Method for efficient shape parametrization of fluid membranes and vesicles

Abstract

In this paper we describe a method for the parametrization of the shapes adopted by fluid membranes and vesicles. The method is based upon a boundary-value approach to geometry description in which smooth surfaces are produced as the solution to an elliptic partial differential equations. Shape parameters are introduced through the boundary conditions, which control the shape of the vesicle models. In combination with a model for the surface energy and a method for numerical minimization, it is shown how the method can accurately approximate the shapes of both axisymmetric and nonaxisymmetric vesicles over a wide range of control parameters. The particular value of the method lies in its ability to parametrize complicated shapes efficiently, a feature that becomes especially valuable when seeking shapes of minimal energy using direct optimization techniques.