Particle-hole symmetry in a sandpile model

Abstract

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.

arXiv commentFour pages, our figures

References in corpus (5)

• Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
• Rare events and breakdown of simple scaling in the Abelian sandpile
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Studying Self-Organized Criticality with Exactly Solved Models
• Avalanche Merging and Continuous Flow in a Sandpile Model

Cited by in corpus (3)

• Multiple and inverse topplings in the Abelian Sandpile Model
• Invasion Sandpile Model
• Freezing transitions in non-Fellerian particle systems