Interface coupling effect and multi-mode Faraday instabilities in a three-layer fluid system
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Bibliographic record
Abstract
We investigate the Faraday instabilities of a three-layer fluid system in a cylindrical container containing low-viscosity liquid metal, sodium hydroxide solution and air by establishing the Mathieu equations with considering the viscous model derived by Labrador et al. ( J. Phys.: Conf. Ser. , vol. 2090, 2021, 012088). The Floquet analysis, asymptotic analysis, direct numerical simulation and experimental method are adopted in the present study. We obtain the dispersion relations and critical oscillation amplitudes of zigzag and varicose modes from the analysis of the Mathieu equations, which agree well with the experimental result. Furthermore, considering the coupling strength of two interfaces, besides zigzag and varicose modes, we find a beating instability mode that contains two primary frequencies, with its average frequency equalling half of the external excitation frequency in the strongly coupled system. In the weakly coupled system, the $A$ -interface instability, $B$ -interface instability and $A$ & $B$ -interface instability are defined. Finally, we obtain a critical wavenumber $k_c$ that can determine the transition from zigzag or varicose modes to the corresponding $A$ -interface or $B$ -interface instability.
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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 | 0.001 | 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 | 0.001 |
| 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