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Title: Scaling ansatz for the jamming transition

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.
 [1] ;  [2] ;  [3]
  1. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics; Harvard Univ., Cambridge, MA (United States). School of Engineering and Applied Sciences
  2. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics
  3. Cornell Univ., Ithaca, NY (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
FG02-05ER46199; DMR 1312160
Published Article
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 113; Journal Issue: 35; Journal ID: ISSN 0027-8424
National Academy of Sciences, Washington, DC (United States)
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
Country of Publication:
United States
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; jamming transition; scaling ansatz; nonequilibrium critical phenomena
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1469312