Singular diffusion and criticality in a confined sandpile
arXiv:1404.0632 · doi:10.1209/0295-5075/109/14007
Abstract
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.
arXiv comment5 pages, 5 figures
References in corpus (12)
- Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
- Thermostatistics of overdamped motion of interacting particles
- Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
- Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
- Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
- Escape time in anomalous diffusive media
- Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums
- Flux front penetration in disordered superconductors
- N-dimensional nonlinear Fokker-Planck equation with time-dependent coefficients
- Superfast non-linear diffusion: Capillary transport in particulate porous media
- Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation
- Nonlinear diffusion effects on biological population spatial patterns