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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".