Heterogeneities in granular dynamics

Abstract

The absence of Brownian motion in granular media is a source of much complexity, including the prevalence of heterogeneity, whether static or dynamic, within a given system. Such strong heterogeneities can exist as a function of depth in a box of grains; this is the system we study here. First, we present results from three-dimensional, cooperative and stochastic Monte Carlo shaking simulations of spheres on heterogeneous density fluctuations. Next, we juxtapose these with results obtained from a theoretical model of a column of grains under gravity; frustration via competing local fields is included in our model, whereas the effect of gravity is to slow down the dynamics of successively deeper layers. The combined conclusions suggest that the dynamics of a real granular column can be divided into different phases-ballistic, logarithmic, activated, and glassy-as a function of depth. The nature of the ground states and their retrieval (under zerotemperature dynamics) is analyzed; the glassy phase shows clear evidence of its intrinsic (''crystalline'') states, which lie below a band of approximately degenerate ground states. In the other three phases, by contrast, the system jams into a state chosen randomly from this upper band of metastable states. granular physics ͉ heterogeneous phases ͉ glassy dynamics ͉ intrinsic states M any of the most interesting properties of granular media (1-5) arise from their athermal nature, i.e., that grains are too massive to move in response to the ambient temperature; in particular, granular dynamics are strongly hysteretic and bear the imprint of configurational histories. Heterogeneity is yet another consequence of the lack of Brownian diffusion; different parts of the same system can sustain diverse structures, and have different dynamical behavior, in the absence of sufficiently strong external perturbations.One of the earliest indications of such heterogeneity was found in the experiments of Nagel et al. (6) in their investigation of Edwards' compactivity (7), the ''slow'' effective temperature of a granular medium; their findings indicated that this, along with average density, varied strongly throughout the system. For an interesting generalization of this idea, see also ref. 8. The presence of force chains (9, 10) is another strong indicator of heterogeneity; it has been argued recently (11) that the carriers of these force chains are granular bridges (12), which are structural heterogeneities unique to granular media.The aspect of heterogeneity that we investigate here is most similar to that investigated experimentally in ref. 6; we examine, analytically and via computer simulations, the heterogeneities that arise as a function of depth in a system of grains, having to do with density fluctuations, as well as the retrieval of ground states. Our computer simulation algorithm (13, 14) is a stochastic and cooperative hybrid Monte Carlo scheme, which models the shaking of spheres in three dimensions via alternating periods of dilation and quench; it has long been recogniz...

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“…Prior work indicated that the particles rearrange in cooperative groups [23], similar to what is seen in supercooled liquids [3,33,45,46,47,48,49,50,51] and granular materials [52,53]. A starting point to look for cooperativity is to ask where the mobile particles are located [23,46,49]; Fig.…”

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“…First, computer simulations [7] of shaken sphere assemblies verified that the time-averaged value of density about which temporal fluctuations occur, is an increasing function of depth ( Fig. 2) and additionally predicted that the range of density fluctuations is greatest in the middle of the box [13,14]. Initially surprising, this is easily explained as follows: the top is barely fluidized, with few fluctuations about an overall low density while the jammed region near the bottom also has only very slow density fluctuations.…”

Heterogeneities in granular materials

“…More specifically, they verified that the time-averaged value of density, about which temporal fluctuations occur, is an increasing function of depth. 13 One of the most surprising features of those results, at least at first glance, is that the range of density fluctuations is greatest near the middle of the column, as seen in figure 3. However, that feature can be simply explained.…”

“…That theoretical tool monitors the propagation of order in a system at minimal perturbation; here, the dynamics are reflected in the behavior of the ordering length-that is, the length over which the column is ordered-at zero vibrational intensity (see figure 5). 13 A complete picture of spatiotemporal heterogeneity emerges from particle behavior in different regions. At the top of the column, the dynamics are ballistic: Grains move fast and freely in response to vibrational excitations.…”

“…13 Figure 4 tracks the history of a particle that begins in the middle of the box and subsequently traverses the whole system.…”