Directed Abelian sandpile with multiple downward neighbors
نویسندگان
چکیده
منابع مشابه
Directed Abelian sandpile with multiple downward neighbors.
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors per site, K>2. The K=3 case is solved exactly, which extends the earlier known solution for the K=2 case. For K>2, the avalanche clusters can have holes and side branches and are thus qualitatively different from the K=2 case where avalanche clusters are compact. However, we find that the critical expone...
متن کاملAsymmetric Abelian Sandpile Models
In the Abelian sandpile models introduced by Dhar, long-time behavior is determined by an invariant measure supported uniformly on a set of implicitly defined recurrent configurations of the system. Dhar proposed a simple procedure, the burning algorithm, as a possible test of whether a configuration is recurrent, and later with Majumdar verified the correctness of this test when the toppling r...
متن کاملConvergence of the Abelian Sandpile
The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice Zd, in which sites with at least 2d chips topple, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of n chips placed at a single vertex, the rescaled stable configuration seems ...
متن کاملTwo-component Abelian sandpile models.
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models wi...
متن کاملUniversality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the ab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2016
ISSN: 2470-0045,2470-0053
DOI: 10.1103/physreve.93.042107