Pattern selection in extended periodically forced systems: A continuum coupled map approach - art. no. 046202

We propose that a useful approach to the modeling of periodically forced ex tended systems is through continuum coupled map (CCM) models. CCM models ar e discrete time, continuous space models, mapping a continuous spatially va rying field xi (n)(x) from time n to time n+1. The efficacy of CCM models i s illustrated by an application to experiments of Umbanhowar, Melo, and Swi nney [Nature 382, 793 (1996)] on vertically vibrated granular layers. Using a simple CCM model incorporating temporal period doubling and spatial patt erning at a preferred length scale, we obtain results that bear remarkable similarities to the experimental observations. The fact that the model does not make use of physics specific to granular layers suggests that similar phenomena may be observed in other (nongranular) periodically forced, stron gly dissipative systems. We also present a framework for the analysis of pa ttern selection in CCM models using a truncated modal expansion. Through th e analysis, we predict scaling laws of various quantities, and these laws m ay be verifiable experimentally.