Pattern formation in growing sandpiles with multiple sources or sinks

DOI10.1007/s10955-009-9901-3zbMath1187.82077arXiv0909.3192OpenAlexW1980498361MaRDI QIDQ963318

Deepak Dhar, Tridib Sadhu

Publication date: 19 April 2010

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3192

zbMATH Keywords

pattern formationself-organized criticality

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20)

Related Items (16)

The Apollonian structure of integer superharmonic matrices ⋮ Apollonian structure in the abelian sandpile ⋮ A growth model based on the arithmetic \(Z\)-game ⋮ Scaling and complex avalanche dynamics in the abelian sandpile model ⋮ Integer superharmonic matrices on the \(F\)-lattice ⋮ The spectrum of the abelian sandpile model ⋮ A sandpile model for proportionate growth ⋮ Proportionate growth in patterns formed in the rotor-router model ⋮ Scaling Limit for a Long-Range Divisible Sandpile ⋮ Pattern formation in growing sandpiles with multiple sources or sinks ⋮ Sandpiles and dominos ⋮ Cut-off for sandpiles on tiling graphs ⋮ Abelian Networks I. Foundations and Examples ⋮ Fast Simulation of Large-Scale Growth Models ⋮ Abelian Logic Gates ⋮ Stability of patterns in the abelian sandpile

Cites Work

• Scaling limits for internal aggregation models with multiple sources
• Discrete holomorphicity at two-dimensional critical points
• Pattern formation in growing sandpiles with multiple sources or sinks
• On the identity of the sandpile group
• Patterns formed by addition of grains to only one site of an Abelian sandpile
• Internal DLA and the Stefan problem.
• Limiting shapes for deterministic centrally seeded growth models
• A Finite-Difference Approximation of a Two-Layer System for Growing Sandpiles
• Spherical asymptotics for the rotor-router model in $\mathbb{Z}^d$
• Explicit characterization of the identity configuration in an Abelian sandpile model
• Discrete Riemann surfaces and the Ising model.
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