The equilibrium phase in heterogeneous Hertzian chains

Abstract

We examine the long-term behaviour of non-integrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. We previously showed that in homogeneous configurations of such systems, energy is equipartitioned at sufficiently long times, thus these systems ultimately reach thermal equilibrium. Here we expand on our previous work to show that heterogeneous configurations of grains also reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. We investigate the transition to equilibrium in detail and introduce correlation functions that indicate the onset of the transition.

arXiv comment21 pages, 5 figures

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• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves
• Nanoptera in nonlinear woodpile chains with zero precompression
• Nanoptera in weakly nonlinear woodpile and diatomic granular chains
• Wave-packet spreading in disordered soft architected structures