Volume 36, Issue 2
Inside the Light Boojums: a Journey to the Land of Boundary Defects

Stan Alama, Lia Bronsard & Petru Mironescu

Anal. Theory Appl., 36 (2020), pp. 128-160.

Published online: 2020-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35J20, 35B25, 35J61, 49K20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-36-128, author = {Alama , Stan and Bronsard , Lia and Mironescu , Petru}, 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 = {http://global-sci.org/intro/article_detail/ata/17127.html} }
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

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.

Stan Alama, Lia Bronsard & Petru Mironescu. (2020). Inside the Light Boojums: a Journey to the Land of Boundary Defects. Analysis in Theory and Applications. 36 (2). 128-160. doi:10.4208/ata.OA-0020
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