Numerical studies of domains and bubbles of langmuir monolayers

A numerical algorithm based on the finite element method has been developed to accurately determine the shape of the boundary of a domain containing "boojum" textures, which are order-parameter distributions that resemble the structure of the orbital angular momentum in a superfluid 3He droplet [N.D. Mermin, in Quantum Fluids and Solids, edited by S.B. Trickey, E. Adams, and J.Duffy (Plenum, New York, 1997)]. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in an extended region ordered phase.