Calculus of Variations and Geometric Measure Theory

G. Bevilacqua - C. Lonati - L. Lussardi - A. Marzocchi

A variational analysis of nematic axisymmetric films: the covariant derivative case

created by bevilacqua on 02 Jun 2024
modified on 03 Jun 2024



Inserted: 2 jun 2024
Last Updated: 3 jun 2024

Year: 2024

ArXiv: 2405.20154 PDF


Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi 10 and by Napoli and Vergori 27,26. Both penalize the area of the surface and the gradient of the director: in 10 the covariant derivative of the director is considered, while 26 deals with the surface gradient. In this paper, a complete variational analysis of the model proposed by Giomi is performed for revolution surfaces spanning two coaxial rings.