Effects of time-periodic forcing in a Cahn-Hilliard model for Langmuir-Blodgett transfer

The influence of a temporal forcing on the pattern formation in Langmuir-Blodgett transfer is studied employing a generalized Cahn-Hilliard model. The occurring frequency-locking effects allow for controlling the pattern formation process. In the case of one-dimensional (i.e., stripe) patterns one finds various synchronization phenomena such as entrainment between the distance of deposited stripes and the forcing frequency. In two dimensions, the temporal forcing gives rise to the formation of intricate complex patterns such as vertical stripes, oblique stripes, and lattice structures. Remarkably, it is possible to influence the system in the spatial direction perpendicular to the forcing direction leading to synchronization in two spatial dimensions.