Superdiffusive transport and energy localization in disordered granular crystals
We study the spreading of initially localized excitations in onedimensional 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 (Andersonlike) 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 longtime 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 Andersonlike disorder.
 Authors:

^{[1]};
^{[2]};
^{[1]}
 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:
 Report Number(s):
 LAUR1428911
Journal ID: ISSN 15393755; PLEEE8; TRN: US1600511
 Grant/Contract Number:
 AC5206NA25396
 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 15393755
 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 onedimensional 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 (Andersonlike) 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 longtime 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 Andersonlike 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}
}