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Title: Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

Abstract

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.

Authors:
 [1];  [2];  [3];  [3]
  1. ETH-Zurich, Zurich (Switzerland). Dept.of Mechanical and Process Engineering; Bowdoin College, Brunswick, ME (United States)
  2. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Univ. of Colorado, Boulder, CO (United States). Dept. Applied Mathematics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1259966
Alternate Identifier(s):
OSTI ID: 1235959
Report Number(s):
LA-UR-15-25013
Journal ID: ISSN 2470-0045; PLEEE8
Grant/Contract Number:  
DMS-1310200; FA9550-12-1- 0332; AC52-06NA25396; ESC-A 06-14; BSF- 2010239
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 93; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING

Citation Formats

Chong, C., Kevrekidis, P. G., Ablowitz, M. J., and Ma, Yi-Ping. Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices. United States: N. p., 2016. Web. doi:10.1103/PhysRevE.93.012909.
Chong, C., Kevrekidis, P. G., Ablowitz, M. J., & Ma, Yi-Ping. Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices. United States. doi:10.1103/PhysRevE.93.012909.
Chong, C., Kevrekidis, P. G., Ablowitz, M. J., and Ma, Yi-Ping. Mon . "Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices". United States. doi:10.1103/PhysRevE.93.012909. https://www.osti.gov/servlets/purl/1259966.
@article{osti_1259966,
title = {Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices},
author = {Chong, C. and Kevrekidis, P. G. and Ablowitz, M. J. and Ma, Yi-Ping},
abstractNote = {We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. For weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.},
doi = {10.1103/PhysRevE.93.012909},
journal = {Physical Review E},
number = 1,
volume = 93,
place = {United States},
year = {2016},
month = {1}
}

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    Works referencing / citing this record:

    Two interactional solitary waves propagating in two-dimensional hexagonal packing granular system
    journal, July 2018