• Corpus ID: 231925032

# Nanoptera in weakly nonlinear woodpile and diatomic granular chains

@inproceedings{Deng2021NanopteraIW,
title={Nanoptera in weakly nonlinear woodpile and diatomic granular chains},
author={Guo Deng and Christopher J. Lustri and Mason A. Porter},
year={2021}
}
• Published 15 February 2021
• Mathematics
We study “nanoptera”, which are non-localized traveling waves with exponentially small but non-decaying oscillations, in two singularly-perturbed Hertzian chains with precompression. These two systems are woodpile chains (which we model as systems of Hertzian particles and springs) and diatomic Hertzian chains with alternating masses. We demonstrate that nanoptera arise from Stokes phenomena and appear as special curves, which are called “Stokes curves”, are crossed in the complex plane. We use…
1 Citations

## References

SHOWING 1-10 OF 103 REFERENCES

### Metastability of solitary waves in diatomic FPUT lattices$^\dagger$

• Physics, Mathematics
Mathematics in Engineering
• 2019
It is known that long waves in spatially periodic polymer Fermi-Pasta-Ulam-Tsingou lattices are well-approximated for long, but not infinite, times by suitably scaled solutions of Korteweg-de Vries

### Nonlinear waves in disordered diatomic granular chains.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2010
The investigation of the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic units of spheres that interact via Hertzian contact suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highlyNonlinear waves.

### Quasiperiodic granular chains and Hofstadter butterflies

• Physics
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
• 2018
Three different set-ups, inspired by the Aubry–André model, of quasiperiodic chains are proposed and it is demonstrated that the fractal dimension decreases as one approaches the localization transition (when it exists), and also that there exist regimes of ballistic, superdiffusive, diffusive and subdiffusive transport.

### Strongly nonlinear waves in locally resonant granular chains

• Mathematics
• 2016
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the

### New family of solitary waves in granular dimer chains with no precompression.

• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2011
A new family of solitary waves in general one-dimensional dimer chains with elastic interactions between beads obeying a strongly nonlinear Hertzian force law is reported, which indicates that under certain conditions nonlinear antiresonances can increase the speed of disturbance transmission in periodic granular media.

### Nanoptera in a Period2 Toda Chain

• Mathematics
• 2018
We study asymptotic solutions to a singularly perturbed, period-2 Toda lattice and use exponential asymptotics to examine “nanoptera,” which are nonlocal solitary waves with constant-amplitude,

### Nonlinear Resonances Leading to Strong Pulse Attenuation in Granular Dimer Chains

• Physics
J. Nonlinear Sci.
• 2013
The connotation of “resonance” is used to describe this dynamical phenomenon resulting in maximum amplification of the amplitudes of radiated waves that emanate from the propagating pulse, leading to drastic attenuation of traveling pulses due to radiation of traveling waves to the far field.

### Superdiffusive transport and energy localization in disordered granular crystals.

• Physics
Physical review. E
• 2016
We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we