On the Shape of the Tail of a Two Dimensional Sand Pile

TL;DR

This paper investigates the shape of the tail of a two-dimensional sand pile, showing it has a logarithmic correction to the slope, supported by theory, experiments, and cellular automaton simulations.

Contribution

It introduces a theoretical model and cellular automaton simulation that accurately predict the tail shape of a granular heap, including a logarithmic correction.

Findings

The tail adds a logarithmic correction to the slope.

The theoretical prediction matches experimental results.

Cellular automaton simulations confirm the shape prediction.

Abstract

We study the shape of the tail of a heap of granular material. A simple theoretical argument shows that the tail adds a logarithmic correction to the slope given by the angle of repose. This expression is in good agreement with experiments. We present a cellular automaton that contains gravity, dissipation and surface roughness and its simulation also gives the predicted shape.