First integrals of the axisymmetric shape equation of lipid membranes

doi:10.1088/1674-1056/27/3/038704

中国物理B ›› 2018, Vol. 27 ›› Issue (3): 38704-038704.doi: 10.1088/1674-1056/27/3/038704

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

First integrals of the axisymmetric shape equation of lipid membranes

Yi-Heng Zhang(张一恒), Zachary McDargh, Zhan-Chun Tu(涂展春)

1 Department of Physics, Beijing Normal University, Beijing 100875, China;
2 Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh PA 15213, USA

收稿日期:2017-09-30 修回日期:2017-12-07 出版日期:2018-03-05 发布日期:2018-03-05
通讯作者: Zhan-Chun Tu E-mail:tuzc@bnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

First integrals of the axisymmetric shape equation of lipid membranes

Yi-Heng Zhang(张一恒)¹, Zachary McDargh², Zhan-Chun Tu(涂展春)¹

1 Department of Physics, Beijing Normal University, Beijing 100875, China;
2 Department of Physics, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh PA 15213, USA

Received:2017-09-30 Revised:2017-12-07 Online:2018-03-05 Published:2018-03-05
Contact: Zhan-Chun Tu E-mail:tuzc@bnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

摘要/Abstract

摘要：

The shape equation of lipid membranes 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 (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler-Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor.

关键词: lipid membrane, shape equation, first integral, Noether theorem

Abstract:

Key words: lipid membrane, shape equation, first integral, Noether theorem

中图分类号: (Membranes, bilayers, and vesicles)

87.16.D-

张一恒, 涂展春. First integrals of the axisymmetric shape equation of lipid membranes[J]. 中国物理B, 2018, 27(3): 38704-038704.

Yi-Heng Zhang(张一恒), Zachary McDargh, Zhan-Chun Tu(涂展春). First integrals of the axisymmetric shape equation of lipid membranes[J]. Chin. Phys. B, 2018, 27(3): 38704-038704.

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First integrals of the axisymmetric shape equation of lipid membranes

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