A mathematical examination of squeezing and stretching of spherical vesicles. (English) Zbl 1095.74019

Hadzhilazova, Mariana T.; Mladenov, Ivaïlo M.

Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 231-239 (2005).

Summary: The geometry of a few simple models closely related to the Cole’s and Yoneda’s experiments [K. Cole, J. Cell. Comp. Physiol. 1, 1–9 (1932); M. Yoneda, J. Exp. Biol. 41, 893–906 (1964)] are studied in some detail. Their principal difference stems from the boundary conditions at the points where the membranes detach from the compressing planes. Mathematically this affects the equilibrium configurations, because in all these cases the mean curvature suffers a discontinuity while this is not valid for the tangent vector. We also derive a new parametrization of Delaunay’s nodoids.
For the entire collection see [Zbl 1066.53003].

MSC:

74K15	Membranes
74L15	Biomechanical solid mechanics
92C10	Biomechanics

Keywords:

Cole model; discontinuous curvature; parametrization; Delaunay’s nodoids