Vertically-Vibrated Granular Chains

Experimental apparatus & Some Movies

The apparatus consists of a mechanical shaker driving a a flat plate via a square-air bearing shaft. The large aluminum pieces help to vibration isolate the plate from the shaker except through the direct coupling of the shaft. The plate is anodized aluminum that is thicker in the middle and tapered towards the edges with numerous holes machined from the bottom to minimize weight but maximize plate stiffness. An accelerometer measures the instantaneous vertical acceleration of the plate.

Viewed from the side at high speed, vertical motion is generated by a complex collision process between the chain and the plate and, on faster time scales, between balls on the chain:

Movie (side motion fast)

A simple knot place at the center of a chain and vibrated at about 2 g will diffuse along the length of the chain and become unknotted. Details and theoretical modeling are presented in Ben Naim et al, PRL (2001). Here the dynamics of this process are presented:

Movie (unknotting dynamics)

At slightly lower vertical acceleration, we consider the motion of a figure eight configuration. The motion is seen at close to the drive frequency of 15 Hz and at high speed to elucidate the hopping motion. The dynamics of the figure eight roughly obeys detailed balance but the non-equilibrium state of the system is measureable in small deviations from detailed balance, see M. Hastings et al, PRE (2002):

Movie (slow time scale)

Movie (fast time scale)

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