Mixed mode growth of an ellipsoidal precipitate: Analytical solution for shape preserving growth in the quasi-stationary regime
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Bibliographic record
Abstract
The growth of an ellipsoidal precipitate has been analysed in the mixed-mode regime for a binary system. Under the assumption that the precipitate grows with constant eccentricities, an analytical solution was developed giving the time evolution of the size of the precipitate and the non-equilibrium concentration of the solute in the matrix. The mathematical analysis revealed that the evolution of the growth is characterized by a constant k called the interface migration coefficient. This coefficient was found to be equal to 12υc/ac, where ac is the critical size of nucleation and υc is the maximum growth velocity attainable with the applied driving force. This velocity, which was found to be proportional to the square root of the interface mobility, was assumed to be constant during the nucleation stage, making ac/υc to be the nucleation time. This finding suggests that there is a close link between the nucleation time and the mobility of the interface separating the nucleus from the matrix.
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it