Diffusion in stochastic sandpiles

• Published in: The European physical journal. B, Condensed matter physics Vol. 72; no. 3; pp. 441 - 449
• Main Authors: da Cunha, S. D., Vidigal, R. R., da Silva, L. R., Dickman, R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-12-2009; EDP Sciences
• Subjects: Classical transport; Complex Systems; Computational methods in statistical physics and nonlinear dynamics; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Solid State Physics; Statistical and Nonlinear Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Stochastic analysis methods (fokker-planck, langevin, etc.); Transport processes; System Size; Particle Density; Universality Class; Activity Density; Discrete Fourier Transform; Sandpile models; Stochastic model; Root mean square displacement; Asymptotic behavior; Scaling laws; Series expansion; Collective process; Order parameters; Diffusion coefficient; Diffusion; Critical phenomena
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2009-00367-0

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is possible, but with a narrow scaling region. We also develop a series expansion, in inverse powers of the density, for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with n particles is n(n-1), and compare the theoretical prediction with simulation results.