Gaussian vector fields on triangulated surfaces

Anisotropic elasticity in the plane of the lipid membrane appears in a multitude of biophysical problems. It poses a major theoretical challenge due to the inherent curvature of fluid membranes which is coupled to the inplane elastic deformations. Computer simulations by triangulated surfaces have proven to be very useful to resolve the complex interplay between in-plane ordering of membranes and membrane conformations. In the present work we have developed a procedure for realistic representations of Gaussian models with in-plane vector degrees of freedoms on a triangulated surface. The method opens possibilities for simulations of membranes for a variety of problems involving in-plane orientational degrees of freedoms and direct correspondence to continuum models.