Two-dimensional melting far from equilibrium in a granular monolayer

We report an experimental investigation of the transition from a hexagonally ordered solid phase to a disordered liquid in a monolayer of vibrated spheres. The transition occurs as the intensity of the vibration amplitude is increased. Measurements of the density of dislocations and the positional and orientational correlation functions show evidence for a dislocation-mediated continuous transition from a solid phase with long-range order to a liquid with only short-range order. The results show a strong similarity to simulations of melting of hard disks in equilibrium, despite the fact that the granular monolayer is far from equilibrium due to the effects of interparticle dissipation and the vibrational forcing.Comment: 4 pages, 4 figure

Comment on ”Long-Lived giant number fluctuations in a swarming granular nematic

Narayan et al. (Reports, 6 July 2007, p. 105) reported giant number fluctuations attributed to curvature-driven active currents specific for nonequilibrium nematic systems. We present data demonstrating that similar results can be found in systems of spherical particles due either to inelastic clustering or persistent density inhomogeneity, suggesting two alternative explanations for their results. (1) presented experimental evidence that a fluidized monolayer of macroscopic granular rods in the active nematic phase exhibits giant number fluctuations consistent with a standard deviation growing linearly with the mean, in contrast to the behavior expected for any situation in which the central limit theorem applies. These giant number fluctuations were attributed to curvature-driven active currents specific for nonequilibrium nematic systems. Granular systems often exhibit statistical properties sharply distinct from their equilibrium counterparts, for example, non-Gaussian velocity distributions in dissipative gases (2, 3). Giant number fluctuations were predicted on the basis of perturbation analysis of a nearly spatially uniform state of a generic phenomenological model for active nematics (4). Although we do not question the possibility that giant fluctuations associated with nematic ordering may be present in the system analyzed by Narayan et al., on the basis of two complementary experiments with spherical particles we demonstrate that the linear growth of the standard deviation DN with the mean N can arise either from dynamic inelastic clustering or from persistent density inhomogeneity. We performed experiments with monolayers of spherical grains energized either by mechanical vertical vibration (5) or by an alternating vertical electric field (6). Although the driving mechanisms are very different, the observed behavior is similar: a transition from the uniform gas state for high amplitude driving (vibration or electric field amplitude) to inhomogeneous phaseseparated states at lower amplitudes of the driving. We analyzed DN versus N using two different coarse-graining procedures. The first procedure (P1, temporal averaging first) is identical to that used by Narayan et al. (1). We partitioned the experimental system into M small subsystems of equal size L and measured the number of particles N i in each subsystem. The fluctuation in a given subsystem was calculated from the series of N i versus time by measuring the mean square deviation from the average N for that subsystem. The values of DN for all of the subsystems in the frame were then averaged and plotted against the average N for the experiment. The results of our analyses . This dependence follows from the bimodal probability distribution. , which implies that the standard deviation DN~N To highlight the importance of spatial heterogeneity, we also employed a second procedure (P2, spatial averaging first). The fluctuations in a single image were calculated as the root mean square deviation of the number of particles N i in each subsystem from the global mean N = N 0 /M for that image (N 0 is the total number of particles in all of the subsystems). Then, the standard deviation extracted from a single image was averaged over all images and plotted versus the average of the global mean. For a homogeneous system with spatial and temporal correlations that are small compared with the system size and experiment duration, respectively, the two procedures should give the same result. For those conditions in which the data analyzed included only a single phas

Forcing and Velocity Correlations in a Vibrated Granular Monolayer

The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anti-correlation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.Comment: 4 pages, 5 figure

The dynamics of thin vibrated granular layers

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure

Clustering, Order, and Collapse in a Driven Granular Monolayer

Steady state dynamics of clustering, long range order, and inelastic collapse are experimentally observed in vertically shaken granular monolayers. At large vibration amplitudes, particle correlations show only short range order like equilibrium 2D hard sphere gases. Lowering the amplitude "cools" the system, resulting in a dramatic increase in correlations leading either to clustering or an ordered state. Further cooling forms a collapse: a condensate of motionless balls co-existing with a less dense gas. Measured velocity distributions are non-Gaussian, showing nearly exponential tails.Comment: 9 pages of text in Revtex, 5 figures; references added, minor modifications Paper accepted to Phys Rev Letters. Tentatively scheduled for Nov. 9, 199