Energy spreading, equipartition and chaos in lattices with non-central forces

TL;DR

This study investigates how nonlinearities and disorder affect energy spreading, localization, and chaos in a one-dimensional lattice model relevant to bending waves, revealing distinct behaviors depending on the type of nonlinearity.

Contribution

It introduces a nonlinear lattice model with unique dispersion properties and analyzes how cubic and quartic nonlinearities influence energy delocalization, equipartition, and chaos.

Findings

Cubic nonlinearity leads to energy equipartition and delocalization beyond a certain energy threshold.

Quartic nonlinearity maintains localization and prevents equipartition at studied energies.

Chaos appears at high energies for all nonlinearities, with energy spreading linked to cubic nonlinearity.

Abstract

We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quartic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quartic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.