Scaling ansatz for the jamming transition

Goodrich, Carl P.; Liu, Andrea J.; Sethna, James P.

doi:10.1073/pnas.1601858113

Title: Scaling ansatz for the jamming transition

Journal Article · Wed Aug 10 00:00:00 EDT 2016 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.1601858113· OSTI ID:1290302

Goodrich, Carl P.; Liu, Andrea J.; Sethna, James P.

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.

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Research Organization:: Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF); Simons Foundation

Grant/Contract Number:: FG02-05ER46199; DMR-1312160

OSTI ID:: 1290302

Alternate ID(s):: OSTI ID: 1469312

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Vol. 113 Journal Issue: 35; ISSN 0027-8424

Publisher:: National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 46 works

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