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

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Poghosyan, Su S. Poghosyan, Vahagn S. Priezzhev, Vyacheslav B. Ruelle, Philippe [UCL]

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) h0. During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density ρc(h0), the system changes its behavior and relaxes exponentially to the stationary state of the ASM with densityρs.Consideringinitialheights−1􏰁h0 􏰁4,weobserveadramaticdecreaseofthedifferenceρc(h0)−ρs when h0 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 ρth(h0) of the FES converges rapidly to ρs for h_0 <1.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2011
Language Anglais
Journal information "Physical Review E, Statistical, Nonlinear, and Soft Matter Physics" - Vol. 84, no.6, p. 066119 (2011)
Peer reviewed yes
Publisher American Physical Society (Maryland)
issn 1539-3755
e-issn 1550-2376
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords sandpile model
Links
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Bibliographic reference Poghosyan, Su S. ; Poghosyan, Vahagn S. ; Priezzhev, Vyacheslav B. ; Ruelle, Philippe. Numerical study of the correspondence between the dissipative and fixed-energy Abelian sandpile models. In: Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 84, no.6, p. 066119 (2011)
Permanent URL http://hdl.handle.net/2078.1/216901