Pattern control via multi-frequency parametric forcing

Jeff Porter, Universidad Complutense de Madrid
Chad M. Topaz, Macalester College
Mary Silber, Northwestern University

Abstract

We use symmetry considerations to investigate control of a class of resonant three-wave interactions relevant to pattern formation in weakly damped, parametrically forced systems near onset. We classify and tabulate the most important damped, resonant modes and determine how the corresponding resonant triad interactions depend on the forcing parameters. The relative phase of the forcing terms may be used to enhance or suppress the nonlinear interactions. We compare our symmetry-based predictions with numerical and experimental results for Faraday waves. Our results suggest how to design multifrequency forcing functions that favor chosen patterns in the lab.