Bibliographic record
Abstract
Unbounded capillary surfaces in domains with a sharp corner or a cusp are studied.It is shown how numerical study using a proposed computational methodology leads to two new conjectures for open problems on the asymptotic behavior of capillary surfaces in domains with a cusp.The numerical methodology contains two simple but important ingredients, a change of variable and a change of coordinates, which are inspired by known asymptotic approximations for unbounded capillary surfaces.These ingredients are combined with the finite volume element or Galerkin finite element methods.Extensive numerical tests show that the proposed computational methodology leads to a global approximation method for singular solutions of the Laplace-Young equation that recovers the proper asymptotic behavior at the singular point, is more accurate and has better convergence properties than numerical methods considered for singular capillary surfaces before.Using this computational methodology, two open problems on the asymptotic behavior of capillary surfaces in domains with a cusp are studied numerically, leading to two conjectures that may guide future analytical work on these open problems.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".