From waves to avalanches: two different mechanisms of sandpile dynamics

Prior research has shown that sandpile models exhibit self-organized criticality through avalanches. Established knowledge includes the Bak-Tang-Wiesenfeld model's behavior in two dimensions. No prior work had resolved how wave decomposition affects correlation patterns. This gap motivated a closer look at temporal coarse graining effects. The Manna model's role in sandpile dynamics remains less understood. Existing studies focus on finite size scaling and multifractal properties. Little is known about how wave and avalanche dynamics differ in these systems. This paper's contribution is to clarify these distinct correlation patterns.

The aim is to distinguish two mechanisms of sandpile dynamics using wave decomposition. The specific problem involves analyzing how correlation patterns differ between avalanche and wave dynamics. This study seeks to clarify the role of long-range correlations in the Bak-Tang-Wiesenfeld model. The motivation stems from the lack of clarity in how these dynamics relate in different dimensions. The researchers propose that wave decomposition can reveal distinct scaling behaviors. They also aim to compare the Manna model's properties with those of the Bak-Tang-Wiesenfeld model. The study's focus is on temporal coarse graining effects and their impact on scaling. The ultimate goal is to better understand sandpile dynamics in two and three dimensions.

The researchers used time series analysis to decompose avalanches into waves. They applied coarse graining in time to assess how wave size distributions change. Multifractal scaling was calculated to evaluate avalanche properties in the Bak-Tang-Wiesenfeld model. The Manna model was analyzed for avalanche and wave distribution equivalence. Finite size scaling was tested to determine if wave correlations exist. The study compared results from two- and three-dimensional systems. Statistical methods were used to quantify correlation patterns. The approach allowed for a direct comparison between the two sandpile models.

The Bak-Tang-Wiesenfeld model shows long-range correlations affecting wave size distribution. Multifractal scaling was observed in avalanches for this model in two dimensions. Coarse graining in time modifies the wave size distribution in this system. In contrast, the Manna model's avalanche and wave distributions are identical. Waves in the Manna model are uncorrelated and follow finite size scaling. The results suggest distinct mechanisms for wave and avalanche dynamics. The Bak-Tang-Wiesenfeld model's behavior differs from the Manna model's in this regard. These findings support the hypothesis of two separate dynamical mechanisms.

The authors propose that two distinct mechanisms govern sandpile dynamics in the models studied. The Bak-Tang-Wiesenfeld model exhibits multifractal scaling due to long-range correlations. The Manna model's avalanches and waves are indistinguishable and uncorrelated. These results suggest different statistical properties for each model's dynamics. The findings imply that wave decomposition can reveal underlying correlation patterns. The study supports the idea that sandpile models can be classified by their scaling behaviors. The authors suggest that these differences may reflect deeper structural properties. Their conclusion is that wave and avalanche dynamics are not always equivalent in sandpile systems.