Explorations for alternating FPU-chains with large mass

TL;DR

This paper investigates the interactions between high- and low-frequency modes in periodic alpha-FPU chains with alternating large masses, especially focusing on chains with a prime number of particle pairs, using symmetry reduction and computational tools.

Contribution

It introduces a method to analyze mode interactions in large alternating mass FPU chains by identifying symmetric invariant manifolds, enabling explicit analysis up to 100 particles and generalization to larger chains.

Findings

Explicit interaction demonstrated for chains up to 100 particles

Symmetry-based reduction significantly simplifies the analysis

Strong evidence for interactions in arbitrarily large chains

Abstract

We show interaction between high- and low-frequency modes in periodic $\alpha$-FPU chains with alternating large masses. The treatment discusses the difficult case where the number of particles $N=2p$ involves $p$ prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a Mathematica programme focused on these systems. We could show explicitly interaction for systems up to 100 particles with in addition strong arguments for interactions in arbitrary large chains.