We closely examine a single vortex formation in an infinitely long cylinder with a rectangular crossection through field-cooling process with Temperature and Time-dependent Ginzburg–Landau model. We identify a solution for which components of vector potential and order function display a certain symmetry, which we name symmetric vortex solution. Furthermore, we observe that single vortex formation is associated with a jump discontinuity in all components of solution and associated observables, and illustrate graphically dynamics of transition. We carry out simulations in a vectorial algorithm using a variable order stiff ODE integration scheme of MATLAB.

我们通过与温度和时间有关的Ginzburg-Landau模型进行场冷却，仔细检查了无限长圆柱体中具有矩形截面的单个涡流的形成。我们确定了一个向量势和阶次函数的分量显示一定对称性的解决方案，我们将其称为对称涡旋解决方案。此外，我们观察到单个涡旋的形成与溶液和相关可观测值的所有分量中的跳跃不连续性有关，并以图形方式说明了跃迁的动力学。我们使用MATLAB的变阶刚性ODE积分方案在矢量算法中进行了仿真。