Leapfrog/Dufort-Frankel explicit scheme for diffusion-controlled moving interphase boundary problems with variable diffusion coefficient and solute conservation
Bibliographic record
Abstract
Abstract A new numerical model with solute conservation is developed to study diffusion-controlled interphase-interface migration kinetics. The new model which can directly incorporate variable and constant diffusion coefficients is a fully explicit numerical method based on Leapfrog and Dufort-Frankel’s explicit schemes. The stability and consistency analysis of this model show that applying the Leapfrog/Dufort-Frankel scheme to Landau transformed Fick’s second law problem, results in a more stable solution that ensures computational accuracy and enhances the computation efficiency when compared to the classical explicit model. The new explicit model is more accurate, direct and faster than implicit models because it does not involve non-trivial assumptions that decrease the accuracy of implicit models. This model is used in this work to modify the classical Heckel’s criteria for second-phase growth, to predict factors that affect the growth rate, homogenization time, and the extent of second-phase growth, in a two-phase alloy.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".