Volume 9, Issue 3
Motion of Singularities in the Heat Flow of Harmonic Maps into a Sphere

Chunmei Luo, Hui Zhang & Zhengru Zhang

East Asian J. Appl. Math., 9 (2019), pp. 580-600.

Published online: 2019-06

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  • Abstract

Numerical experiments are used to determine the motion of singularities in the heat flow of harmonic maps into a unit sphere. These singularities are closely related to point defects in a nematic liquid crystals. The motion of singularities is affected by initial positions and interaction between singularities and boundary conditions. In particular, it is shown that the motion of singularities is the same as the motion of point defects in nematic liquid crystals under Neumann boundary conditions. For Dirichlet boundary conditions, the results do not properly reflect the crystal defect motion due to the shortcoming of the model.

  • Keywords

Heat flow of harmonic maps, singularity, boundary effect, interaction.

  • AMS Subject Headings

65M99, 65S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-580, author = {}, title = {Motion of Singularities in the Heat Flow of Harmonic Maps into a Sphere}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {580--600}, abstract = {

Numerical experiments are used to determine the motion of singularities in the heat flow of harmonic maps into a unit sphere. These singularities are closely related to point defects in a nematic liquid crystals. The motion of singularities is affected by initial positions and interaction between singularities and boundary conditions. In particular, it is shown that the motion of singularities is the same as the motion of point defects in nematic liquid crystals under Neumann boundary conditions. For Dirichlet boundary conditions, the results do not properly reflect the crystal defect motion due to the shortcoming of the model.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.061018.240119}, url = {http://global-sci.org/intro/article_detail/eajam/13168.html} }
TY - JOUR T1 - Motion of Singularities in the Heat Flow of Harmonic Maps into a Sphere JO - East Asian Journal on Applied Mathematics VL - 3 SP - 580 EP - 600 PY - 2019 DA - 2019/06 SN - 9 DO - http://doi.org/10.4208/eajam.061018.240119 UR - https://global-sci.org/intro/article_detail/eajam/13168.html KW - Heat flow of harmonic maps, singularity, boundary effect, interaction. AB -

Numerical experiments are used to determine the motion of singularities in the heat flow of harmonic maps into a unit sphere. These singularities are closely related to point defects in a nematic liquid crystals. The motion of singularities is affected by initial positions and interaction between singularities and boundary conditions. In particular, it is shown that the motion of singularities is the same as the motion of point defects in nematic liquid crystals under Neumann boundary conditions. For Dirichlet boundary conditions, the results do not properly reflect the crystal defect motion due to the shortcoming of the model.

Chunmei Luo, Hui Zhang & Zhengru Zhang. (2019). Motion of Singularities in the Heat Flow of Harmonic Maps into a Sphere. East Asian Journal on Applied Mathematics. 9 (3). 580-600. doi:10.4208/eajam.061018.240119
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