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Chaos and Anderson-like localization in polydisperse granular chains
V Achilleos1, G Theocharis1, Ch Skokos2
1Laboratoire d'Acoustique de l'Université du Maine, UMR CNRS 6613 Av. O. Messiaen, F-72085 LE MANS Cedex 9, France.
Physical Review. E
|May 16, 2018
Summary
Granular chains exhibit chaotic dynamics. Specific excitations can lead to long-lasting energy localization, even with nonlinearities, but strong nonlinearities cause energy equipartition.
Area of Science:
- Physics
- Nonlinear Dynamics
- Granular Materials Science
Background:
- Investigating energy dynamics in granular chains is crucial for understanding wave propagation and energy transport.
- Polydisperse granular chains present complex behaviors due to variations in particle size and properties.
Purpose of the Study:
- To determine if nonlinearities and chaotic dynamics disrupt energy localization in granular chains.
- To identify conditions for energy localization and equipartition in finite granular chains.
Main Methods:
- Analysis of spatiospectral properties of small vibrations.
- Numerical simulations of granular chain dynamics under various nonlinear conditions.
Main Results:
- Identified specific single-particle displacements causing energy localization.
- Observed chaotic energy spreading for moderate nonlinearities.
- Found long-lasting chaotic energy localization for particular excitations with nonsmooth nonlinearities.
- Demonstrated energy equipartition and equilibrium chaotic state for strong nonlinearities.
Conclusions:
- Granular nonlinearities can lead to chaotic dynamics, but do not always destroy energy localization.
- Nonsmooth nonlinearities play a key role in sustaining chaotic energy localization.
- Strong nonlinearities drive the system towards energy equipartition, irrespective of initial excitation.
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