Abstract
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.
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