Bibliographic record
Abstract
This paper is an extension of our earlier paper in which it was shown that the meniscus shape in a cylindrical capillary could be computed by solving the Young-Laplace equation via optimization of a Bézier curve. This work extends the previous work by demonstrating that the method is applicable to predict the meniscus shape not only in a cylindrical capillary but also in other cases, such as at a tilted plate, between two plates, and for a sessile drop. Numerous works have attempted previously to solve the Young-Laplace equation, and their results all agree with this paper's validating its method. All the preceding approaches, however, used special techniques to solve the differential equation, while the Bézier curve method proposed in this work is more simple, which allows it to maintain greater computational simplicity. Moreover, the Bézier curve method can be applied to solve many other different differential equations in the same way as shown in this work. The effect of the Bézier curve degree on the precision of prediction was also thoroughly investigated. It was found that the 4th degree Bézier curve was required to predict the meniscus shape precisely in a cylindrical capillary, against a tilted plate, and between two plates, while the 5th degree was required for the shape of the sessile drop.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".