Regularized shock solutions in coating flows with small surface tension
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Bibliographic record
Abstract
We study the dynamics of thin liquid films on the surface of a rotating horizontal cylinder in the presence of gravity in the small surface tension limit. Using dynamical system methods, we show that the continuum of shock solutions increasing across the jump point persists in the small surface tension limit, whereas the continuum of shock solutions decreasing across the jump point terminates in the limit. Using delicate numerical computations, we show that the number of steady states with equal mass increases as the surface tension parameter goes to zero. This corresponds to an increase in the number of loops on the mass-flux bifurcation diagram. If n is the number of loops in the mass-flux diagram with 2n + 1 solution branches, we show that n + 1 solution branches are stable with respect to small perturbations in the time evolution of the liquid film.
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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 | 0.000 |
| 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 it