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Discrete breathers in one-dimensional diatomic granular crystals
N Boechler1, G Theocharis, S Job
1Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125, USA.
Physical Review Letters
|September 28, 2010
Summary
Modulational instability generates localized breathing modes in diatomic granular crystals. These discrete breathers, observed experimentally, match theoretical predictions for wave propagation in granular materials.
Area of Science:
- Physics
- Nonlinear Dynamics
- Materials Science
Background:
- Granular crystals exhibit unique wave propagation properties due to inter-particle interactions.
- Modulational instability is a key phenomenon in nonlinear systems, leading to wave localization.
- Discrete breathers are localized, time-periodic solutions in nonlinear discrete systems.
Purpose of the Study:
- To experimentally observe and theoretically characterize modulational instability and discrete breathers in a one-dimensional diatomic granular crystal.
- To investigate the formation and properties of these nonlinear phenomena.
- To validate theoretical models with experimental observations.
Main Methods:
- Experimental characterization of the linear spectrum of the granular crystal.
- Theoretical and numerical illustration of modulational instability at the optical band edge.
- Computation of breather solutions within the linear spectral gap.
- Experimental observation and quantitative analysis of generated localized breathing modes.
Main Results:
- Experimental confirmation of modulational instability in the granular crystal.
- Dynamical formation of long-lived discrete breathers.
- Quantitative agreement between experimental observations and numerical/theoretical predictions.
- Characterization of the linear spectrum and spectral gap.
Conclusions:
- Modulational instability is a viable mechanism for generating discrete breathers in diatomic granular crystals.
- The study provides experimental evidence for nonlinear wave phenomena in granular media.
- The findings contribute to the understanding of nonlinear dynamics in discrete systems and materials.
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