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

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.