The Fermi-Pasta-Ulam problem: scaling laws vs. initial conditions

DOI10.1007/s10955-008-9660-6zbMath1375.82058OpenAlexW1983131770MaRDI QIDQ833350

Roberto Livi, Antonio Ponno, Giancarlo Benettin

Publication date: 12 August 2009

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-008-9660-6

zbMATH Keywords

scaling lawsenergy transferFermi-Pasta-Ulam problem

Mathematics Subject Classification ID

Foundations of time-dependent statistical mechanics (82C03) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

Related Items (21)

Variable energy flux in turbulence ⋮ Packets of resonant modes in the Fermi-Pasta-Ulam system ⋮ Thermalization without chaos in harmonic systems ⋮ Understanding the FPU state in FPU-like models ⋮ Wave turbulence and thermalization in one-dimensional chains ⋮ On the role of the integrable Toda model in one-dimensional molecular dynamics ⋮ Kolmogorov turbulence, Anderson localization and KAM integrability ⋮ Effective stochastic model for chaos in the Fermi-Pasta-Ulam-Tsingou chain ⋮ On the numerical integration of FPU-like systems ⋮ Time-scales to equipartition in the Fermi-Pasta-Ulam problem: finite-size effects and thermodynamic limit ⋮ Numerical study on Fermi-Pasta-Ulam-Tsingou problem for 1D shallow-water waves ⋮ Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems ⋮ Chopping time of the FPU \({\alpha }\)-model ⋮ Extensive adiabatic invariants for nonlinear chains ⋮ On the energy distribution in Fermi-Pasta-Ulam lattices ⋮ The Fermi-pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov exponents ⋮ Stages of dynamics in the Fermi-Pasta-Ulam system as probed by the first Toda integral ⋮ Universal route to thermalization in weakly-nonlinear one-dimensional chains ⋮ An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit ⋮ Ergodicity: How Can It Be Broken? ⋮ Korteweg–de Vries and Fermi–Pasta–Ulam–Tsingou: asymptotic integrability of quasi unidirectional waves

Cites Work

• The Fermi-Pasta-Ulam problem: periodic orbits, normal forms and resonance overlap criteria
• On metastability in FPU
• Chaos and the approach to equilibrium in a discrete sine-Gordon equation
• Stages of energy transfer in the FPU model
• Localization of energy in FPU chains
• Exponentially long times to equipartition in the thermodynamic limit
• The Fermi-Pasta-Ulam problem. A status report
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Equipartition of Energy for Nonlinear Systems
• Dynamics of Oscillator Chains
• Resonance, Metastability and Blow up in FPU
• The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data
• Low-energy chaos in the Fermi - Pasta - Ulam problem
• The Fermi–Pasta–Ulam problem: Fifty years of progress
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