Competing interactions and domain-shape instabilities in a monomolecular film at an air-water interface

Domain-shape instabilities are investigated in a two-dimensional binary mixture of near-critical composition, a monomolecular film confined to an air-water interface and composed of a phospholipid and cholesterol. We apply the methodology of spectral analysis to the quantitative description of domain-wall configurations. This permits us to identify an elliptic instability and a branching instability leading into a ``melted'' stripe phase in the vicinity of the consolute point. In between, a regime exists in which domain-wall fluctuations exhibit a capillary-wave spectrum.