On the Ginzburg–Landau model of a superconducting ball in a uniform field
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the three-dimensional Ginzburg–Landau model for a solid spherical superconductor in a uniform magnetic field, in the limit as the Ginzburg–Landau parameter \kappa = 1/ ɛ\rightarrow \infty . By studying a limiting functional, we identify a candidate for the lower critical field H_{c_{1}} , the value of the applied field strength at which minimizers first exhibit vortices. For applied fields of this strength we show the existence of locally minimizing solutions with vortices located along a diameter of the sphere parallel to the applied field direction. To analyze these problems we use a combination of techniques, involving least perimeter problems, weak Jacobians and rectifiable currents, and special Hodge decompositions. Résumé Nous étudions la limite quand le paramètre de Ginzburg–Landau \kappa = {}^{1}/_{ɛ}\rightarrow \infty pour le modèle de Ginzburg–Landau en trois dimension dans le cas d'une boule placée dans un champ magnétique uniforme. Nous identifions une fonctionnelle limite qui nous permet de trouver le premier champ critique H_{c_{1}} , c'est à dire le champ au dessus duquel les minimiseurs commencent à presenter des vortex. Nous montrons qu'il existe des solutions localement minimisantes ayant des vortex le long du diamètre de la boule qui est parallèle au champ appliqué quand sa norme est de l'ordre de H_{c_{1}} . Nous nous servons de techniques provenant de la théorie de la mesure géométrique, incluant les jacobiens faibles et les courants rectifiables, ainsi que de techniques provenant de problèmes de minimisation de périmètre.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 it