We study the Ginzburg–Landau equations of super-conductivity describing the experimental setup of a Stiffnessometer device. In particular, we consider the nonlinear regime which reveals the impact of the superconductive critical current on the Stiffnessometer signal. As expected, we find that at high flux regimes, superconductivity is destroyed in parts of the superconductive region. Surprisingly, however, we find that the superconductivity does not gradually decay to zero as flux increases, but rather the branch of solutions undergoes branch folding. We use asymptotic analysis to characterize the solutions at the numerous parameter regimes in which they exist. An immediate application of the work is an extension of the regime in which experimental measurements of the Stiffnessometer device can be interpreted.

我们研究了描述电导率仪实验装置的超导电性的Ginzburg-Landau方程。特别是，我们考虑了非线性机制，该机制揭示了超导临界电流对刚度计信号的影响。正如预期的那样，我们发现在高通量状态下，超导在部分超导区域中被破坏。然而，令人惊讶的是，我们发现超导性不会随着通量的增加而逐渐衰减为零，而是溶液的分支经历分支折叠。我们使用渐近分析来表征存在于众多参数状态下的解。这项工作的直接应用是扩展了可以解释硬度计装置的实验测量值的范围。