AI 中文总结
研究构建非局域幂律基线模型，分析YBCO薄膜瞬态磁通穿透的参数简并性，发现本构族局限导致振幅差异，确立了可复现的基线模型。
AI 中文摘要
我们评估具有有界、常指数幂律的非局域薄膜模型是否能再现3×3 mm² YBa₂Cu₃O₇₋δ薄膜中瞬态磁通穿透的高速磁光测量结果。该模型以物理单位正向求解，并用作受控本构基线。临界面电流由最终穿透几何约束，而判据场与蠕变指数由转变时间和弛豫时间约束。校准揭示了一种内在简并性：转变时间主要依赖于判据场与饱和参数的乘积，等价于饱和面电阻率，因此这些量无法被独立识别。在参数化该简并性后，模型捕获了约22 ms处的保护电流转变、41.2 ms的弛豫常数（对比测量值37.5 ms与43.7 ms），以及距薄膜边缘约0.92 mm处的后期最大值。振幅仍存在差异：计算得到的瞬态最大值为1.90J_c0，峰值与225 ms的比值为2.13，对比报道值1.20。该过量在蠕变指数、简并参数方向、Kim场依赖关系及网格分辨率变化下均持续存在。通过判据场匹配测量比值将需要比常规尺度低约三个数量级的值，而足以匹配的空间排斥会消除边缘峰值本身。我们还将电场分解为无旋和有旋部分，并量化法拉第定律的谱形式与有限差分形式不一致的边界层。结果确立了可复现的非局域幂律基线，并识别出有界、常指数本构族的局限，而非非局域薄膜电动力学的局限。
英文摘要
We assess whether a non-local thin-film model with a bounded, constant-exponent power law can reproduce high-speed magneto-optical measurements of transient flux penetration in a $3\times3$~mm$^2$ YBa$_2$Cu$_3$O$_{7-δ}$ film. The model is solved forward in physical units and used as a controlled constitutive baseline. The critical sheet current is constrained by the final penetration geometry, while the criterion field and creep exponent are constrained by the turnover and relaxation times. The calibration reveals an intrinsic degeneracy: the turnover time depends primarily on the product of the criterion field and saturation parameter, equivalently on the saturated sheet resistivity, so these quantities cannot be identified independently. After parameterizing this degeneracy, the model captures a guarded-current turnover near 22~ms, a relaxation constant of 41.2~ms compared with the measured 37.5 and 43.7~ms, and a late maximum approximately 0.92~mm from the film edge. The amplitude remains discrepant: the calculated transient maximum is $1.90J_{c0}$ and the peak-to-225-ms ratio is 2.13, compared with the reported 1.20. This excess persists under changes in the creep exponent, the degenerate parameter direction, the Kim field dependence, and mesh resolution. Matching the measured ratio through the criterion field would require a value about three orders of magnitude below the conventional scale, while spatial exclusion sufficient to match it would remove the edge peak itself. We also decompose the electric field into irrotational and solenoidal parts and quantify the boundary layer where spectral and finite-difference forms of Faraday's law disagree. The results establish a reproducible non-local power-law baseline and identify limitations of the bounded, constant-exponent constitutive family rather than of non-local thin-film electrodynamics.
Comments12 pages, 5 figures
