paper

Stability at Random Close Packing

arXiv:1202.0259 · doi:10.1103/PhysRevLett.109.125502

Abstract

The requirement that packings of hard particles, 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) \sim f^θ and g(r) \sim (r-σ)^(-γ), where σ is the particle diameter, one finds that γ \geq 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 is ground to believe that this bound is saturated, offering an explanation for the presence of avalanches of rearrangements with power-law statistics observed in packings.

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