本文研究了调和映射到单位球面上的热流中初值的奇点的运动规律. 利用数值实验模 拟奇点的运动过程,通过观察奇点在不同时刻的形态和位置,我们归纳得出了奇点的运动规 律. 这里的奇点与向列液晶中的点缺陷联系密切. 本文的数值实验中, 在Neumann 边界条件 下奇点的运动过程能很好地反映向列液晶中点缺陷的运动过程. 但是, 由于模型本身的缺 陷, 在Dirichlet 边界条件下的部分结果与向列液晶的点缺陷的运动情况有些出入. 实验表 明,奇点的运动受到奇点的初始位置和本身特性,奇点之间的相互作用以及边界条件等多个 因素的影响.

We focus on the motion of singularities of the initial value in the heat flow of harmonic maps into a unit sphere. By simulating the motion of singularities via numerical experiments, we identify the rule of singularity movement by observing the configurations and positions of singularities at various times. A singularity is closely related to a point defect in a nematic liquid crystal. In our numerical experiments, the motion of a singularity under the Neumann boundary condition is the same as that of a point defect in the nematic liquid crystal. However, the results under the Dirichlet boundary condition differ due to a shortcoming of the model. The motion of a singularity is affected by its initial position and characteristics, the interaction between singularities, and the boundary condition.