MembraneR3 - A spectral model of membrane shape based on Helfrich spontaneous curvature in R

For this first release of MambraneR3 several options for upgrading from MembraneR2 (Frickenhaus & Woelper, 2024) were investigated and some of them implemented. The first idea was to change the integration scheme from 2D-Simpson to one without nodes at the poles where the metric becomes zero that would require regularization by l'Hopitals rule in some numerical integrations. Second, numerical performance was not optimal before, due to several loop-constructs. Next, a simple way to restrict the basis functions to a relevant subset of levels of degree $l$ and order $m$ has been introduced. But the main upgrade is the Helfrich spontaneous curvature energy functional (Helfrich, 1973), that was implemented to remove the hard to solve constraint of fixed integrated mean curvature from the bilayer couple model in MembraneR2.

Finally, the effects of the strength of gradient filtering (parameter $\lambda$) has been investigated experimentally.

The new model is validated against known quantities from the UnduStick reference shape (Frickenhaus & Woelper, 2024), for which the spontaneous curvature parameter $H_0=2.562$ has been derived (input dmp-file for SE included).