Pinning effects and their breakdown for a Ginzburg–Landau model with normal inclusions
Bibliographic record
Abstract
We study a Ginzburg–Landau model for an inhomogeneous superconductor in the singular limit as the Ginzburg–Landau parameter κ=1∕ϵ→∞. The inhomogeneity is represented by a potential term V(ψ)=14(a(x)−∣ψ∣2)2, with a given smooth function a(x) which is assumed to become negative in finitely many smooth subdomains, the “normally included” regions. For bounded applied fields (independent of the Ginzburg–Landau parameter κ=1∕ϵ→∞) we show that the normal regions act as “giant vortices,” acquiring large vorticity for large (fixed) applied field hex. For hex=O(∣lnϵ∣) we show that this pinning effect eventually breaks down, and free vortices begin to appear in the superconducting region where a(x)>0, at a point set which is determined by solving an elliptic boundary-value problem. The associated operators are strictly but not uniformly elliptic, leading to some regularity questions to be resolved near the boundaries of the normal regions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".