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Marginal stability constrains force and pair distributions at random close packing.

Matthieu Wyart1

  • 1Center for Soft Matter Research, New York University, New York, 10003, USA.

Physical Review Letters
|September 26, 2012
PubMed
Summary

Structural glasses made of frictionless hard spheres have a new constraint relating contact forces and particle distribution. This finding may explain the power-law statistics governing plastic flow in these materials.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Packings of frictionless hard spheres are model systems for structural glasses.
  • These packings resist compression via contact network rearrangement.
  • Understanding microscopic structure is key to glass properties.

Purpose of the Study:

  • To derive a new constraint on the microscopic structure of hard sphere packings.
  • To relate the distribution of contact forces to the pair distribution function.
  • To explore the implications of this constraint for glassy dynamics.

Main Methods:

  • Analyzing the incompressibility requirement of hard sphere packings.
  • Deriving a bound relating the contact force distribution P(f) and the pair distribution function g(r).
  • Comparing the derived bound to phenomena in other disordered systems.

Main Results:

  • A new constraint is found: γ ≥ 1/(2 + θ), where P(f)∼f(θ) and g(r)∼(r-σ(0))(-γ).
  • This bound is analogous to those observed in Coulomb gaps and spin glasses.
  • Evidence suggests this bound may be saturated in real systems.

Conclusions:

  • The derived constraint provides a novel link between static structure and force distribution in glasses.
  • A saturated bound offers a potential mechanism for power-law avalanche statistics in plastic flow.
  • This work deepens the understanding of fundamental properties of glassy materials.