SELF-ORGANIZED CRITICAL SCALING AT SURFACES

At dissipative boundaries, models of self-organized criticality show peculiar scalings, different from the bulk ones, in the distributions characterizing avalanches. For Abelian models with Dirichlet boundary conditions, evidence of this is obtained by a mean field approach to semi-infinite sandpiles, and by numerical simulations in two and three dimensions. On the other hand, within the mean field description, closed Neumann conditions restore bulk scaling exponents also at the border. Numerical results are consistent with this property also at finite d.