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arXiv · 1603.00756

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

Michael Helmers
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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.

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Michael Helmers. 2016-03-01. Snapping elastic curves as a one-dimensional analogue of two-component lipid bilayers. https://doi.org/10.1142/s0218202511005234

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