Stresses in lipid membranes

Details Stresses in lipid membranes Stresses in lipid membranes

2002-03-07

arxiv.org/abs/cond-mat/0203148v3

Physics

Condensed Matter

Soft Condensed Matter

16 pages, introduction rewritten, other minor changes, new references added, version to appear in Journal of Physics A

Scientific paper

10.1088/0305-4470/35/30/302

The stresses in a closed lipid membrane described by the Helfrich hamiltonian, quadratic in the extrinsic curvature, are identified using Noether's theorem. Three equations describe the conservation of the stress tensor: the normal projection is identified as the shape equation describing equilibrium configurations; the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes. The corresponding torque tensor is also identified. The use of the stress tensor as a basis for perturbation theory is discussed. The conservation laws are cast in terms of the forces and torques on closed curves. As an application, the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along circles of constant latitude.

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