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

作　　者：Stan Alama Lia Bronsard Petru Mironescu 

机构地区：[1]Department of Mathematics&Statistics,McMaster University,Hamilton,Ontario,L8S 4K1 Canada [2]Universit'e de Lyon,CNRS UMR 5208,Universit´e Lyon 1,Institut Camille Jordan,43 blvd.du 11 Novembre 1918,F-69622 Villeurbanne Cedex,France

出　　处：《Analysis in Theory and Applications》2020年第2期128-160,共33页分析理论与应用（英文刊）

基　　金：supported by the LABEX MILYON(ANR-10-LABX-0070)of Universit'e de Lyon,within the program Investissements d’Avenir(ANR-11-IDEX-0007);the French National Research Agency(ANR).S.A.and L.B.also acknowledge their support from NSERC(Canada)Discovery Grants.

摘　　要：We consider minimizers of the energy Eε(u)=:∫Ω[1/2|■u|^2+1/4ε2(|u|^2-1)^2]dx+1/2ε^s∫■ΩW(u,g)ds,u:Ω→■,0<s<1,in a two-dimensional domain W,with weak anchoring potential W(u,g)=:1/2(|u|^2-1)^2+(<u,g>-cosα)^2,0<a<π/2.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[α^2+(π-α)^2]<π^2/2,any limiting map u*:Ω→S^1 has only boundary vortices,where its phase jumps by either 2α(light boojums)or 2(π-α)(heavy boojums).Our main result is the fine-scale description of the light boojums.

关 键 词：NEMATICS thin-film limit Ginzburg-Landau type energy weak anchoring boundary vortices asymptotic profile 

分 类 号：O175[理学—数学]