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Title: Scaling ansatz for the jamming transition

Abstract

Here, we propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Pennsylvania, Philadelphia, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF); Simons Foundation
OSTI Identifier:
1290302
Alternate Identifier(s):
OSTI ID: 1469312
Grant/Contract Number:  
FG02-05ER46199; DMR-1312160
Resource Type:
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 113 Journal Issue: 35; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; jamming transition; scaling ansatz; nonequilibrium critical phenomena

Citation Formats

Goodrich, Carl P., Liu, Andrea J., and Sethna, James P. Scaling ansatz for the jamming transition. United States: N. p., 2016. Web. doi:10.1073/pnas.1601858113.
Goodrich, Carl P., Liu, Andrea J., & Sethna, James P. Scaling ansatz for the jamming transition. United States. doi:10.1073/pnas.1601858113.
Goodrich, Carl P., Liu, Andrea J., and Sethna, James P. Wed . "Scaling ansatz for the jamming transition". United States. doi:10.1073/pnas.1601858113.
@article{osti_1290302,
title = {Scaling ansatz for the jamming transition},
author = {Goodrich, Carl P. and Liu, Andrea J. and Sethna, James P.},
abstractNote = {Here, we propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.},
doi = {10.1073/pnas.1601858113},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 35,
volume = 113,
place = {United States},
year = {2016},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1073/pnas.1601858113

Citation Metrics:
Cited by: 8 works
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