| Issue |
EPL
Volume 83, Number 4, August 2008
|
|
|---|---|---|
| Article Number | 44001 | |
| Number of page(s) | 6 | |
| Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/83/44001 | |
| Published online | 31 July 2008 | |
Localization behavior of vibrational modes in granular packings
1
Instituut - Lorentz, Universiteit Leiden - Postbus 9506, 2300 RA Leiden, The Netherlands
2
Department of Physics, Harvard University - Cambridge, MA 02138, USA
Corresponding author: zorana@lorentz.leidenuniv.nl
Received:
21
February
2008
Accepted:
25
June
2008
We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization length 
is much less than the linear size L and in the regime 
when modes are extended throughout our finite system. Our very lowest frequency modes show ”quasi-localized” resonances away from the jamming point; the spatial extent of these regions increases as the jamming point is approached, as expected theoretically. Throughout the remaining frequency range, our data show no signature of the nearness of the jamming point and collapse well when properly rescaled with the system size. Using Random Matrix Theory, we derive the scaling relation 
for the regime 
in d dimensions.
PACS: 45.70.-n – Granular systems / 63.50.-x – Vibrational states in disordered systems / 71.23.An – Theories and models; localized states
© EPLA, 2008
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