Ratcheting and transitions: short granular chain in a gradient of vibration

Self-propulsion of a grain-filled dimer in a vertically vibrated channel

Steady dissipation of energy is a crucial property that distinguishes active particles from Brownian particles. However, it is not straightforward to explicitly model the dissipative property of existing active particles driven by a vibrating plate. We present a novel active particle that can be explicitly modeled by Newtonian dynamics of a conservative force field plus two asymmetrical dissipative terms. The particle is a dimer consisting of two ping-pong balls connected by a rigid rod, and its two balls are filled with granular particles of the same total mass but of different grain size. This dimer placed on a vibrating plate exhibits 3 types of motion – by tuning the frequency and the amplitude of the vibration, the dimer undergoes either a directed motion toward the small (or large) grain-filled side or an unbiased random motion. We investigate the various modes of motion both experimentally and numerically and show that the directed motion is a result of the asymmetric damping due to the size difference in the filling grains. Furthermore, the numerical simulation reveals that the dimer’s dynamics in either directed motion mode resembles a limit cycle attractor that is independent of its initial condition.

Translocation of a granular chain in a horizontally vibrated saw-tooth channel

We study the translocation mechanism of a granular chain in a horizontally vibrated saw-tooth channel using MD simulations and macro-scale experiments and show that the translocation speed is independent of the chain length as long as the chain length is larger than the spatial period of the saw-tooth. With the help of simulation, we explore the effect of geometry of the container and frequency and amplitude of vibration as well as chain flexibility on the chain drift speed. We observe that the most efficient transport is achieved when one of the channel walls is shifted with respect to the other wall by an amount equal to half the spatial period of the saw-tooth. We define a persistence length for the chain and show that the translocation speed depends on the ratio of persistence length over the spatial period of the saw-tooth. The optimum translocation occurs when this ratio is about 0.4. We also determine the optimum saw-tooth angle for the translocation of the chain as well as the optimum distance between the two walls. Some properties of this system are similar to those of polymer systems.

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.