The Kirchhoff-Plateau problem

Abstract

The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament being modeled as a Kirchhoff rod and the action of the spanning surface being solely due to surface tension. Giusteri, Lussardi and Fried in [2] established the existence of an equilibrium shape that minimizes the total energy of the system under the physical constraint of noninterpenetration of matter, but allowing for points on the surface of the bounding loop to come into contact. In [1], we use this result to generalize the situation studying a system composed by several rods linked in an arbitrary way and tied by a soap film and we perform some experiments to validate our result. 
The talk is based on a joint work with Luca Lussardi (DISMA – Politecnico di Torino, luca.lussardi [at] polito.it) and Alfredo Marzocchi (Università Cattolica del Sacro Cuore, alfredo.marzocchi [at] unicatt.it).

References 
[1] G. Bevilacqua, L. Lussardi, A. Marzocchi, Soap film spanning an elastic link, Quart.Appl.Math. 77(3) (2019), 507–523. 
[2] G.G. Giusteri, L. Lussardi, E. Fried, Solution of the Kirchhoff-Plateau problem, J.Nonlinear Sci. 27 (2017), 1043–1063.
 

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