Relaxation Dynamics of a Granular Pile on a Vertically-Vibrating Plate

TL;DR

This study investigates the nonlinear relaxation behavior of a granular pile under vertical vibration, modeling the process with a nonlinear transport law and demonstrating its potential relevance to astrophysical phenomena.

Contribution

The paper introduces a nonlinear transport law model for granular pile relaxation and shows that the relaxation efficiency parameter remains constant across different conditions.

Findings

The relaxation efficiency is a constant independent of experimental conditions.

The model accurately reproduces the relaxation dynamics.

Application potential to astrophysical phenomena is demonstrated.

Abstract

Nonlinear relaxation dynamics of a vertically-vibrated granular pile is experimentally studied. In the experiment, the flux and slope on the relaxing pile are measured by using a high-speed laser profiler. The relation of these quantities can be modeled by the nonlinear transport law assuming the uniform vibro-fluidization of an entire pile. The fitting parameter in this model is only the relaxation efficiency, which characterizes the energy conversion rate from vertical vibration into horizontal transport. We demonstrate that this value is a constant independent of experimental conditions. The actual relaxation is successfully reproduced by the continuity equation with the proposed model. Finally its specific applicability toward an astrophysical phenomenon is shown.