Propagative mode in a lattice-grain ca: Time evolution and timestep synchronization

Abstract

The void propagation defines a long-range interaction in granular matter. We detail a logic scheme simulating the propagation and implemented in a 2d cellular automata applied to granular flow. The CA belongs to the family of lattice-grain automata (LGrA) with one particle per cell. We focus first on the influence of inertia, or memory effect, on the flow patterns. The propagative mode is presented afterwards: it implies that transition and timestep must be considered at two different time scales. Although a CA is usually driven by local, nearest-neighbor communications, it follows here that the timestep termination must be detected at each transition, that involves a perpetual and global communication within the network to synchronize the timestep. An all-to-all systolic gossiping underlies the framework of this void propagation model. © 2012 Springer-Verlag Berlin Heidelberg.