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  • 1
    Electronic Resource
    Electronic Resource
    Geometrical methods for the elasticity theory of membranes (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 711-717 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The elasticity theory of curved membranes is developed using geometrical methods. The strain tensor is shown to be the Lie derivative of the metric tensor with respect to a flow. This formulation is coordinate-free, and can be expressed in any convenient coordinate system. A useful fixed coordinate system for the neighborhood of any given membrane surface is constructed. The formalism is used to expand the curvature free energy of a membrane about its minimum and to find the induced flow which minimizes shear dissipation in a curved membrane when the membrane is deformed at constant density. The shear free energy is expanded about its minimum for deformations of the shape at constant density. The curvature free energy is explicitly expanded about its minimum for shape changes of a closed membrane which conserve area and interior volume.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526612
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  • 2
    Electronic Resource
    Electronic Resource
    An instability of the red blood cell shape (1985)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 57 (1985), S. 1739-1742 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The infinitesimal stability of fluid vesicle shapes is studied as a function of vesicle volume and spontaneous membrane curvature at fixed area. It is found that the azimuthally symmetric shapes are infinitesimally unstable for some values of these parameters. A possible connection with the sickling of red blood cells is pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.334447
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