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

Speaker: Leroy Jia, Flatiron Research Fellow at Center for Computational Biology, Flatiron Institute

Abstract: A timeless problem in the theory of fluid interfaces is to show that an area-minimizing soap film connecting two symmetric rings forms a catenoid. Inspired by the exotic phase transitions of colloidal membranes studied at the Sharma (IISc Bangalore) and Dogic (UCSB) Labs, we use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with fixed area and bending resistance that is suspended in this classic geometry. This simple problem turns out to be surprisingly rich: various iconic shapes such as catenoids, thin tethers, and elastica-like buckled surfaces can appear as different limits of this system depending on the area and extension. A perturbation theory argument directly relates the tensions of catenoidal membranes to the stability properties of catenoidal soap films. We also investigate the effects of including a Gaussian curvature modulus, which, for small enough membranes, causes the axial force to diverge as the ring separation approaches its maximal value.

**Please note, this event will be held online via Zoom at the following link: https://northwestern.zoom.us/j/95506901758.

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