Waves in liquid films on vibrating substrates
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Bibliographic record
Abstract
This paper is concerned with liquid films on horizontally vibrating substrates. Using an equation derived by Shklyaev [Phys. Rev. E 79, 051603 (2009)], we show that all periodic and solitary-wave solutions of this equation are unstable regardless of their parameters. Some of the solitary waves, however, are metastable--i.e., still unstable, but with extremely small growth rates--and, thus, can persist without breaking up for a very long time. The crests of these metastable waves are flat and wide, and they all have more or less the same amplitude (determined by the problem's global parameters). The metastable solitary waves play an important role in the evolution of films for which the state of uniform thickness is unstable. Those were simulated numerically, with two basic scenarios observed depending on the parameter A=3(omega/2nu);1/2U02/g , where nu is the kinematic viscosity, g is the acceleration due to gravity, and omega and U0 are the frequency and amplitude (maximum velocity) of the substrate's vibration. (i) If A <or=25 , a small number of metastable solitary waves with flat/wide crests emerge from the evolution and exist without coalescing (or even moving) for an extremely long time. (ii) If A <or=25 , the solution of the initial-value problem breaks up into a set of noninteracting pulses separated by regions where the film's thickness rapidly tends to zero.
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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