We investigate the behavior of a two-state sandpile model subjected to a
confining potential in one and two dimensions. From the microdynamical
description of this simple model with its intrinsic exclusion mechanism, it is
possible to derive a continuum nonlinear diffusion equation that displays
singularities in both the diffusion and drift terms. The stationary-state
solutions of this equation, which maximizes the Fermi-Dirac entropy, are in
perfect agreement with the spatial profiles of time-averaged occupancy obtained
from model numerical simulations in one as well as in two dimensions.
Surprisingly, our results also show that, regardless of dimensionality, the
presence of a confining potential can lead to the emergence of typical
attributes of critical behavior in the two-state sandpile model, namely, a
power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure
