Variability in Fermi--Pasta--Ulam--Tsingou Arrays Prevents Recurrences

TL;DR

This paper investigates how inherent parameter variations in physical FPUT arrays disrupt the energy recurrence phenomenon observed in idealized models, highlighting limitations for real-world applications.

Contribution

It demonstrates through numerical simulations that tolerances in nonlinear oscillator arrays significantly impair recurrence, emphasizing the importance of heterogeneity considerations in physical systems.

Findings

Tolerances degrade recurrence in FPUT arrays

Heterogeneity can lead to complete loss of recurrence

Results suggest limitations for physical implementations

Abstract

In 1955, Fermi, Pasta, Ulam, and Tsingou reported recurrence over time of energy between modes in a one-dimensional array of nonlinear oscillators. Subsequently, there have been myriad numerical experiments using homogenous FPUT arrays, which consist of chains of ideal, nonlinearly-coupled oscillators. However, inherent variations --- e.g., due to manufacturing tolerance --- introduce heterogeneity into the parameters of any physical system. We demonstrate that such tolerances degrade the observance of recurrence, often leading to complete loss in moderately sized arrays. We numerically simulate heterogeneous FPUT systems to investigate the effects of tolerances on dynamics. Our results illustrate that tolerances in real nonlinear oscillator arrays may limit the applicability of results from numerical experiments on them to physical systems, unless appropriate heterogeneities are taken into account.