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

## TL;DR

This study investigates how time-periodic forcing influences pattern formation in a generalized Cahn-Hilliard model for Langmuir-Blodgett transfer, revealing synchronization phenomena and complex pattern control in one and two dimensions.

## Contribution

It demonstrates the control of pattern formation through temporal forcing, including frequency locking and synchronization effects in both one- and two-dimensional systems.

## Key findings

- Frequency locking enables pattern control.
- Temporal forcing induces complex patterns like stripes and lattices.
- Synchronization occurs in both spatial directions.

## Abstract

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.