【Seminar】"Axisymmetric membranes under external force: buckling, minimal surfaces, and tethers" by Prof. Thomas Powers

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

Speaker: Prof. Thomas Powers (Brown University)

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.