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Disordered spring networks near surfaces exhibit low-frequency vibrational modes. Their number and decay depend on coordination and approach the jamming transition.

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Area of Science:

  • Physics
  • Materials Science
  • Network Science

Background:

  • Bulk disordered spring networks from jammed sphere packings exhibit a plateau in vibrational mode density down to a characteristic frequency ω*.
  • This frequency is governed by ΔZ, the difference between average coordination and twice the spatial dimension, vanishing at the jamming transition.

Purpose of the Study:

  • Investigate vibrational properties of disordered spring networks near a free surface.
  • Characterize the emergence and behavior of low-frequency surface modes.

Main Methods:

  • Analysis of vibrational modes in disordered spring networks derived from jammed sphere packings.
  • Theoretical investigation of systems with a free surface.

Main Results:

  • A density of low-frequency vibrational modes exists near the free surface, extending below ω*.
  • The quantity of these surface modes is controlled by ΔZ.
  • The decay profile of these modes into the bulk exhibits two length scales, diverging as ΔZ(-1/2) and ΔZ(-1) near the jamming transition.

Conclusions:

  • Free surfaces introduce distinct low-frequency vibrational modes in disordered spring networks.
  • The behavior of these surface modes provides insights into critical phenomena near the jamming transition.