Effects of compression on the vibrational modes of marginally jammed solids

Matthieu Wyart, Leonardo E. Silbert, Sidney R. Nagel, Thomas A. Witten

    Research output: Contribution to journalArticle

    Abstract

    Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze, in particular, two systems whose density D(ω) of vibrational modes of angular frequency ω display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed (a) convergence of D(ω) toward a nonzero constant as ω→0, (b) appearance of a low-frequency cutoff ω*, and (c) power-law increase of ω* with compression. Differences between these two systems occur at a lower frequency. The density of states of the modified system displays an abrupt plateau that appears at ω*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle δz:δz≥p12, which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.

    Original languageEnglish (US)
    Article number051306
    JournalPhysical Review E
    Volume72
    Issue number5
    DOIs
    StatePublished - Nov 2005

    Fingerprint

    vibration mode
    Compression
    low frequencies
    Excess
    Low Frequency
    Contact
    Scaling Behavior
    scaling
    elastic bodies
    Packing
    display devices
    rigidity
    plateaus
    cut-off
    low pressure
    simulation
    Normal Modes
    Elastic body
    Zero
    Density of States

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Condensed Matter Physics
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Effects of compression on the vibrational modes of marginally jammed solids. / Wyart, Matthieu; Silbert, Leonardo E.; Nagel, Sidney R.; Witten, Thomas A.

    In: Physical Review E, Vol. 72, No. 5, 051306, 11.2005.

    Research output: Contribution to journalArticle

    Wyart, Matthieu ; Silbert, Leonardo E. ; Nagel, Sidney R. ; Witten, Thomas A. / Effects of compression on the vibrational modes of marginally jammed solids. In: Physical Review E. 2005 ; Vol. 72, No. 5.
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