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

COŞKUN E.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 626
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.physa.2023.129036
  • Dergi Adı: Physica A: Statistical Mechanics and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Artic & Antarctic Regions, Compendex, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Method of planes, Numerical study of stability, Superconductivity, Time-dependent Ginzburg–Landau model
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.