TY - JOUR T1 - Inside the Light Boojums: A Journey to the Land of Boundary Defects AU - Alama , Stan AU - Bronsard , Lia AU - Mironescu , Petru JO - Analysis in Theory and Applications VL - 2 SP - 128 EP - 160 PY - 2020 DA - 2020/06 SN - 36 DO - http://doi.org/10.4208/ata.OA-0020 UR - https://global-sci.org/intro/article_detail/ata/17127.html KW - Nematics, thin-film limit, Ginzburg-Landau type energy, weak anchoring, boundary vortices, asymptotic profile. AB -

We consider minimizers of the energy


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


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.