency Combs via Nonlinear Resonances
• Metastable Modular Metastructures for On-Demand Reconfiguration of Band Structures and Non-Reciprocal Wave Propagation
• Energy transfer in strained graphene assisted by discrete breathers excited by external ac driving
• On the propagation of binary signals in damped mechanical systems of oscillators
• An application of nonlinear supratransmission to the propagation of binary signals in weakly damped, mechanical systems of coupled oscillators
• On the wave propagation analysis and supratransmission prediction of a metastable modular metastructure for non-reciprocal energy transmission
• Boundary driven waveguide arrays: Supratransmission and saddle-node bifurcation
• Transmission thresholds in time-periodically driven nonlinear disordered systems
• Discrete breathers assist energy transfer to ac driven nonlinear chains
• Hysteresis Loops and Multi-stability: From Periodic Orbits to Chaotic Dynamics (and Back) in Diatomic Granular Crystals
• Generation of travelling sine-Gordon breathers in noisy long Josephson junctions
• All-phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in Anharmonic Oscillator Ladder
• Supratransmission-induced travelling breathers in long Josephson junctions
• A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Modulation instability gain and localized waves by modified Frenkel-Kontorova model of higher order nonlinearity
• Glassiness and Lack of Equipartition in Random Lasers: the common roots of Ergodicity Breaking in Disordered and Non-linear Systems
• Interaction of phonons with discrete breather in strained graphene
• On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system
• Stochastic Resonance in the Fermi-Pasta-Ulam Chain
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• All-phononic Amplification in Coupled Cantilever Arrays based on Gap Soliton Dynamics
• Sine-Gordon breathers generation in driven long Josephson junctions
• Thermally driven classical Heisenberg model in one dimension with a local time-varying field
• Pearl supratransmission in a boundary-driven two-dimensional nonlinear Schrödinger equation with a hole