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Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences.
Salvatore D Pace1, David K Campbell1
1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Chaos (Woodbury, N.Y.)
|March 3, 2019
Summary
We numerically investigate higher-order recurrences (HoRs) in Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Singularities in HoR periods are observed, with differing breakdown mechanisms in alpha and beta FPUT models.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Computational physics
Background:
- The Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is a fundamental model for studying nonlinear phenomena in discrete systems.
- Higher-order recurrences (HoRs), including super-recurrences, are complex dynamical behaviors observed in the FPUT lattice.
- Previous work by Tuck and Menzel pioneered the study of super-recurrences.
Purpose of the Study:
- To numerically investigate the existence and stability of higher-order recurrences (HoRs) in both alpha and beta FPUT lattices.
- To extend the understanding of super-recurrences beyond the initial work by Tuck and Menzel.
- To analyze the behavior of HoRs for initial conditions in the fundamental normal mode.
Main Methods:
- Numerical simulations of the alpha and beta FPUT lattices.
- Investigation of initial conditions set to the fundamental normal mode.
- Analysis of apparent singularities in HoR periods and their dependence on parameters.
Main Results:
- Observed and studied apparent singularities in the periods of HoRs, potentially linked to nonlinear resonances.
- Demonstrated sensitive dependence of these singularities on initial energy and nonlinear parameters.
- Identified distinct breakdown mechanisms for super-recurrences in alpha and beta FPUT lattices as energy increases.
Conclusions:
- Super-recurrence breakdown in the beta-FPUT lattice is tied to the destruction of the metastable state and relaxation to equilibrium.
- In the alpha-FPUT lattice, super-recurrences break down while the system remains metastable and far from equilibrium.
- The study provides insights into the generality of these findings across different lattice sizes.
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