Regularization of the Ostwald supersaturation model for Liesegang bands
Bibliographic record
Abstract
In a previous paper, we analysed the Keller-Rubinow formulation of Ostwald's supersaturation theory for the formation of Liesegang rings or Liesegang bands, and found that the model is ill-posed, in the sense that after the termination of the first crystal front growth, secondary bands form, as in the experiment, but these are numerically found to be a single grid space wide, and thus an artefact of the numerical method. This ill-posedness is due to the discontinuity in the crystal growth rate, which itself reflects the supersaturation threshold inherent in the theory. Here we show that the ill-posedness can be resolved by the inclusion of a relaxation mechanism describing an impurity coverage fraction, which physically enables the transition in heterogeneous nucleation from precipitate-free impurity to precipitate-covered impurity.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".