Locking of periodic patterns in Cahn-Hilliard models for Langmuir-Blodgett transfer

Abstract: The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model is studied in order to describe the pattern formation in Langmuir-Blodgett transfer onto prestructured substrates. The occurring synchronization effects enable a control mechanism for the pattern formation process. In the one dimensional case the parameter range in which patterns are created is increased and the patterns' properties can be adjusted in a broader range. In two dimensions, one dimensional stripe patterns can be destabilized, giving rise to a multitude of new two dimensional patterns, including oblique and lattice patterns.