Marginal stability constrains force and pair distributions at random close packing

Matthieu Wyart

    Research output: Contribution to journalArticle

    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)∼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.

    Original languageEnglish (US)
    Article number125502
    JournalPhysical Review Letters
    Volume109
    Issue number12
    DOIs
    StatePublished - Sep 18 2012

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    force distribution
    plastic flow
    spin glass
    avalanches
    distribution functions
    statistics
    insulators
    requirements
    glass
    interactions

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Marginal stability constrains force and pair distributions at random close packing. / Wyart, Matthieu.

    In: Physical Review Letters, Vol. 109, No. 12, 125502, 18.09.2012.

    Research output: Contribution to journalArticle

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