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Contact nonlinearities and linear response in jammed particulate packings.

Carl P Goodrich1, Andrea J Liu1, Sidney R Nagel2

  • 1Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.

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Frictionless particle packings exhibit a jamming transition. Mechanical response near this transition is predictable, even with particles changing contact, confirming a linear regime in the thermodynamic limit.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Jamming transition is a key phenomenon in condensed matter physics.
  • Disordered particle packings form the basis of jamming theory.
  • Mechanical response in jamming is theorized to depend solely on proximity to the transition.

Purpose of the Study:

  • Investigate the validity of measurements using the harmonic approximation in jamming theory.
  • Assess the utility of these measurements in understanding particle packings.
  • Determine if a well-defined linear regime exists despite dynamic particle contacts.

Main Methods:

  • Studied frictionless athermal particle packings.
  • Analyzed systems at varying packing densities.
  • Employed the harmonic approximation for mechanical response analysis.

Main Results:

  • Confirmed a jamming transition as a function of packing density.
  • Demonstrated that mechanical response depends predictably on the distance to the transition.
  • Showed a well-defined linear regime exists in the thermodynamic limit, even with particles entering and exiting contact.

Conclusions:

  • The harmonic approximation is a valid and useful tool for studying jamming.
  • The theory of jamming accurately predicts mechanical response near the transition.
  • Disordered systems exhibit predictable behavior in the thermodynamic limit.