Textures and the shapes of domains in Langmuir monolayers

Two-dimensional domains containing an XY-like order parameter exhibit non-trivial internal structure and take on shapes controlled by the configuration that the order parameter adopts. The textures exhibited by the order parameter in such domains are controlled by the interplay between bulk and surface contributions to the energy. We report calculations of the internal texture and the shape of such domains. These calculations lead to the determination of the equilibrium properties of two-dimensional domains, such as those observed in Langmuir monolayers. This allows for the unambiguous exploration of the implications of experimental findings.