Continuous Abelian Sandpile Model in Two Dimensional Lattice

2007/10/17 by N. Azimi-Tafreshi, E. Lotfi, El Mehdi Lotfi +5
Engineering · Environmental Science · Physics and Astronomy · #FOS: Physical sciences #Landslides and related hazards #Soil and Unsaturated Flow #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.0710.3292

10 Pages, 5 Figures

openalex publication_date 2007/10/17 · arxiv created 2007/10/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as effect of very small mass on the height probabilities, different boundary conditions, etc.

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