Spectral responses in granular compaction

Abstract

The slow compaction of a gently tapped granular packing is reminiscent of the low-temperature dynamics of structural and spin glasses. Here, I probe the dynamical spectrum of granular compaction by measuring a complex (frequency-dependent) volumetric susceptibility ${\tilde{\chi }}_v$. While the packing density $\rho$ displays glass-like slow relaxations (aging) and history-dependence (memory) at low tapping amplitudes, the susceptibility ${\tilde{\chi }}_v$ displays very weak aging effects, and its spectrum shows no sign of a rapidly growing timescale. These features place ${\tilde{\chi }}_v$ in sharp contrast to its dielectric and magnetic counterparts in structural and spin glasses; instead, ${\tilde{\chi }}_v$ bears close similarities to the complex specific heat of spin glasses. This, I suggest, indicates the glass-like dynamics in granular compaction are governed by statistically rare relaxation processes that become increasingly separated in timescale from the typical relaxations of the system. Finally, I examine the effect of finite system size on the spectrum of compaction dynamics. Starting from the ansatz that low frequency processes correspond to large scale particle rearrangements, I suggest the observed finite size effects are consistent with the suppression of large-scale collective rearrangements in small systems.

18 pages, 17 figures. Submitted to PRE

References in corpus (5)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Glassy dynamics of kinetically constrained models
• The packing of granular polymer chains
• Equivalence of glass transition and colloidal glass transition in the hard-sphere limit
• Experimental study of the jamming transition at zero temperature

Cited by in corpus (2)

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• A model for approximately stretched-exponential relaxation with continuously varying stretching exponents