Long-range effects in granular avalanching

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Granular materials exhibit complex dynamics, including avalanche events.
• Experimental observations in rice piles show crossovers between power law and stretched exponential behaviors.

Purpose of the Study:

• To introduce a model for granular flow in a one-dimensional rice pile.
• To incorporate long-range rolling effects of individual grains into the model.
• To explain the observed crossover in granular dynamics.

Main Methods:

• Developed a model for granular flow incorporating grain rolling probability proportional to r(-rho).
• Analyzed the exponent rho's control over average rolling distance.
• Investigated the relationship between rho and avalanche distribution behaviors.

Main Results:

• The model successfully describes the crossover from power law to stretched exponential behaviors.
• Stretched exponential avalanche distributions are linked to a long-range regime (1
• Power law distributions are associated with a short-range regime (rho>2).

Conclusions:

• The crossover in granular dynamics is attributed to long-range effects and altered grain transport properties.
• The exponent rho dictates whether average rolling distance scales with system size.
• The model provides a framework for understanding avalanche dynamics in granular media.