Diffusion of granular rods on a rough vibrated substrate.

We investigate the effect of shape anisotropy and number density on the dynamics of granular rods on a substrate with experiments using a mono-layer of bead chains in a vibrated container. Statistical measures of the translational and rotational degrees of freedom indicate a dramatic slowing down of dynamics because of steric interactions at a value well below the highest packing fraction of the chains. In particular, the in-plane orientation auto-correlation function decays exponentially with time at low densities, but increasingly slowly as density is increased with a form which is not described by a simple exponential function. While the mean square displacement of the chain center of mass is observed to grow linearly at low densities, it is observed to grow increasingly slowly and non-linearly as number density is increased. Decomposing the displacements parallel and perpendicular to the long axis of the chain, we find that the ratio of diffusion in the parallel and perpendicular direction to their long axis is less than one in the dilute regime. However, as the density of the chains is increased, the ratio rapidly increases above one with a greater value for higher aspect ratios. This anisotropic behavior can be explained by considering a higher effective drag on the rods by the substrate in the perpendicular direction compared with the parallel direction, and by tube-like dynamics at higher densities.

Dynamics of a bouncing dimer.

We investigate the dynamics of a dimer bouncing on a vertically oscillated plate. The dimer, composed of two spheres rigidly connected by a light rod, exhibits several modes depending on initial and driving conditions. The first excited mode has a novel horizontal drift in which one end of the dimer stays on the plate during most of the cycle, while the other end bounces in phase with the plate. The speed and direction of the drift depend on the aspect ratio of the dimer. We employ event-driven simulations based on a detailed treatment of frictional interactions between the dimer and the plate in order to elucidate the nature of the transport mechanism in the drift mode.

Collision statistics of driven granular materials.

We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side wall. The data is obtained by high-speed imaging and particle tracking techniques. We identify all particles in the system and link their positions to form trajectories over long times. Thus, we identify particle collisions to measure the effective coefficient of restitution and find a broad distribution of values for the same impact angles. We find that the energy inelasticity can take on values greater than one, which implies that the rotational degrees of freedom play an important role in energy transfer. We also measure the distance and the time between collision events in order to directly determine the distribution of path lengths and the free times. These distributions are shown to deviate from expected theoretical forms for elastic spheres, demonstrating the inherent clustering in this system. We describe the data with a two-parameter fitting function and use it to calculate the mean free path and collision time. We find that the ratio of these values is consistent with the average velocity. The velocity distributions are observed to be strongly non-Gaussian and do not demonstrate any apparent universal behavior. We report the scaling of the second moment, which corresponds to the granular temperature, and higher order moments as a function of distance from the driving wall. Additionally, we measure long-time correlation functions in both space and in the velocities to probe diffusion in a dissipative gas.

Vortices in vibrated granular rods.

We report the experimental observation of vortex patterns in vertically vibrated granular rods. Above a critical packing fraction, moving ordered domains of nearly vertical rods spontaneously form and coexist with horizontal rods. The domains of vertical rods coarsen in time to form large vortices. We investigate the conditions under which the vortices occur by varying the number of rods, vibration amplitude, and frequency. The size of the vortices increases with the number of rods. We characterize the growth of the ordered domains by measuring the area fraction of the ordered regions as a function of time. A void-filling model is presented to describe the nucleation and growth of the vertical domains. We track the ends of the vertical rods and obtain the velocity fields of the vortices. The rotation speed of the rods is observed to depend on the vibration velocity of the container and on the packing. To investigate the impact of the direction of driving on the observed phenomena, we performed experiments with the container vibrated horizontally. Although vertical domains form, vortices are not observed. We therefore argue that the motion is generated due to the interaction of the inclination of the rods with the bottom of a vertically vibrated container. We also perform simple experiments with a single row of rods in an annulus. These experiments directly demonstrate that the rod motion is generated when the rods are inclined from the vertical, and is always in the direction of the inclination.

Clustering transitions in vibrofluidized magnetized granular materials.

We study the effects of long-range interactions on the phases observed in cohesive granular materials. At high vibration amplitudes, a gas of magnetized particles is observed with velocity distributions similar to nonmagnetized particles. Below a transition temperature compact clusters are observed to form and coexist with single particles. The cluster growth rate is consistent with a classical nucleation process. However, the temperature of the particles in the clusters is significantly lower than the surrounding gas, indicating a breakdown of equipartition. If the system is quenched to low temperatures, a metastable network of connected chains self-assemble due to the anisotropic nature of magnetic interactions between particles.

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 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.

Angle of repose and segregation in cohesive granular matter.

