Stresses in lipid membranes
By R. Capovilla, J. Guven. 2002
183 citations recorded by the source corpus.
The stresses in a closed lipid membrane described by the Helfrich Hamiltonian, quadratic in th ee xtrinsic curvature, are identified using Noether’s theorem. Three equations describe the conservation of the stress tensor: the norma lp rojection 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 the circles of constant latitude.
Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/e31315a0a602bc53f3bef79aa73e083cdcd0bf53
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In Atomic and Molecular Physics, and Optics
In Biomedical Engineering
In Molecular Biology
Citations in the corpus
- Dynamics of filaments and membranes in a viscous fluid (2009, methodology): “We follow the geometric approach of Guven (2004); see also (Capovilla and Guven, 2002) and (Capovilla and Guven, 2004).”
- Modelling fluid deformable surfaces with an emphasis on biological interfaces (2018, background): “…focused on this model, e.g. in investigations of equilibrium configurations of closed vesicles under geometric constraints, such as fixed surface area or fixed enclosed volume (Steigmann 1999; Capovilla & Guven 2002; Tu & Ou-Yang 2004; Feng & Klug 2006; Rangarajan & Gao 2015; Sauer et al. 2017).”