English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in (J.B. Fournier and P. Galatoa, J. Phys. II 7 (1997) 1509-1520; N. Uchida, Phys. Rev. E 66 (2002) 040902) which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce a fully discrete scheme, consisting of piecewise linear finite elements, show that it is un- conditionally stable for a large range of the elastic moduli in the model, and prove its convergence (up to subsequences) thereby proving the existence of a weak solution to the continuous model. Numer- ical simulations are included that examine typical model situations, confirm our theory, and explore numerical predictions beyond that theory. Mathematics Subject Classification. 35K55, 74K15.

A finite element scheme for the evolution of orientational order in fluid membranes