SINGULAR DIFFUSION LIMITS OF A CLASS OF REVERSIBLE SELF-ORGANIZING PARTICLE-SYSTEMS

We establish hydrodynamic limits for a class of attractive, reversible particle systems with an infinite range of interaction. The limiting nonlinear diffusion equations have diffusion coefficients which are fu nctions of the local density, and which have a singularity at a critic al value of the density. On open driven systems, these singular diffus ion limits explain the observed nontrivial scaling behavior known as s elf-organized criticality.