We study the effect of fluids on the angle of repose and the segregation of granular matter poured into a silo. The experiments are conducted in two regimes where: (i) the volume fraction of the fluid (liquid) is small and it forms liquid bridges between particles thus giving rise to cohesive forces, and (ii) the particles are completely immersed in the fluid. The data is obtained by imaging the pile formed inside a quasi-two-dimensional silo through the transparent glass side walls and using color-coded particles. In the first series of experiments, the angle of repose is observed to increase sharply with the volume fraction of the fluid and then saturates at a value that depends on the size of the particles. We systematically study the effect of viscosity by using water-glycerol mixtures to vary it over at least three orders of magnitude while keeping the surface tension almost constant. Besides surface tension, the viscosity of the fluid is observed to have an effect on the angle of repose and the extent of segregation. In case of bidisperse particles, segregation is observed to decrease and finally saturate depending on the size ratio of the particles and the viscosity of the fluid. The sharp initial change and the subsequent saturation in the extent of segregation and angle of repose occurs over similar volume fraction of the fluid. Preferential clumping of small particles causes layering to occur when the size of the clumps of small particles exceeds the size of large particles. We calculate the azimuthal correlation function of particle density inside the pile to characterize the extent of layering. In the second series of experiments, particles are poured into a container filled with a fluid. Although the angle of repose is observed to be unchanged, segregation is observed to decrease with an increase in the viscosity of the fluid. The viscosity at which segregation decreases to zero depends on the size ratio of the particles.

Swarming ring patterns in bacterial colonies exposed to ultraviolet radiation.

We report a novel morphological transition in a Bacillus subtilis colony initially growing under ambient conditions, after ultraviolet radiation exposure. The bacteria in the central regions of the colonies are observed to migrate towards the colony edge forming a ring during uniform spatial exposure. When the radiation is switched off, the colonies were observed to grow both inward into the evacuated regions as well as outward indicating that the pattern is not formed due to depletion of nutrients at the center of the colony. We also propose a reaction-diffusion model in which waste-limited chemotaxis initiated by the UV radiation leads to the observed phenomenology.

Spectral properties of a mixed system using an acoustical resonator.

We experimentally study the spectral properties of a mixed system using the flexural modes of a clover shaped plate. The system is called mixed because the corresponding ray dynamics has both chaotic and integrable regions in its phase space. The eigenvalue statistics show intermediate properties between the universal statistics corresponding to chaotic geometries which show Gaussian orthogonal ensemble statistics and integrable geometries that show Poisson statistics. We further investigate the Fourier transform of the peaks to study the influence of the length scales of the plate on the properties of the acoustic resonances. We observe a weak signal of the periodic orbits in the experimental data. Although some of the peaks in the Fourier transform of the eigenvalue spectrum correspond to the shortest stable periodic orbits, other strong peaks are also observed. To understand the role of symmetries, we start with a clover shaped plate belonging to the C(4v) point symmetry group, and progressively reduce the symmetry by sanding one of the edges. A Shnirelman peak in P(s) is observed for the highly symmetric situation due to level clustering.

Scarred patterns in surface waves.

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.

Segregation transitions in wet granular matter

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid V(f) is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation s and the angle of repose straight theta. We show that the sharp initial change and the subsequent saturation in s and straight theta occurs over similar V(f). We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.

Extinction transition in bacterial colonies under forced convection.

We report the spatiotemporal response of Bacillus subtilis growing on a nutrient-rich layer of agar to ultraviolet (UV) radiation. Below a crossover temperature, the bacteria are confined to regions that are shielded from UV radiation. A forced convection of the population is effected by rotating a UV radiation shield relative to the Petri dish. The extinction speed at which the bacterial colony lags behind the shield is found to be qualitatively similar to the front velocity of the colony growing in the absence of a hostile environment as predicted by the model of Dahmen, Nelson, and Shnerb. A quantitative comparison is not possible without considering the slow dynamics and time-dependent interaction of the population with the hostile environment.

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.

Experimental investigation of universal parametric correlators using a vibrating plate.

The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure is used to isolate this symmetry class of modes and simplify the data analysis. The size of the plate is used as the external parameter and the eigenvalues are observed to undergo one or two oscillations in the experimental window. The correlations of the eigenvalues are in good agreement with statistical measures such as the parametric number variance, the velocity autocorrelation, and the intralevel velocity autocorrelation derived for the Gaussian orthogonal ensemble of random matrix theory. Our results show that the theory can be also applied to wave systems other than quantum systems.

Size segregation of granular matter in silo discharges.

We present an experimental study of segregation of granular matter in a quasi-two-dimensional silo emptying out of an orifice. Size separation is observed when multisized particles are used with the larger particles found in the center of the silo in the region of fastest flow. We use imaging to study the flow inside the silo and quantitatively measure the concentration profiles of bidisperse beads as a function of position and time. The angle of the surface is given by the angle of repose of the particles, and the flow occurs in a few layers only near the top of this inclined surface. The flowing region becomes deeper near the center of the silo and is confined to a parabolic region centered at the orifice which is approximately described by the kinematic model. The experimental evidence suggests that the segregation occurs on the surface and not in the flow deep inside the silo where velocity gradients also are present. We report the time development of the concentrations of the bidisperse particles as a function of size ratios, flow rate, and the ratio of initial mixture. The qualitative aspects of the observed phenomena may be explained by a void filling model of segregation.

Velocity statistics in excited granular media.

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) approximately exp(-mid R:v/v(c)mid R:(1.5)), in agreement with a recent theory. The characteristic velocity v(c) is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. (c) 1999 American Institute of Physics.