|Title||Pinning Susceptibility: The effect of dilute, quenched disorder on jamming|
|Publication Type||Journal Article|
|Year of Publication||Submitted|
|Authors||Graves, Amy L., Nashed Samer, Padgett Elliot, Goodrich Carl P., Liu Andrea J., and Sethna James P.|
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, χp. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as χp∝|ϕ−ϕ∞c|−γp where ϕ∞c is the jamming threshold in the absence of pins. Finite-size scaling arguments yield γp=1.018±0.026 in 2d and γp=1.534±0.120 in 3d. Logarithmic corrections raise the exponent in 2d, making 2d and 3d values of γp consistent, but systematic errors are sufficiently large that the issue of whether γp depends on dimension is an open question.
Pinning Susceptibility: The effect of dilute, quenched disorder on jamming