Superdiffusive transport and energy localization in disordered granular crystals
Abstract
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 demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.
- Authors:
-
- Univ. of Oxford, Oxford (United Kingdom)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1234648
- Alternate Identifier(s):
- OSTI ID: 1237989
- Report Number(s):
- LA-UR-14-28911
Journal ID: ISSN 1539-3755; PLEEE8; TRN: US1600511
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
- Additional Journal Information:
- Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics; Journal ID: ISSN 1539-3755
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING
Citation Formats
Martinez, Alejandro J., Kevrekidis, Panagiotis G., and Porter, Mason A. Superdiffusive transport and energy localization in disordered granular crystals. United States: N. p., 2016.
Web. doi:10.1103/PhysRevE.93.022902.
Martinez, Alejandro J., Kevrekidis, Panagiotis G., & Porter, Mason A. Superdiffusive transport and energy localization in disordered granular crystals. United States. https://doi.org/10.1103/PhysRevE.93.022902
Martinez, Alejandro J., Kevrekidis, Panagiotis G., and Porter, Mason A. 2016.
"Superdiffusive transport and energy localization in disordered granular crystals". United States. https://doi.org/10.1103/PhysRevE.93.022902. https://www.osti.gov/servlets/purl/1234648.
@article{osti_1234648,
title = {Superdiffusive transport and energy localization in disordered granular crystals},
author = {Martinez, Alejandro J. and Kevrekidis, Panagiotis G. and Porter, Mason A.},
abstractNote = {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 demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.},
doi = {10.1103/PhysRevE.93.022902},
url = {https://www.osti.gov/biblio/1234648},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
issn = {1539-3755},
number = ,
volume = ,
place = {United States},
year = {Fri Feb 12 00:00:00 EST 2016},
month = {Fri Feb 12 00:00:00 EST 2016}
}
Web of Science
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