Emergence of order in an oscillated granular layer

Our experiments on a vertically oscillated granular layer reveal that spatial patterns emerge in two stages following a change of parameter into the pattern-forming regime: an initial, domain-forming stage and a later stage in which domains coarsen to form ultimately an extended regular pattern. We characterize the evolution of the pattern using a “disorder function” δ̄(β), where β is a moment of the disorder operator (Gunaratne et al., Phys. Rev. E 57 (1998) 5146). The disorder in the initial stage is found to be consistent with a decay given by δ̄(β)∼t−β/2, in accord with theory that predicts that behavior in this stage should be universal for pattern forming systems. The final stage is non-universal.