Three-parameter model of a sand pile

TL;DR

This paper develops a Lorenz-based three-parameter model for a sand pile, analyzing steady-state avalanche formation, and explores how noise influences avalanche domains and sand velocity behaviors.

Contribution

It introduces a novel three-parameter Lorenz model for sand pile avalanches, incorporating noise effects to better understand avalanche conditions.

Findings

Stationary sand velocity and slope depend on external parameters.

Noise intensity critically affects avalanche domain boundaries.

Vertical velocity noise significantly influences avalanche occurrence.

Abstract

The theory of a flux steady-state (avalanche) formation is presented for the simplest model of a real sand pile within the framework of Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of controlling parameter (externally driven sandpile slope). The additive noises of above values are taken into account to build the phase diagram, where the noise intensities determine a domain of the avalanche appearance. This domain shows to be crucial to the noise intensity of vertical component of sand velocity.