论文标题
二维富铁负体，规范的谐波图和最小连接
Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections
论文作者
论文摘要
我们研究了“超稀释”制度中二维结构域中氟化学的变异模型。自由能功能由列出阶参数的降低的Landau-de Gennes能量组成，用于自发磁化的Ginzburg-Landau型能量以及一个有利于夜间导演的共对准的耦合项和磁性。在适当的渐近状态下，我们证明了列级参数参数会收敛到具有不可取向点缺陷的规范谐波图，而磁化率则收敛到单数矢量场，线缺陷沿最小的连接连接不可方向的点缺陷。
We study a variational model for ferronematics in two-dimensional domains, in the "super-dilute" regime. The free energy functional consists of a reduced Landau-de Gennes energy for the nematic order parameter, a Ginzburg-Landau type energy for the spontaneous magnetisation, and a coupling term that favours the co-alignment of the nematic director and the magnetisation. In a suitable asymptotic regime, we prove that the nematic order parameter converges to a canonical harmonic map with non-orientable point defects, while the magnetisation converges to a singular vector field, with line defects that connect the non-orientable point defects in pairs, along a minimal connection.
