TY - JOUR

T1 - Marginal stability constrains force and pair distributions at random close packing

AU - Wyart, Matthieu

PY - 2012/9/18

Y1 - 2012/9/18

N2 - 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)∼fθ 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.

AB - 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)∼fθ 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.

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U2 - 10.1103/PhysRevLett.109.125502

DO - 10.1103/PhysRevLett.109.125502

M3 - Article

AN - SCOPUS:84866526845

VL - 109

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 12

M1 - 125502

ER -