Hypocoordinated solids in particulate media

Thibault Bertrand, Carl F. Schreck, Corey S. O'Hern, and Mark D. Shattuck
Phys. Rev. E 89, 062203 – Published 12 June 2014

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 T0 and packing fraction deviation from jamming onset Δϕ=ϕϕJ using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value ziso. 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 ωkd 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 ωkd, but it does possess a common form over a range of Δϕ and T0.

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  • Received 1 July 2013

DOI:https://doi.org/10.1103/PhysRevE.89.062203

©2014 American Physical Society

Authors & Affiliations

Thibault Bertrand1,4, Carl F. Schreck1,2, Corey S. O'Hern1,2,3,4, and Mark D. Shattuck1,5

  • 1Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA
  • 2Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA
  • 3Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8120, USA
  • 4Center for Research on Interface Structures and Phenomena, Yale University, New Haven, Connecticut 06520, USA
  • 5Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, USA

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Vol. 89, Iss. 6 — June 2014

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