Narrow Results

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 Γ-converge to an energy for curves with a finite number of kinks. The theoretical result is illustrated by some numerical examples.

We are interested in defining new energy functionals and solving them by using the variational approach method and Darboux equations. That is, we aim to define a new class of elastic curves on the regular surface $\mathrm{\Lambda }$. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves on $\mathrm{\Lambda }$. As a result, we classify these critical curves as elastic magnetic curves of the Darboux vector family.