Emergence of order in textured patterns

A characterization of textured patterns, referred to as the disorder functi on <(delta)over bar>(beta), is used to study propel-ties of patterns genera ted in the Swift-Hohenberg equation (SHE). It is shown to be an intensive, configuration-independent measure. The evolution of random initial states u nder the SHE exhibits two stages of relaxation. The initial phase, where lo cal striped domains emerge from a noisy background, is quantified by a powe r-law decay <(delta)over bar>(beta)similar to t(-(1/2)beta). Beyond a sharp transition, a slower power-law decay of delta(beta), 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 <(delta)over bar>(beta) leads to the coll apse of distinct curves. The decay of <(delta)over bar>(beta) during the in itial phase remains unchanged when nonvariational terms are added to the un derlying equations, suggesting the possibility of observing it in experimen tal systems. In contrast, the rate of relaxation during domain coarsening i ncreases with the coefficient of the nonvariational term. [S1063-651X(99)09 405-2].