Dr. Norihiro Oyama, 31 Jan 2019

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Speaker: Dr. Oyama (MathAM-OIL)

Title: Avalanche Interpretation of the Power-law of the Energy Spectrum in Three-Dimensional Dense Granular Flow

Abstract:
Molecular dynamics simulations on dense granular packings under a very slow simple shear flow have revealed that the statistical properties of the non-affine velocity field are consistent with those of classical turbulence of viscous fluid. However, such observations have been limited to two-dimensional systems and knowledge about three dimensional systems is still missing[1]. In this work[2], we conducted direct numerical simulations on three-dimensional dense granular flow and found that the statistical property is not turbulent-like in three dimension.
We propose a new understanding from the perspective of avalanche dynamics. This interpretation can explain the power law behavior of energy spectra both in two and three dimension, although the turbulent- like interpretation is valid only in two dimension. Furthermore, we analyzed the spatial structures of collectively moving particles by looking at the vorticity field. Although the system does not show the turbulent-like behavior in three dimension, the structural analysis based on the vorticity field allows us to extract a diverging length scale which a conventional simple spatial correlation function cannot detect.

[1] F. Radjai, and S. Roux, Phys. Rev. Lett. 89, 064302 (2002).
K. Saitoh, and H. Mizuno, Soft Matter 12, 1360 (2016).
[2] N. Oyama, H. Mizuno, and K. Saitoh, arXiv: 1805.05449 (2018).

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