ar X iv : c on d - m at / 9 50 51 22 v 1 2 5 M ay 1 99 5 Wulff Construction for Deformable Media
نویسندگان
چکیده
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 large domains. The most striking result is that, under general conditions, such domains will inevitably develop a cusp. We show that the development of cusps is mathematically related to phase transitions. The present approach is equivalent to a Landau mean-field version of the theory.
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