Title: Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming

Abstract

Here, we study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, ${\chi }_p$. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as ${\chi }_p\propto |\phi -{\phi }_c^{\infty }{|}^{-{\gamma }_p}$ where ${\phi }_c^{\infty }$ is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors ${\gamma }_p=1.018\pm 0.026\left(0.291\right)$ in $d=2$ and ${\gamma }_p=1.534\pm 0.120\left(0.822\right)$ in $d=3$. Logarithmic corrections raise the exponent in $d=2$ to close to the $d=3$ value, while the systematic errors are very large.

Authors:

Graves, Amy L. ^[1]; Nashed, Samer ^[1]; Padgett, Elliot ^[2]; Goodrich, Carl P. ^[3]; Liu, Andrea J. ^[3]; Sethna, James P. ^[4]

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+ Show Author Affiliations

1. Swarthmore College, Swarthmore, PA (United States)
2. Swarthmore College, Swarthmore, PA (United States); Cornell Univ., Ithaca, NY (United States)
3. Univ. of Pennsylvania, Philadelphia, PA (United States)
4. Cornell Univ., Ithaca, NY (United States)

Publication Date:

Fri Jun 10 00:00:00 EDT 2016

Research Org.:

Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:

National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; American Chemical Society Petroleum Research Fund

OSTI Identifier:

1596534

Alternate Identifier(s):

OSTI ID: 1256764

Grant/Contract Number:  

FG02-05ER46199; DMR-1312160

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review Letters

Additional Journal Information:

Journal Volume: 116; Journal Issue: 23; Journal ID: ISSN 0031-9007

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; jamming; scaling