Numerical study of the correspondence between the dissipative and fixed-energy Abelian sandpile models

作者：Poghosyan Su S^*; Poghosyan V S; Priezzhev V B; Ruelle P

来源：Physical Review E, 2011, 84(6): 066119.

DOI：10.1103/PhysRevE.84.066119

We consider the Abelian sandpile model (ASM) on the square lattice with a single dissipative site (sink). Particles are added one by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) h(0). During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density rho(c)(h(0)), the system changes its behavior and relaxes exponentially to the stationary state of the ASM with density rho(s). Considering initial heights-1 <= h(0) <= 4, we observe a dramatic decrease of the difference rho(c) (h(0)) - rho(s) when h(0) is zero or negative. In parallel with the ASM, we consider the conservative fixed energy sandpile (FES). The extensive Monte Carlo simulations show that the threshold density rho(th)(h(0)) of the FES converges rapidly to rho s for h(0) < 1.

• 出版日期2011-12-27