title: Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming.
abstract: 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, χ_{p}. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χ_{p}∝|ϕ-ϕ_{c}^{∞}|^{-γ_{p}} where ϕ_{c}^{∞} is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors γ_{p}=1.018±0.026(0.291) in d=2 and γ_{p}=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large.
authors.affiliation: Department of Physics and Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081, USA.
authors.forename: Amy L
authors.initials: AL
authors.lastname: Graves
authors.affiliation: Department of Physics and Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081, USA.
authors.forename: Samer
authors.initials: S
authors.lastname: Nashed
authors.affiliation: Department of Physics and Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081, USA.|School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA.
authors.forename: Elliot
authors.initials: E
authors.lastname: Padgett
authors.affiliation: Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Carl P
authors.initials: CP
authors.lastname: Goodrich
authors.affiliation: Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
authors.forename: Andrea J
authors.initials: AJ
authors.lastname: Liu
authors.affiliation: Department of Physics, Cornell University, Ithaca, New York 14583, USA.
authors.forename: James P
authors.initials: JP
authors.lastname: Sethna