Critical density of the Abelian Manna model via a multitype branching process.
basic_science · Level V
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- Record sourced from PubMed, PMID 31639922.
- Also identified by DOI 10.1103/PhysRevE.100.032116.
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Abstract
A multitype branching process is introduced to mimic the evolution of the avalanche activity and determine the critical density of the Abelian Manna model. This branching process incorporates partially the spatiotemporal correlations of the activity, which are essential for the dynamics, in particular in low dimensions. An analytical expression for the critical density in arbitrary dimensions is derived, which significantly improves the results over mean-field theories, as confirmed by comparison to the literature on numerical estimates from simulations. The method can easily be extended to lattices and dynamics other than those studied in the present work.