A two-phase problem for capillary-gravity waves and theBenjamin-Ono equation
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Bibliographic record
Abstract
The Benjamin-Ono equation is known as a model of internal long waves instratified fluids or two-fluid systems.In this paper, we consider the validity of this type of modeling of atwo-phase problem for capillary-gravity waves, which is a free boundaryproblem for the incompressible Euler equation with the irrotational condition.We show that the solutions of the free boundary problem split upinto two waves and the shape of each wave is governed bythe Benjamin-Ono equation in a slow time scale.
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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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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