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Spatial Periodic Forcing Can Displace Patterns It Is Intended to Control


  Yair Mau [1]  ,  Aric Hagberg [2]  ,  Ehud Meron [1,3]  
 [1] Physics Department, Ben-Gurion University of the Negev
[2] Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
[3] Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus

Spatial periodic forcing of pattern-forming systems is an important, but lightly studied, method of controlling patterns. It can be used to control the amplitude and wave number of one-dimensional periodic patterns, to stabilize unstable patterns, and to induce them below instability onset. We show that, although in one spatial dimension the forcing acts to reinforce the patterns, in two dimensions it acts to destabilize or displace them by inducing two-dimensional rectangular and oblique patterns.