ICMCS seminar - Axisymmetric membranes under external force: buckling, minimal surfaces, and tethers

Title: Axisymmetric membranes under external force: buckling, minimal surfaces, and

tethers

Abstract: Motivated by deformations of artificial fluid membranes consisting of rod-like colloidal particles, we use theory and numerical computation to determine the shape of an axisymmetric membrane with constant area and a resistance to bending. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a soap film. In our problem, we find infinitely many branches of solutions for the shape and external force as functions of the separation of the rings, analogous to the infinite family of eigenmodes for the Euler buckling of a slender rod. Special attention is paid to the catenoid, which emerges as the shape of maximal allowable separation when the area is less than a critical area equal to the planar area enclosed by the two rings. A perturbation theory argument directly relates the tension of catenoidal membranes to the stability of catenoidal soap films in this regime. When the membrane area is larger than the critical area, we find additional cylindrical tether solutions to the shape equations at large ring separation, and that arbitrarily large ring separations are possible.

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Meeting ID: 812 1147 0751
Passcode: ICMCS123