The Anti-FPU Problem

Abstract

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.

References in corpus (17)

• Discrete Breathers
• Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
• Localization and Equipartition of Energy in the beta-FPU Chain : Chaotic Breathers
• Riemannian theory of Hamiltonian chaos and Lyapunov exponents
• Symmetry and resonance in periodic FPU chains
• On modulational instability and energy localization in anharmonic lattices at finite energy density
• Bushes of vibrational modes for Fermi-Pasta-Ulam chains
• Finite times to equipartition in the thermodynamic limit
• Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization
• Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice
• Fano resonances with discrete breathers
• Energy Relaxation in Nonlinear One-Dimensional Lattices
• Modulational Estimate for Fermi-Pasta-Ulam Chain Lyapunov Exponents
• Wave scattering by discrete breathers
• Cooling nonlinear lattices toward localisation
• Slow energy relaxation and localization in 1D lattices
• Numerical analysis of the one-mode solutions in the Fermi-Pasta-Ulam system

Cited by in corpus (17)

• Discrete Breathers in One-Dimensional Diatomic Granular Crystals
• Limiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Stability of low-dimensional bushes of vibrational modes in the Fermi-Pasta-Ulam chains
• Energy transfer in strained graphene assisted by discrete breathers excited by external ac driving
• Long-range energy transfer in proteins
• Stability analysis of dynamical regimes in nonlinear systems with discrete symmetries
• Wave Turbulence and thermalization in one-dimensional chains
• Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscilliatory chain
• Discrete Symmetry and Stability in Hamiltonian Dynamics
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Stability of Nonlinear Normal Modes in the FPU-$\beta$ Chain in the Thermodynamic Limit
• Stochastic Resonance in the Fermi-Pasta-Ulam Chain
• The $\beta$ Fermi-Pasta-Ulam-Tsingou Recurrence Problem
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices
• Limiting Phase Trajectories: a new paradigm for the study of highly non-stationary processes in Nonlinear Physics