Wulff Construction for Deformable Media
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A domain in a Langmuir monolayer can be expected to have a shape that reflects the textural anisotropy of the material it contains. This paper explores the consequences of XY-like ordering. It is found that an extension of the Wulff construction allows for the calculation of two-dimensional domain shapes when each segment of the perimeter has an energy that depends both on its orientation and its location. This generalized Wulff construction, and newly-derived exact expressions for the order parameter texture in a circular domain, lead to results for the shape of a large domain. The most striking result is that under general conditions such domains will inevitably develop cusps. We show that the onset of a cusp is mathematically related to a phase transition. The present approach is equivalent to a Landau mean-field version of the theory.
34 pages, REVTEX, 8 figures available on request. Please contact Joseph Rudnick (jrudnick@uclaph.physics.ucla.edu)
34 pages, REVTEX, 8 figures available on request. Please contact Joseph Rudnick (jrudnick@uclaph.physics.ucla.edu)