title: Hypocoordinated solids in particulate media.
abstract: We propose a "phase diagram" for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom T_{0} and packing fraction deviation from jamming onset Δϕ=ϕ-ϕ_{J} using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value z_{iso}. ICS display "strict" harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ω_{k}{d} of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ω_{k}{d}, but it does possess a common form over a range of Δϕ and T_{0}.
authors.affiliation: Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA.
authors.forename: Thibault
authors.initials: T
authors.lastname: Bertrand
authors.affiliation: Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA.
authors.forename: Carl F
authors.initials: CF
authors.lastname: Schreck
authors.affiliation: Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA.
authors.forename: Corey S
authors.initials: CS
authors.lastname: O'Hern
authors.affiliation: Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, USA.
authors.forename: Mark D
authors.initials: MD
authors.lastname: Shattuck
mesh_terms: D003102:Colloids / Q000737:chemistry; D003198:Computer Simulation; D005583:Fourier Analysis; D007700:Kinetics; D008956:Models, Chemical; D052638:Particulate Matter / Q000737:chemistry*; D013696:Temperature; D014732:Vibration
chemical_list: D003102:Colloids; D052638:Particulate Matter