Inside the Light Boojums: A Journey to the Land of Boundary Defects

Year:    2020

Author:    Stan Alama, Lia Bronsard, Petru Mironescu

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 128–160

Abstract

We consider minimizers of the energy

a.PNG

in a two-dimensional domain $\Omega$, with weak anchoring potential

b.PNG

This functional was previously derived as a thin-film limit of the Landau-de Gennes energy, assuming weak anchoring on the boundary favoring a nematic director lying along a cone of fixed aperture, centered at the normal vector to the boundary.

In the regime where $s [\alpha^2+(\pi-\alpha)^2]<\pi^2/2$, any limiting map $u_\ast:\Omega\to{\mathbb S}^1$ has only boundary vortices, where its phase jumps by either $2\alpha$ (light boojums) or $2(\pi-\alpha)$ (heavy boojums). Our main result is the fine-scale description of the light boojums.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0020

Analysis in Theory and Applications, Vol. 36 (2020), Iss. 2 : pp. 128–160

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Nematics thin-film limit Ginzburg-Landau type energy weak anchoring boundary vortices asymptotic profile.

Author Details

Stan Alama

Lia Bronsard

Petru Mironescu

  1. On minimizers of the 2D Ginzburg–Landau energy with tangential anchoring

    Alama, Stan

    Bronsard, Lia

    van Brussel, Lee

    Nonlinear Analysis, Vol. 232 (2023), Iss. P.113276

    https://doi.org/10.1016/j.na.2023.113276 [Citations: 1]