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Register a new userCollective motion of granular matter subjected to swirling excitation
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A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes depending on the strength of the oscillation and the global packing density. For intermediate packing density and oscillation amplitude, a high density phase travels along the containers side wall in clockwise direction, while the oscillation itself is anti-clockwise. Further increasing packing density towards the hexagonal packing, the whole packing rotates collectively in 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.
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We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular fashion at the driving frequency, even exceeds the speed of driving. It turns out that the observed clustering is due to the formation of density wave. The analysis of a phenomenological model shows that the instability of the uniform density profile arises by increasing the oscillation amplitude and captures the non-monotonic dependence of the transition amplitude of the clustering on the global density of the system. Here, the key ingredient is that the velocity of individual grains increases with the local density. The interplay of dissipative particle-particle interaction and the frictional driving of the substrate results into this dependence, which is tested with discrete element method simulations.
We analyze a recent experiment [Phys. Rev. Lett., {bf103}, 224501 (2009)] in which the shock, created by the impact of a steel ball on a flowing monolayer of glass beads, is quantitatively studied. We argue that radial momentum is conserved in the process, and hence show that in two dimensions the shock radius increases in time $t$ as a power law $t^{1/3}$. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction, and is shown to compare well at intermediate times. At late times, the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to accumulation of particles at the shock front, and propose a simple hard sphere model which incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.
Recent experiments with rotational diffusion of a probe in a vibrated granular media revealed a rich scenario, ranging from the dilute gas to the dense liquid with cage effects and an unexpected superdiffusive behavior at large times. Here we setup a simulation that reproduces quantitatively the experimental observations and allows us to investigate the properties of the host granular medium, a task not feasible in the experiment. We discover a persistent collective rotational mode which emerges at high density and low granular temperature: a macroscopic fraction of the medium slowly rotates, randomly switching direction after very long times. Such a rotational mode of the host medium is the origin of probes superdiffusion. Collective motion is accompanied by a kind of dynamical heterogeneity at intermediate times (in the cage stage) followed by a strong reduction of fluctuations at late times, when superdiffusion sets in.
The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently fluidized by a vertical shaker, acting as a heat bath for the Brownian-like motion of the probe. Two ball bearings supporting the probe exert nonlinear Coulomb friction upon it. The experimental velocity distribution of the probe, autocorrelation function, and power spectra are compared with the predictions of a linear Boltzmann equation with friction, which is known to simplify in two opposite limits: at high collision frequency, it is mapped to a Fokker-Planck equation with nonlinear friction, whereas at low collision frequency, it is described by a sequence of independent random kicks followed by friction-induced relaxations. Comparison between theory and experiment in these two limits shows good agreement. Deviations are observed at very small velocities, where the real bearings are not well modeled by Coulomb friction.
When dense granular systems are exposed to external forcing, they evolve on the time scale that is typically related to the externally imposed one (shear or compression rate, for example). This evolution could be characterized by observing temporal evolution of contact networks. However, it is not immediately clear whether the force networks, defined on contact networks by considering force interactions between the particles, evolve on a similar time scale. To analyze the evolution of these networks, we carry out discrete element simulations of a system of soft frictional disks exposed to compression that leads to jamming. By using the tools of computational topology, we show that close to jamming transition, the force networks evolve on the time scale which is much faster than the externally imposed one. The presentation will discuss the factors that determine this fast time scale.
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