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

Research paper by Matthieu M Wyart

Indexed on: 26 Sep '12Published on: 26 Sep '12Published in: Physical review letters



Abstract

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 those found in some glassy materials with long-range interactions, such as the Coulomb gap in Anderson insulators or the distribution of local fields in mean-field spin glasses. There are grounds to believe that this bound is saturated, yielding a mechanism to explain the avalanches of rearrangements with power-law statistics that govern plastic flow in packings.