Article
Scattering of Waves by Impurities in Precompressed Granular Chains
Physical Review E
(2016)
Abstract
We study scattering of waves by impurities in strongly precompressed granular chains. We ex-
plore the linear scattering of plane waves and identify a closed-form expression for the re
ection
and transmission coecients for the scattering of the waves from both a single impurity and a dou-
ble impurity. For single-impurity chains, we show that, within the transmission band of the host
granular chain, high-frequency waves are strongly attenuated (such that the transmission coecient
vanishes as the wavenumber k ! ), whereas low-frequency waves are well-transmitted through
the impurity. For double-impurity chains, we identify a resonance | enabling full transmission at a
particular frequency | in a manner that is analogous to the Ramsauer{Townsend (RT) resonance
from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance
to any value in the pass band of the host chain. We corroborate our theoretical predictions both
numerically and experimentally, and we directly observe complete transmission for frequencies close
to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence
of re
ectionless modes even in granular chains (including disordered ones) with multiple double
impurities.
Keywords
- Pattern Formation and Solitons,
- Materials Science,
- Dynamical Systems
Disciplines
Publication Date
2016
Citation Information
Panos Kevrekidis, Alejandro J. Martinez, Hiromi Yasuda, Eunho Kim, et al.. "Scattering of Waves by Impurities in Precompressed Granular Chains" Physical Review E Vol. 93 (2016) Available at: http://works.bepress.com/panos_kevrekidis/413/