Axially symmetric membranes with polar tethers
arXiv:cond-mat/0608230 · doi:10.1088/1751-8113/40/16/002
Abstract
Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as would be expected on the basis of axial symmetry. Modulo a translation along the axis, this equation involves a single free parameter c.If c\ne 0, a geometry with spherical topology will possess curvature singularities at its poles. The physical origin of the singularity is identified by examining the Noether charge associated with the translational invariance of the energy; it is consistent with an external axial force acting at the poles. A one-parameter family of exact solutions displaying a discocyte to stomatocyte transition is described.
13 pages, extended and revised version of Non-local sine-Gordon equation for the shape of axi-symmetric membranes
References in corpus (9)
- Formation and Interaction of Membrane Tubes
- Fluid-membrane tethers: minimal surfaces and elastic boundary layers
- Stresses in lipid membranes
- Membrane geometry with auxiliary variables and quadratic constraints
- Interface mediated interactions between particles -- a geometrical approach
- Geometry of surface mediated interactions
- Descriptions of membrane mechanics from microscopic and effective two-dimensional perspectives
- Hamilton's equations for a fluid membrane
- Self-Dual Bending Theory for Vesicles
Cited by in corpus (9)
- Recent theoretical advances in elasticity of membranes following Helfrich's spontaneous curvature model
- Compatibility between shape equation and boundary conditions of lipid membranes with free edges
- Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution
- Force dipoles and stable local defects on fluid vesicles
- Toroidal membrane vesicles in spherical confinement
- Some observations on variational elasticity and its application to plates and membranes
- Equatorial deformation of homogeneous spherical fluid vesicles by a rigid ring
- Small equatorial deformation of homogeneous spherical fluid vesicles
- Absence of Buckling in Nerve Fiber