Journal Article10.1103/PHYSREVA.41.4517
Anchor ring-vesicle membranes.
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TL;DR: In this article, a family of exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found, which are anchor rings with generating circles of radii in the ratio 1/ \ensuremath{surd}2.
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Abstract: A family of the exact and analytical solutions of the equilibrium shape equation of vesicle membranes is found. They are anchor rings with generating circles of radii in the ratio 1/ \ensuremath{\surd}2 . It is shown that these ring vesicles are stable for some negative values of their spontaneous curvatures, such that experimental construction of such vesicles seems possible. A discussion shows that a positive Gauss-curvature elastic modulus favors the formation of these special vesicles.
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Citations
Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model.
Zhanchun Tu,Z.C. Ou-Yang +1 more
TL;DR: Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review.
Vesicles of toroidal topology.
TL;DR: The present study shows, however, that fluid vesicles can also be expected to form such shapes, which should even exhibit qualitatively new features not present for shapes of spherical topology.
Counterexample to some shape equations for axisymmetric vesicles.
TL;DR: Three different shape equations for axisymmetric vesicles have been derived from the same spontaneous-curvature model in literature and the validity of these equations has been examined by means of a rigorous analytical solution.
Helfrich shape equation for axisymmetric vesicles as a first integral.
Wei-Mou Zheng,Ji-Xing Liu +1 more
TL;DR: In this paper, the relation between the widely used Helfrich shape equation and the general shape equation is clarified and a modified version of the Helmberg shape equation that is equivalent to the general equation is proposed.
Overview of the Study of Complex Shapes of Fluid Membranes, the Helfrich Model and New Applications
Z. C. Ou-Yang,Zhanchun Tu +1 more
TL;DR: Based on the Helfrich model, Wang et al. as mentioned in this paper predicted the exact solution for discoidal shape of red blood cells and a special kind of toroidal vesicle with the ratio of two generation radii being root 2.
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