Identification of Two-Phase Free Boundary Arising in Plasma Physics
Bibliographic record
Abstract
We try to estimate the shape and the location of two-phase free boundary which has been studied in [A. Friedman and Y. Liu, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 22 (1995), pp. 375--448] to model a stationary magnetohydrodynamics system. A sufficient condition is obtained to check whether a test disk is included in the plasma region D surrounded by a two-phase free boundary. In the test disk technique, only two simply verifiable conditions are used and indispensableness of the conditions is demonstrated using an example. The technique is applicable to select some of test disks placed in the domain $\Omega$, which gives a rough guess on the shape of plasma region. Next we draw some geometrical properties of plasma region D when the domain $\Omega$ possesses a kind of convexity. It is proved that if $\Omega$ itself contains the mirror image of the right portion $\{x \in \Omega : x \cdot \xi > t \}$ of the domain with respect to a line $\{x: x \cdot \xi = t \}$ for all t > t 0 , then so does the plasma region.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".