Non-Gaussian velocity distributions in excited granular matter in the absence of clustering

The velocity distribution of spheres rolling on a slightly tilted rectangular two dimensional surface is obtained by high speed imaging. The particles are excited by periodic forcing of one of the side walls. Our data suggests that strongly non-Gaussian velocity distributions can occur in dilute granular materials even in the absence of significant density correlations or clustering. When the surface on which the particles roll is tilted further to introduce stronger gravitation, the collision frequency with the driving wall increases and the velocity component distributions approach Gaussian distributions of different widths.Comment: 4 pages, 5 figures. Additional information at http://physics.clarku.edu/~akudrolli/nls.htm

Velocity correlations in dense granular gases

We report the statistical properties of spherical steel particles rolling on an inclined surface being driven by an oscillating wall. Strong dissipation occurs due to collisions between the particles and rolling and can be tuned by changing the number density. The velocities of the particles are observed to be correlated over large distances comparable to the system size. The distribution of velocities deviates strongly from a Gaussian. The degree of the deviation, as measured by the kurtosis of the distribution, is observed to be as much as four times the value corresponding to a Gaussian, signaling a significant breakdown of the assumption of negligible velocity correlations in a granular system.Comment: 4 pages, 4 Figure

Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments: (i) non-magnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is consistent with kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.Comment: 4 pages, 3 figure

Two-dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving

We study a two-dimensional granular gas of inelastic spheres subject to multiplicative driving proportional to a power $|v(\vec{x})|^{\delta}$ of the local particle velocity $v(\vec{x})$. The steady state properties of the model are examined for different values of $\delta$, and compared with the homogeneous case $\delta=0$. A driving linearly proportional to $v(\vec{x})$ seems to reproduce some experimental observations which could not be reproduced by a homogeneous driving. Furthermore, we obtain that the system can be homogenized even for strong dissipation, if a driving inversely proportional toComment: 4 pages, 5 figures (accepted as Phys. Rev. Lett.

Model of coarsening and vortex formation in vibrated granular rods

Neicu and Kudrolli observed experimentally spontaneous formation of the long-range orientational order and large-scale vortices in a system of vibrated macroscopic rods. We propose a phenomenological theory of this phenomenon, based on a coupled system of equations for local rods density and tilt. The density evolution is described by modified Cahn-Hilliard equation, while the tilt is described by the Ginzburg-Landau type equation. Our analysis shows that, in accordance to the Cahn-Hilliard dynamics, the islands of the ordered phase appear spontaneously and grow due to coarsening. The generic vortex solutions of the Ginzburg-Landau equation for the tilt correspond to the vortical motion of the rods around the cores which are located near the centers of the islands.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Shocks in supersonic sand

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge and calculate a speed of granular pressure disturbances (sound speed) equal to 10% of the flow speed. The flow is supersonic, forming shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of the Boltzmann equation yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure

Coarsening of granular clusters: two types of scaling behaviors

We report on an experimental study of small cluster dynamics during the coarsening process in driven granular submonolayers of 120mkm bronze particles. The techniques of electrostatic and vertical mechanical vibration were employed to excite the granular gas. We measure the scaling exponent for the evaporation of small clusters during coarsening. It was found that the surface area of small clusters S vs time t behaves as S ~ (t_0-t)^(2/3) for lower frequencies and S ~ (t_0-t) for higher frequencies. We argue that the change in the scaling exponent is related to the transition from three dimensional to two dimensional character of motion in the granular gas.Comment: 4 pages,5 figures, submitted to Phys.Rev.

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

Granular Collapse as a Percolation Transition

Inelastic collapse is found in a two-dimensional system of inelastic hard disks confined between two walls which act as an energy source. As the coefficient of restitution is lowered, there is a transition between a state containing small collapsed clusters and a state dominated by a large collapsed cluster. The transition is analogous to that of a percolation transition. At the transition the number of clusters n_s of size s scales as $n_s \sim s^{-\tau}$ with $\tau \approx 2.7$.Comment: 10 pages revtex, 5 figures, accepted by Phys Rev E many changes and corrections from previous submissio

Propagating front in an excited granular layer

A partial monolayer of ~ 20000 uniform spherical steel beads, vibrated vertically on a flat plate, shows remarkable ordering transitions and cooperative behavior just below 1g maximum acceleration. We study the stability of a quiescent disordered or ``amorphous'' state formed when the acceleration is switched off in the excited ``gaseous'' state. The transition from the amorphous state back to the gaseous state upon increasing the plate's acceleration is generally subcritical: An external perturbation applied to one bead initiates a propagating front that produces a rapid transition. We measure the front velocity as a function of the applied acceleration. This phenomenon is explained by a model based on a single vibrated particle with multiple attractors that is perturbed by collisions. A simulation shows that a sufficiently high rate of interparticle collisions can prevent trapping in the attractor corresponding to the nonmoving ground state.Comment: 16 pages, 9 figures, revised version, to appear in Phys. Rev. E, May 199