Stability of jammed packings II: the transverse length scale

Schoenholz, Samuel S.; Goodrich, Carl P.; Kogan, Oleg; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1039/c3sm51096d

Stability of jammed packings II: the transverse length scale

Journal Article · Tue Oct 08 00:00:00 EDT 2013 · Soft Matter

DOI:https://doi.org/10.1039/c3sm51096d· OSTI ID:1596349

Schoenholz, Samuel S. ^[1]; Goodrich, Carl P. ^[2]; Kogan, Oleg ^[3]; Liu, Andrea J. ^[2]; Nagel, Sidney R. ^[4]

Univ. of Pennsylvania, Philadelphia, PA (United States); The University of Chicago
Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Chicago, IL (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Chicago, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: FG02-03ER46088

OSTI ID:: 1596349

Journal Information:: Soft Matter, Journal Name: Soft Matter Journal Issue: 46 Vol. 9; ISSN SMOABF; ISSN 1744-683X

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

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Aspects of jamming in two-dimensional athermal frictionless systems Reichhardt, C.; Reichhardt, C. J. Olson Soft Matter, Vol. 10, Issue 17 https://doi.org/10.1039/c3sm53154f	journal	January 2014
Breakdown of continuum elasticity in amorphous solids Lerner, Edan; DeGiuli, Eric; Düring, Gustavo Soft Matter, Vol. 10, Issue 28 https://doi.org/10.1039/c4sm00311j	journal	January 2014
Spatial structure of states of self stress in jammed systems Sussman, Daniel M.; Goodrich, Carl P.; Liu, Andrea J. Soft Matter, Vol. 12, Issue 17 https://doi.org/10.1039/c6sm00094k	journal	January 2016
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. Soft Matter, Vol. 12, Issue 28 https://doi.org/10.1039/c6sm00875e	journal	January 2016
Scaling ansatz for the jamming transition Goodrich, Carl P.; Liu, Andrea J.; Sethna, James P. Proceedings of the National Academy of Sciences, Vol. 113, Issue 35 https://doi.org/10.1073/pnas.1601858113	journal	August 2016
Phonons and elasticity in critically coordinated lattices Lubensky, T. C.; Kane, C. L.; Mao, Xiaoming Reports on Progress in Physics, Vol. 78, Issue 7 https://doi.org/10.1088/0034-4885/78/7/073901	journal	June 2015
Unified theory of inertial granular flows and non-Brownian suspensions DeGiuli, E.; Düring, G.; Lerner, E. Physical Review E, Vol. 91, Issue 6 https://doi.org/10.1103/physreve.91.062206	journal	June 2015
Elasticity of frictionless particles near jamming Karimi, Kamran; Maloney, Craig E. Physical Review E, Vol. 92, Issue 2 https://doi.org/10.1103/physreve.92.022208	journal	August 2015
Exploring the jamming transition over a wide range of critical densities Ozawa, Misaki; Berthier, Ludovic; Coslovich, Daniele SciPost Physics, Vol. 3, Issue 4 https://doi.org/10.21468/scipostphys.3.4.027	journal	January 2017
Breakdown of continuum elasticity in amorphous solids Lerner, Edan; DeGiuli, Eric; Düring, Gustavo arXiv https://doi.org/10.48550/arxiv.1312.2146	text	January 2013
Phonons and elasticity in critically coordinated lattices Lubensky, T. C.; Kane, C. L.; Mao, Xiaoming arXiv https://doi.org/10.48550/arxiv.1503.01324	preprint	January 2015
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. arXiv https://doi.org/10.48550/arxiv.1512.04480	text	January 2015
Exploring the jamming transition over a wide range of critical densities Ozawa, Misaki; Berthier, Ludovic; Coslovich, Daniele arXiv https://doi.org/10.48550/arxiv.1705.10156	text	January 2017

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Transverse length scale
jammed packings
stability

Stability of jammed packings II: the transverse length scale

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