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arXiv · 1611.07747

First integrals of the axisymmetric shape equation of lipid membranes

Y. H. Zhang·Z. McDargh·Z. C. Tu
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Abstract

The shape equation of lipid membranes [Zhong-can and Helfrich(1987) PRL 59 2486] is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu [Zheng and Liu(1993) PRE 48 2856]. Here we try to further reduce this second-order ODE to a first-order ODE by seeking for first integrals according to the Noether theorem. We indeed find a first integral when the second-order ODE is invariant under conformation transformations. We obtain the mechanical interpretation of the first integral by using the membrane stress tensor.

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Y. H. Zhang, Z. McDargh, Z. C. Tu. 2016-11-23. First integrals of the axisymmetric shape equation of lipid membranes. https://doi.org/10.1088/1674-1056%2F27%2F3%2F038704

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