Periodic-cylinder vesicle with minimal energy
Abstract
We give some details about the periodic cylindrical solution found by Zhang and Ou-Yang in [Phys. Rev. E 53, 4206(1996)] for the general shape equation of vesicle. Three different kinds of periodic cylindrical surfaces and a special closed cylindrical surface are obtained. Using the elliptic functions contained in mathematic, we find that this periodic shape has the minimal total energy for one period when the period-amplitude ratio β1.477, and point out that it is a discontinuous deformation between plane and this periodic shape. Our results also are suitable for DNA and multi-walled carbon nanotubes (MWNTs)
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