Swirling granular solidlike clusters

State-dependent driving: a route to non-equilibrium stationary states

We study three different experiments that involve dry friction and periodic driving, and which employ both single- and many-particle systems. These experimental set-ups, besides providing a playground for investigation of frictional effects, are relevant in broad areas of science and engineering. Across all these experiments, we monitor the dynamics of objects placed on a substrate that is being moved in a horizontal manner. The driving couples to the degrees of freedom of the substrate and this coupling in turn influences the motion of the objects. Our experimental findings suggest emergence of stationary-states with non-trivial features. We invoke a minimalistic phenomenological model to explain our experimental findings. Within our model, we treat the injection of energy into the system to be dependent on its dynamical state, whereby energy injection is allowed only when the system is in its suitable-friction state. Our phenomenological model is built on the fact that such a state-dependent driving results in a force that repeatedly toggles the frictional states in time and serves to explain our experimental findings.

Collective motion of granular matter subjected to swirling excitation

A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes where nonuniform density distribution and correlated dynamics are present. For intermediate packing density and oscillation amplitude, a condensed phase travels around the container's side wall in the clockwise direction, while the oscillation itself is set anticlockwise. Further increasing the packing density towards that of hexagonal packing, the whole packing rotates collectively in the clockwise direction. The core of the packing rotates as a solid and is separated from the boundary by a fluid-like layer. Both motion modes are associated with the asymmetric motion of particles close to the side wall in one oscillation cycle, where the dependence of particle velocity on the local density plays a key role.

Geometric frustration induces the transition between rotation and counterrotation in swirled granular media

Granular material in a swirled container exhibits a curious transition as the number of particles is increased: At low densities, the particle cluster rotates in the same direction as the swirling motion of the container, while at high densities it rotates in the opposite direction. We investigate this phenomenon experimentally and numerically using a corotating reference frame in which the system reaches a statistical steady state. In this steady state, the particles form a cluster whose translational degrees of freedom are stationary, while the individual particles constantly circulate around the cluster's center of mass, similar to a ball rolling along the wall within a rotating drum. We show that the transition to counterrotation is friction dependent. At high particle densities, frictional effects result in geometric frustration, which prevents particles from cooperatively rolling and spinning. Consequently, the particle cluster rolls like a rigid body with no-slip conditions on the container wall, which necessarily counterrotates around its own axis. Numerical simulations verify that both wall-disk friction and disk-disk friction are critical for inducing counterrotation.

Granular self-organization by autotuning of friction

A monolayer of granular spheres in a cylindrical vial, driven continuously by an orbital shaker and subjected to a symmetric confining centrifugal potential, self-organizes to form a distinctively asymmetric structure which occupies only the rear half-space. It is marked by a sharp leading edge at the potential minimum and a curved rear. The area of the structure obeys a power-law scaling with the number of spheres. Imaging shows that the regulation of motion of individual spheres occurs via toggling between two types of motion, namely, rolling and sliding. A low density of weakly frictional rollers congregates near the sharp leading edge whereas a denser rear comprises highly frictional sliders. Experiments further suggest that because the rolling and sliding friction coefficients differ substantially, the spheres acquire a local time-averaged coefficient of friction within a large range of intermediate values in the system. The various sets of spatial and temporal configurations of the rollers and sliders constitute the internal states of the system. Experiments demonstrate and simulations confirm that the global features of the structure are maintained robustly by autotuning of friction through these internal states, providing a previously unidentified route to self-organization of a many-body system.

Order-disorder transition in swirled granular disks

We study the order-disorder transition of horizontally swirled dry and wet granular disks by means of computer simulations. Our systematic investigation of the local order formation as a function of amplitude and period of the external driving force shows that a large cluster of hexagonally ordered particles forms for both dry and wet granular particles at intermediate driving energies. Disordered states are found at small and large driving energies. Wet granular particles reach a higher degree of local hexagonal order with respect to the dry case. For both cases we report a qualitative phase diagram showing the amount of local order at different state points. Furthermore, we find that the transition from hexagonal order to a disordered state is characterized by the appearance of particles with square local order.

On-off intermittency and intermingledlike basins in a granular medium

Molecular dynamic simulations of a medium consisting of disks in a periodically tilted box yield two dynamic modes differing considerably in the total potential and kinetic energies of the disks. Depending on parameters, these modes display the following features: (i) hysteresis (coexistence of the two modes in phase space); (ii) intermingledlike basins of attraction (uncertainty exponent indistinguishable from zero); (iii) two-state on-off intermittency; and (iv) bimodal velocity distributions. Bifurcations are defined by a cross-shaped phase diagram.

Segregation in granular matter under horizontal swirling excitation

A segregation phenomenon in a horizontally vibrated monolayer of granular matter is studied experimentally. In a binary mixture of small spheres and larger disks, the collapse speed of the disks increases dramatically with increasing granular temperature. The scaling behavior can be understood by applying arguments from kinetic gas theory.

Intermingled basins due to finite accuracy

We investigate numerically first a chaotic map interrupted by two small neighborhoods, each containing an attracting point, and secondly a periodically tilted box within which disorderly colliding disks can reach different attracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leading to one attractor contains points leading to the other attractor. A bifurcation destabilizing the fixed points or the disk configurations causes on-off intermittency; the disks then alternate between a "frozen" and a gaslike state.