Bibliographic record
Abstract
The behaviour of the one‐phase Stefan problem with nonlinear kinetic undercooling is studied. This system is physically relevant in a number of contexts, in particular as the sharp‐interface (fast‐reaction) limit of a variety of reaction–diffusion systems. The similarities and differences with the linear kinetic condition (studied by Evans and King (2000)) are highlighted for both one‐ and two‐dimensional problems. Asymptotic results (both in time and in the Stefan number) are obtained for the power‐law form of the kinetic condition. Significantly, the one‐dimensional growth behaviour of the moving boundary is seen to be relatively insensitive to the precise form of the nonlinear kinetic condition, and this in effect has hindered its experimental determination in applications such as silicon oxidation. By contrast, the two‐dimensional development of the moving boundary around a mask edge depends strongly on the form of the kinetic condition and consequently a method, similar to the Boltzmann–Matano method for determining nonlinear diffusivities, is described to determine the kinetic undercooling relation from experiment.
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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 | 0.006 |
| 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 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".