@Article{ATA-36-2, author = {Stan, Alama and Lia, Bronsard and Petru, Mironescu}, title = {Inside the Light Boojums: A Journey to the Land of Boundary Defects}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0020}, url = {https://global-sci.com/article/73810/inside-the-light-boojums-a-journey-to-the-land-of-boundary-defects} }