Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2005-09-26
J. Phys. A: Math Gen. 39, 10323 (2006)
Physics
Condensed Matter
Soft Condensed Matter
37 pages, 3 figures, minor changes
Scientific paper
10.1088/0305-4470/39/33/005
Mechanics of fluid membranes may be described in terms of the concepts of mechanical deformations and stresses, or in terms of mechanical free-energy functions. In this paper, each of the two descriptions is developed by viewing a membrane from two perspectives: a microscopic perspective, in which the membrane appears as a thin layer of finite thickness and with highly inhomogeneous material and force distributions in its transverse direction, and an effective, two-dimensional perspective, in which the membrane is treated as an infinitely thin surface, with effective material and mechanical properties. A connection between these two perspectives is then established. Moreover, the functional dependence of the variation in the mechanical free energy of the membrane on its mechanical deformations is first studied in the microscopic perspective. The result is then used to examine to what extent different, effective mechanical stresses and forces can be derived from a given, effective functional of the mechanical free energy.
Lomholt Michael A.
Miao Ling
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