Broader impact

1. Simulations of Jamming in the presence of PinningArjun G. Yodh, University of Pennsylvania, DMR 1062638 Systems as diverse as liquids, sand and foams can “jam” – go from a fluid-like to a disordered, solid-like phase. Three traditional paths to jamming (Liu and Nagel, 1998) involve increasing the density, external stress, or decreasing the effective temperature. Our study investigates a fourth route, adding a collection of “pinned” particles, which form a supporting framework for jamming. Our work involves computer simulations of a mixture containing two sizes of disc-like grains in two dimensions. It is the first careful exploration of how pinned particles affect not only the onset of jamming but also give rise to a “pinning” susceptibilityanalogous to the magnetic susceptibility in a ferromagnet. Near phase transitions, such quantities can diverge and our preliminary calculations indicate that indeed the pinning susceptibilityseems to diverge at the jamming transition with a critical exponent of g = 5/4. Fig. 1 In systems with a high concentration of randomly pinned disks (thick black circles), mobile disks (thin blue circles) can jam (i.e. become rigid) at a low packing fraction. Shown, a jammed system with packing fraction of only 77%, with 36% of discs pinned. (Over half of the mobile discs are removed as “rattlers” – not adding to rigidity of the solid.) Eq. 1 defines susceptibility, c. P is the probability of jamming for an arbitrary configuration of particles with packing fraction f, and pinned fraction n. Eq. 2 is the hypothesized div-ergence of c with distance from the critical packing fraction,fJ . Fig. 2Suceptibilityc vs. packing fraction f for 200, 600, 1000, and 2000 particles. As size grows, curves become more peaked at the threshold fJ. An argument known as “finite size scaling” allows us to extrapolate to the infinite size limit, Eq. 2.

2. Simulations of Jamming in the presence of PinningArjun G. Yodh, University of Pennsylvania, DMR 1062638 Broader impact 1. Penn Prof. Andrea Liu supervised REU student Elliot Padgett (Swarthmore ’13). Amandine Lee (Swarthmore ’13) and advisor Prof. Amy Graves participated in the rich environment of collaborative research, lectures, group meetings, and more, under the MRSEC at U. Penn An overlap in the projects of students Padgett and Lee resulted in a collaboration: Lee’s Java-based visualization of Padgett’s connected “percolating” clusters (green) that indicated jamming in a system with pinned (black) particles. Padgett’sdetection of percolating clusters allowed Prof. Amy Graves to extend jamming threshold data shown at the APS March, 2012 meeting far beyond the limit of a low number of pinned particles. Threshold packing fraction Number pinned