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Shape equations of the axisymmetric vesicles
Phys. Rev. E 47, 461 – Published 1 January, 1993
DOI: https://doi.org/10.1103/PhysRevE.47.461
Abstract
Based on the same bending energy of the spontaneous curvature model, three shape equations for axisymmetric vesicles are derived from different variational methods. They are degenerate for the spherical vesicle, while for the cylindrical vesicle, two of them are the same. They all have a special toroidal solution, Clifford tori, but the constraints on the Lagrange multipliers ΔP and λ and the spontaneous curvature are different. We consider the physical mode of variation and introduce an arbitrary parameter for the axisymmetric action; we get the shape equation in terms of this parameter from it. When this parameter is identified as the parameter ρ, it reduces to the same equation that is from the general shape equation.
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