Time Dependent Behavior of Granular Material in a Vibrating Box

TL;DR

This study investigates the time-dependent behavior of granular materials in a vibrating box using numerical simulations and kinetic theory, revealing discrepancies between theoretical predictions and observed localized particle movements.

Contribution

The paper compares molecular dynamics simulations with kinetic theory predictions, highlighting the limitations of the theory in capturing localized particle dynamics.

Findings

Pressure and height fluctuations scale with A f

Velocity and temperature fluctuations do not scale simply

Active particle regions are localized and propagate like sound waves

Abstract

Using numerical and analytic methods, we study the time dependent behavior of granular material in a vibrating box. We find, by molecular dynamics simulation, that the temporal fluctuations of the pressure and the height expansion scale in $A f$, where $A$ ($f$) is the amplitude (frequency) of the vibration. On the other hand, the fluctuations of the velocity and the granular temperature do not scale in any simple combination of $A$ and $f$. Using the kinetic theory of Haff, we study the temporal behaviors of the hydrodynamic quantities by perturbing about their time averaged values in the quasi-incompressible limit. The results of the kinetic theory disagree with the numerical simulations. The kinetic theory predicts that the whole material oscillates roughly as a single block. However, the numerical simulations show that the region of active particle movement is localized and moves with time, behavior very similar to the propagation of a sound wave.