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Hypocoordinated solids in particulate media.

Thibault Bertrand1, Carl F Schreck2, Corey S O'Hern3

  • 1Department 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.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2014
PubMed
Summary
This summary is machine-generated.

We introduce a phase diagram for particulate systems, distinguishing between isocoordinated solids (ICS) and hypocoordinated solids (HCS) based on kinetic energy and packing fraction. ICS exhibit sharp vibrational peaks, while HCS show a common vibrational form.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Particulate systems, like granular media and colloids, exhibit complex behaviors near jamming.
  • Understanding their mechanical response requires characterizing distinct solid phases.

Purpose of the Study:

  • To propose a phase diagram for particulate systems with repulsive contact forces.
  • To differentiate between isocoordinated solids (ICS) and hypocoordinated solids (HCS) based on system parameters.

Main Methods:

  • Simulations of frictionless disks were used.
  • Behavior was characterized as a function of kinetic energy per degree of freedom (T0) and packing fraction deviation from jamming onset (Δϕ).

Main Results:

  • Two distinct solid classes were identified: isocoordinated solids (ICS) and hypocoordinated solids (HCS).
  • ICS, existing above jamming, possess an average contact number equal to the isostatic value (z_iso) and exhibit strict harmonic response with sharp vibrational mode peaks.
  • HCS, occurring above and below jamming, have fluctuating contacts but no cage-breaking rearrangements, displaying a common vibrational frequency form over a range of Δϕ and T0.

Conclusions:

  • The study establishes a phase diagram for repulsive particulate systems.
  • The vibrational properties clearly distinguish between ICS and HCS, offering insights into their mechanical responses.