Snapping elastic curves as a one-dimensional analogue of two-component lipid bilayers

Abstract

In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes we consider planar curves that are made of a material with two phases. Each phase induces a preferred curvature to the curve, and these curvatures as well as phase boundaries may lead to the development of kinks. We introduce a family of energies for smooth curves and phase fields, and we show that these energies $\Gamma$-converge to an energy for curves with a finite number of kinks. The theoretical result is illustrated by some numerical examples.