title: Marginal stability in jammed packings: quasicontacts and weak contacts.
abstract: Maximally random jammed (MRJ) sphere packing is a prototypical example of a system naturally poised at the margin between underconstraint and overconstraint. This marginal stability has traditionally been understood in terms of isostaticity, the equality of the number of mechanical contacts and the number of degrees of freedom. Quasicontacts, pairs of spheres on the verge of coming in contact, are irrelevant for static stability, but they come into play when considering dynamic stability, as does the distribution of contact forces. We show that the effects of marginal dynamic stability, as manifested in the distributions of quasicontacts and weak contacts, are consequential and nontrivial. We study these ideas first in the context of MRJ packing of d-dimensional spheres, where we show that the abundance of quasicontacts grows at a faster rate than that of contacts. We reexamine a calculation of Jin et al. [Phys. Rev. E 82, 051126 (2010)], where quasicontacts were originally neglected, and we explore the effect of their inclusion in the calculation. This analysis yields an estimate of the asymptotic behavior of the packing density in high dimensions. We argue that this estimate should be reinterpreted as a lower bound. The latter part of the paper is devoted to Bravais lattice packings that possess the minimum number of contacts to maintain mechanical stability. We show that quasicontacts play an even more important role in these packings. We also show that jammed lattices are a useful setting for studying the Edwards ensemble, which weights each mechanically stable configuration equally and does not account for dynamics. This ansatz fails to predict the power-law distribution of near-zero contact forces, P(f)∼f(θ).
authors.affiliation: Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Yoav
authors.initials: Y
authors.lastname: Kallus
authors.affiliation: Department of Physics, Princeton University, Princeton, New Jersey 08544, USA; Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA; Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA; and Princeton Institute of the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato
mesh_terms: D060328:Magnetic Phenomena; D008962:Models, Theoretical