The wiper model: avalanche dynamics in an exclusion process

The exclusion-process model (Ciandrini et al 2010 Phys. Rey. E 81 051904) describing traffic of particles with internal stepping dynamics reveals the presence of strong correlations in realistic regimes. Here we study such a model in the limit of an infinitely fast translocation time, where the evolution can be interpreted as a 'wiper' that moves to dry neighbouring sites. We trace back the existence of long-range correlations to the existence of avalanches, where many sites are dried at once. At variance with self-organized criticality, in the wiper model avalanches have a typical size equal to the logarithm of the lattice size. In the thermodynamic limit, we find that the hydrodynamic behaviour is a mixture of stochastic (diffusive) fluctuations and increasingly coherent periodic oscillations that are reminiscent of a collective dynamics.