---
_id: '7775'
abstract:
- lang: eng
  text: As a function of packing fraction at zero temperature and applied stress,
    an amorphous packing of spheres exhibits a jamming transition where the system
    is sensitive to boundary conditions even in the thermodynamic limit. Upon further
    compression, the system should become insensitive to boundary conditions provided
    it is sufficiently large. Here we explore the linear response to a large class
    of boundary perturbations in 2 and 3 dimensions. We consider each finite packing
    with periodic-boundary conditions as the basis of an infinite square or cubic
    lattice and study properties of vibrational modes at arbitrary wave vector. We
    find that the stability of such modes can be understood in terms of a competition
    between plane waves and the anomalous vibrational modes associated with the jamming
    transition; infinitesimal boundary perturbations become irrelevant for systems
    that are larger than a length scale that characterizes the transverse excitations.
    This previously identified length diverges at the jamming transition.
article_number: '11000'
article_processing_charge: No
article_type: original
author:
- first_name: Samuel S.
  full_name: Schoenholz, Samuel S.
  last_name: Schoenholz
- first_name: Carl Peter
  full_name: Goodrich, Carl Peter
  id: EB352CD2-F68A-11E9-89C5-A432E6697425
  last_name: Goodrich
  orcid: 0000-0002-1307-5074
- first_name: Oleg
  full_name: Kogan, Oleg
  last_name: Kogan
- first_name: Andrea J.
  full_name: Liu, Andrea J.
  last_name: Liu
- first_name: Sidney R.
  full_name: Nagel, Sidney R.
  last_name: Nagel
citation:
  ama: 'Schoenholz SS, Goodrich CP, Kogan O, Liu AJ, Nagel SR. Stability of jammed
    packings II: The transverse length scale. <i>Soft Matter</i>. 2013;9(46). doi:<a
    href="https://doi.org/10.1039/c3sm51096d">10.1039/c3sm51096d</a>'
  apa: 'Schoenholz, S. S., Goodrich, C. P., Kogan, O., Liu, A. J., &#38; Nagel, S.
    R. (2013). Stability of jammed packings II: The transverse length scale. <i>Soft
    Matter</i>. Royal Society of Chemistry. <a href="https://doi.org/10.1039/c3sm51096d">https://doi.org/10.1039/c3sm51096d</a>'
  chicago: 'Schoenholz, Samuel S., Carl Peter Goodrich, Oleg Kogan, Andrea J. Liu,
    and Sidney R. Nagel. “Stability of Jammed Packings II: The Transverse Length Scale.”
    <i>Soft Matter</i>. Royal Society of Chemistry, 2013. <a href="https://doi.org/10.1039/c3sm51096d">https://doi.org/10.1039/c3sm51096d</a>.'
  ieee: 'S. S. Schoenholz, C. P. Goodrich, O. Kogan, A. J. Liu, and S. R. Nagel, “Stability
    of jammed packings II: The transverse length scale,” <i>Soft Matter</i>, vol.
    9, no. 46. Royal Society of Chemistry, 2013.'
  ista: 'Schoenholz SS, Goodrich CP, Kogan O, Liu AJ, Nagel SR. 2013. Stability of
    jammed packings II: The transverse length scale. Soft Matter. 9(46), 11000.'
  mla: 'Schoenholz, Samuel S., et al. “Stability of Jammed Packings II: The Transverse
    Length Scale.” <i>Soft Matter</i>, vol. 9, no. 46, 11000, Royal Society of Chemistry,
    2013, doi:<a href="https://doi.org/10.1039/c3sm51096d">10.1039/c3sm51096d</a>.'
  short: S.S. Schoenholz, C.P. Goodrich, O. Kogan, A.J. Liu, S.R. Nagel, Soft Matter
    9 (2013).
date_created: 2020-04-30T11:43:58Z
date_published: 2013-10-08T00:00:00Z
date_updated: 2021-01-12T08:15:27Z
day: '08'
doi: 10.1039/c3sm51096d
extern: '1'
intvolume: '         9'
issue: '46'
language:
- iso: eng
month: '10'
oa_version: None
publication: Soft Matter
publication_identifier:
  issn:
  - 1744-683X
  - 1744-6848
publication_status: published
publisher: Royal Society of Chemistry
quality_controlled: '1'
status: public
title: 'Stability of jammed packings II: The transverse length scale'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2013'
...