Surface Instability of an Elastic Thin Film Interacting With a Suspended Elastic Plate
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Bibliographic record
Abstract
This paper studies surface instability of a compliant elastic thin film on a rigid substrate interacting with a suspended elastic plate through van der Waals forces. The analysis is based on a novel method which permits a simple rational expression for the interaction coefficient as a function of the wave number of instability mode. The critical value of the interaction coefficient and the instability mode of the film-plate system can be determined easily by identifying the minimum of the interaction coefficient within an admissible range. When the stability strength of the plate is lower than the film even for the shortest plate-lengths, the interaction coefficient is found to be an increasing function of the wave number, and thus the film-plate system exhibits a long-wave instability mode determined by the suspended plate. In all other cases, the interaction coefficient admits an internal local minimum representing the short-wave mode of the film, and the critical value and instability mode of the film-plate system are determined by the internal local minimum for shorter plates, or by the long-wave mode of the plate for longer plates. Some numerical examples are given to illustrate the results.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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