On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity


Physica A: Statistical Mechanics and its Applications, vol.626, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 626
  • Publication Date: 2023
  • Doi Number: 10.1016/j.physa.2023.129036
  • Journal Name: Physica A: Statistical Mechanics and its Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Artic & Antarctic Regions, Compendex, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Keywords: Method of planes, Numerical study of stability, Superconductivity, Time-dependent Ginzburg–Landau model
  • Karadeniz Technical University Affiliated: Yes


We consider Semi-Discretized Time-Dependent Ginzburg–Landau model of superconductivity(SDTDGL), a nonlinear system of ordinary differential equations, and at first numerically investigate stability of minimizers of Ginzburg–Landau free energy with respect to variations in initial conditions and show computationally that the system may lead to unstable minimizers for certain range of initial conditions via comparative results of several high-order ODE solvers of MATLAB. In particular, we observe that MATLAB's explicit solvers implemented with a vectorized code are very effective for obtaining equilibrium state and that all the solvers lead to same geometric alignment of vortices in a mixed state through indistinguishable GL energy dependence of time variable. Finally, we show that temporal evolution of a mixed state in zero-field cooling can be classified as of five substages based on qualitative properties of condensation, kinetic and field energy components of Ginzburg–Landau Energy functional.