2000/05/31 by Maya Paczuski, Kevin E. Bassler · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Abelian sandpile model #Amplitude #Complex Systems and Time Series Analysis #Computer science #Critical phenomena #Criticality #Granularity #Langevin equation #Mathematical physics #Mathematics #Phase transition #Physics #Quantum mechanics #Renormalization group #Self-organized criticality #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.62.5347
7 pages, 1 included figure. Some typos fixed and minor changes made. To appear in Phys. Rev. E
arxiv created 2000/08/11 · openalex publication_date 2000/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study a directed stochastic sandpile model of self-organized criticality, which exhibits multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Using this fact, we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing avalanches. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies.