Towards two-component lipid bilayer membranes: snapping elastic curves

Studying a one-dimensional analogue of the spontaneous curvature model for twocomponent lipid bilayer membranes we consider planar curves that are made of a material with two phases. Each phase induces a different preferred curvature, and these curvatures as well as phase boundaries may cause the curves to develop kinks. We introduce a family of models for smooth curves and phase fields that approximates the above situation in the sense of Γ-convergence of energies. The theoretical result is illustrated by some numerical examples.