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Title: Superdiffusive transport and energy localization in disordered granular crystals

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:
 [1] ;  [2] ;  [1]
  1. Univ. of Oxford, Oxford (United Kingdom)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)
Publication Date:
Report Number(s):
LA-UR-14-28911
Journal ID: ISSN 1539-3755; PLEEE8; TRN: US1600511
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)
Additional Journal Information:
Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print); Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1234648
Alternate Identifier(s):
OSTI ID: 1237989

Martinez, Alejandro J., Kevrekidis, Panagiotis G., and Porter, Mason A.. Superdiffusive transport and energy localization in disordered granular crystals. United States: N. p., 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. doi: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. doi: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},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {2}
}