Nonlinear waves in disordered diatomic granular chains.
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granul...
| Main Authors: | , , , , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1797085993098018816 |
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| author | Ponson, L Boechler, N Lai, Y Porter, M Kevrekidis, P Daraio, C |
| author_facet | Ponson, L Boechler, N Lai, Y Porter, M Kevrekidis, P Daraio, C |
| author_sort | Ponson, L |
| collection | OXFORD |
| description | We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves. |
| first_indexed | 2024-03-07T02:15:41Z |
| format | Journal article |
| id | oxford-uuid:a229babb-801b-4e60-8c6b-d652dd86b0ae |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:15:41Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:a229babb-801b-4e60-8c6b-d652dd86b0ae2022-03-27T02:18:13ZNonlinear waves in disordered diatomic granular chains.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a229babb-801b-4e60-8c6b-d652dd86b0aeEnglishSymplectic Elements at Oxford2010Ponson, LBoechler, NLai, YPorter, MKevrekidis, PDaraio, CWe investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin," so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: in low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves. |
| spellingShingle | Ponson, L Boechler, N Lai, Y Porter, M Kevrekidis, P Daraio, C Nonlinear waves in disordered diatomic granular chains. |
| title | Nonlinear waves in disordered diatomic granular chains. |
| title_full | Nonlinear waves in disordered diatomic granular chains. |
| title_fullStr | Nonlinear waves in disordered diatomic granular chains. |
| title_full_unstemmed | Nonlinear waves in disordered diatomic granular chains. |
| title_short | Nonlinear waves in disordered diatomic granular chains. |
| title_sort | nonlinear waves in disordered diatomic granular chains |
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