Avalanches on a conical bead pile: scaling with tuning parameters
Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law described the avalanche size distribution as predicted by se...
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Zusammenfassung: | Uniform spherical beads were used to explore the behavior of a granular
system near its critical angle of repose on a conical bead pile. We found two
tuning parameters that could take the system to a critical point where a simple
power-law described the avalanche size distribution as predicted by
self-organized criticality, which proposed that complex dynamical systems
self-organize to a critical point without need for tuning. Our distributions
were well described by a simple power-law with the power {\tau} = 1.5 when
dropping beads slowly onto the apex of a bead pile from a small height.
However, we could also move the system from the critical point using either of
two tuning parameters: the height from which the beads fell onto the top of the
pile or the region over which the beads struck the pile. As the drop height
increased, the system did not reach the critical point yet the resulting
distributions were independent of the bead mass, coefficient of friction, or
coefficient of restitution. All our apex-dropping distributions for any type of
bead (glass, stainless steel, zirconium) showed universality by scaling onto a
common curve with {\tau} = 1.5 and {\sigma} = 1.0, where 1/{\sigma} is the
power of the tuning parameter. From independent calculations using the moments
of the distribution, we find values for {\tau} = 1.6 \pm 0.1 and {\sigma} =
0.91 \pm 0.15. When beads were dropped across the surface of the pile instead
of solely on the apex, then the system also moved from the critical point and
again the avalanche size distributions fell on a common curve when scaled
similarly using the same values of {\tau} and {\sigma}. We also observed that
an hcp structure on the base of the pile caused an emergent structure in the
pile that had six faces with some fcc or hcp structure. |
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DOI: | 10.48550/arxiv.1201.0528 |