Visualization of collisional substructure in granular shock waves

Rescaling invariance and anomalous energy transport in a small vertical column of grains

It is well known that energy dissipation and finite size can deeply affect the dynamics of granular matter, often making usual hydrodynamic approaches problematic. Here we report on the experimental investigation of a small model system, made of ten beads constrained into a 1D geometry by a narrow vertical pipe and shaken at the base by a piston excited by a periodic wave. Recording the beads motion with a high frame rate camera allows to investigate in detail the microscopic dynamics and test hydrodynamic and kinetic models. Varying the energy, we explore different regimes from fully fluidized to the edge of condensation, observing good hydrodynamic behavior down to the edge of fluidization, despite the small system size. Density and temperature fields for different system energies can be collapsed by suitable space and time rescaling, and the expected constitutive equation holds very well when the particle diameter is considered. At the same time, the balance between dissipated and fed energy is not well described by commonly adopted dependence due to the up-down symmetry breaking. Our observations, supported by the measured particle velocity distributions, show a different phenomenological temperature dependence, which yields equation solutions in agreement with experimental results.

Nonvibrating granular model for a glass-forming liquid: Equilibration and aging

We studied experimentally a model of a glass-forming liquid on the basis of a nonvibrating magnetic granular system under an unsteady magnetic field. A sudden quenching was produced that drove the system from a liquid state to a different final state with lower temperature; the latter could be a liquid state or a solid state. We determined the mean-squared displacement in temporal windows to obtain the dynamic evolution of the system, and we determined the radial distribution function to obtain its structural characteristics. The results were analyzed using the intermediate scattering function and the effective potential between two particles. We observed that when quenching drives the system to a final state in the liquid phase far from the glass-transition temperature, equilibration occurs very quickly. When the final state has a temperature far below the glass-transition temperature, the system reaches its equilibrium state very quickly. In contrast, when the final state has an intermediate temperature but is below that corresponding to the glass transition, the system falls into a state that evolves slowly, presenting aging. The system evolves by an aging process toward more ordered states. However, after a waiting time, the dynamic behavior changes. It was observed that some particles get close enough to overpass the repulsive interactions and form small stable aggregates. In the effective potential curves, it was observed that the emergence of a second effective well due to the attraction quickly evolves and results in a deeper well than the initial effective well due to the repulsion. With the increase in time, more particles fall in the attractive well forming inhomogeneities, which produce a frustration in the aging process.

Short granular chain under vibration: Spontaneous switching of states

We study experimentally a short chain of N(≤8) loosely connected spheres bouncing against a horizontal surface that vibrates sinusoidally at intensity Γ. Distinct states are identified: a base state of uniform bouncing in-sync with the substrate prevails at low values of Γ, whereas increasing Γ can induce transitions to two excited states with appreciable storage of energy around one or both ends of the chain. We find that, in a transitional window of Γ, the chain can even switch spontaneously among states, resolving the mystery why different modes of motion can be initiated at the same position in our previous work along a gradient of vibration [Phys. Rev. Lett. 112, 058001 (2014)]. Preliminary interpretations on the parametric dependences and the optimal frequency window for seeing these transitions are offered, based on the microscopic and statistical evidence in our experiments up to date.

Simulations of granular gravitational collapse

A freely cooling granular gas in a gravitational field undergoes a collapse to a multicontact state in a finite time. Previous theoretical [D. Volfson et al., Phys. Rev. E 73, 061305 (2006)] and experimental work [R. Son et al., Phys. Rev. E 78, 041302 (2008)] have obtained contradictory results about the rate of energy loss before the gravitational collapse. Here we use a molecular dynamics simulation in an attempt to recreate the experimental and theoretical results to resolve the discrepancy. We are able to nearly match the experimental results, and find that to reproduce the power law predicted in the theory we need a nearly elastic system with a constant coefficient of restitution greater than 0.993. For the more realistic velocity-dependent coefficient of restitution, there does not appear to be a power-law decay and the transition from granular gas to granular solid is smooth, making it difficult to define a time of collapse.

The origin of granular convection in vertically vibrated particle beds: The differential shear flow field

This paper investigates the particle scale dynamics of granular convection in vertically vibrated granular beds. The onset of the convection is found to coincide with the noticeable particle transverse migrations from the side walls towards the centre of the bed, which only take place in the wake of the gravity wave front dividing the upward moving particles and the falling ones. The mechanism driving the particle inward flows and thus sustaining the complete convection rolls can be understood in light of a convection model based on void penetration. This stochastic convection model reveals that the underlying driving force is a distinctive differential shear flow field arising from the combined effect of frictional holdback by the walls and the downward pull of gravity. The changes of the convection pattern with inceasing acceleration amplitude, in terms of the convection strength and the thickness of the bottom of the convection rolls, can be accounted for by this model.

Spherical shock-wave propagation in three-dimensional granular packings

We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.