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

@article{Wyart2012MarginalSC,
  title={Marginal stability constrains force and pair distributions at random close packing.},
  author={Matthieu Wyart},
  journal={Physical review letters},
  year={2012},
  volume={109 12},
  pages={
          125502
        }
}
The requirement that packings of frictionless hard spheres, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes the form a bound between the distribution of contact forces P(f) and the pair distribution function g(r): if P(f)∼f(θ) and g(r)∼(r-σ(0))(-γ), where σ(0) is the particle diameter, one finds that γ ≥ 1/(2 + θ). This bound plays a role similar to… CONTINUE READING
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