4/3-Law of Granular Particles Flowing through a Vertical Pipe

Abstract

Density waves of granular material (sand) flowing through a vertical pipe have been investigated. Clear density waves emerge when the cock attached to bottom end of the pipe is closed. The FFT power spectra were found to show a stable power-law form $P(f)\sim f^{-\alpha }.$ The value of the exponent was evaluated as $\alpha \cong 4/3$. We also introduce a simple one-dimensional model which reproduces $\alpha =4/3$ from both simulation and theoretical analysis. (to be published in Phys.Rev.Lett.)

4 pages, 4 figures, a style file

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