Long-wavelength structural anomalies in jammed systems

Abstract

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wavenumber k, we argue that the anomalous behavior in the static structure factor, S(k) ∼ k, is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that S(0) → 0 at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that jamming transitions of frictional spheres lie at lower packing fractions that that for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids

“…This surprising saturation effect has not been reported before, although we notice that previous literature [22,26] indicates that the smallest S 0 (k → 0) values achieved in computer simulations are always of the order 10 −3 or more, which is consistent with our own results. This saturation would not be observed if the data in Fig.…”

“…For monodisperse spherical particles of diameter σ, this reduces to studying the ordinary static structure factor, S(k), whose low-wavevector behavior obeys a nontrivial, characteristic linear behaviour, S(kσ ≪ 1) ∼ k, which shows that density fluctuations are suppressed at large scale [22,23]. This behavior has been observed numerically in particle packings prepared exactly at the jamming transition [22][23][24][25][26], and experimentally in athermal granular materials [25]. Experiments performed with colloidal particles appear challenging and report only very weak signs of hyperuniformity [27][28][29].…”

Role of Disorder in the Thermodynamics and Atomic Dynamics of Glasses

“…Theseincludelow-energy optical modes [1], onset of mechanical instability related to saddle points in the energy landscape [2] or to jamming [3][4][5], local vibrationalmodes of clusters [6] or locally favoured structures [7], librations [8] or other coherent motions [9] of molecular fragments, crossover of local and acoustic modes [10], quasilocal vibrations of atoms in an anharmonic potential [11], broadening of vibrational states in the Ioffe-Regel crossover regime [12], spatial variation of the elastic moduli [13], breakdown of the continuum approximation [14,15], and topologically diverse defects [16], to cite the most important ones.…”

Force statistics and correlations in dense granular packings

“…However, the issue whether these correlations (and possibly anticorrelations due to vortex formation) depend on the system size [28] or not [29,30] is not completely resolved yet.…”