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Variational problems in inelastic theory of biomembranes, smectic-A liquid crystals, and carbon related structures. (English) Zbl 1112.74018
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 237-248 (2006).
Summary: After a brief introduction to several variational problems in the study of shapes of thin structures, we deal with variational problems on two-dimensional surface in three-dimensional Euclidian space by using exterior differential forms and the moving frame method. The morphological problems of lipid bilayers and stabilities of cell membranes are also discussed. The key point is that the first- and second-order variations of free energy determine equilibrium shapes and mechanical stabilities of structures.
MSC:
74G65Energy minimization (equilibrium problems in solid mechanics)
74K15Membranes (solid mechanics)
74L15Biomechanical solid mechanics
82D30Random media, disordered materials (statistical mechanics)