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

Only some special open surfaces satisfying the shape equation of lipidmembranes can be compatible with the boundary conditions. As a result of thiscompatibility, the first integral of the shape equation should vanish foraxisymmetric lipid membranes, from which two theorems of non-existence areverified: (i) There is no axisymmetric open membrane being a part of torussatisfying the shape equation; (ii) There is no axisymmetric open membranebeing a part of a biconcave discodal surface satisfying the shape equation.Additionally, the shape equation is reduced to a second-order differentialequation while the boundary conditions are reduced to two equations due to thiscompatibility. Numerical solutions to the reduced shape equation and boundaryconditions agree well with the experimental data [A. Saitoh \emph{et al.},Proc. Natl. Acad. Sci. USA \textbf{95}, 1026 (1998)].

Compatibility between shape equation and boundary conditions of lipid membranes with free edges