Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition

Abstract

We investigate the dynamics of highly polydispersed finite granular chains. From the spatio-spectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities lead to chaotic dynamics and if so, does chaos destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, although the overall system behaves chaotically, it can exhibit long lasting energy localization for particular single particle excitations. On the other hand, for sufficiently strong nonlinearities, connected with contact breaking, the granular chain reaches energy equipartition and an equilibrium chaotic state, independent of the initial position excitation.

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Cited by in corpus (10)

• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Direct measurement of superdiffusive and subdiffusive energy transport in disordered granular chains
• Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices
• Quantifying chaos using Lagrangian descriptors
• Chaos and Anderson Localisation in Disordered Classical Chains: Hertzian vs FPUT models
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Scaling of energy spreading in a disordered Ding-Dong lattice
• Elastic Wannier-Stark Ladders and Bloch Oscillations in 1D Granular Crystals
• Chaotic behaviour of disordered nonlinear lattices
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems