A Quantitative Description of the Relaxation of Textured Patterns

A characterization of textured patterns, referred to as the disorder function δ(β), is used to study the dynamics of patterns generated in the Swift-Hohenberg equation (SHE). The evolution of random initial states under the SHE exhibits two stages of relaxation. The initial phase, where local striped domains emerge from a noisy background, is quantified by a power law decay δ(β) ~t-1/2 Beyond a sharp transition a slower power law decay of δ(β), which corresponds to the coarsening of striped domains, is observed. The transition between the phases advances as the system is driven further from the onset of patterns, and suitable scaling of time and δ(β) leads to the collapse of distinct curves.