The propulsive effect generated by fast travelling-wave vibrations
Bibliographic record
Abstract
Abstract A prototype problem for the propulsion arising from a spatially-dependent source is analysed asymptotically. Such driving is a phenomenon that, while fairly common in biological settings, is less well understood in mechanical and engineering contexts. If two parallel plates bound a fluid and the plates are free to translate relative to each other, recent calculations have shown that vibrations applied to one plate in the form of travelling waves may induce motion of the other. The degree of the propulsion obtained is a function of both the wavelength and the phase speed of the imposed vibrations and there seems to an optimal wavelength for which propulsion is greatest. In order to shed light on these observations, here we undertake a formal asymptotic analysis of the process in the circumstance when the vibrations move quickly. It is shown how the flow structure takes on a form consisting of a bulk core layer supplemented by suitable edge layers attached to the two plates. The efficiency of the mechanism relies on the generation of a mean flow component whose properties are considered. It is found that there is excellent agreement between our analytical predictions and the previous simulations; in particular we are able to find the critical wavelength for maximum propulsion and explain the modifications that arise in the short and long wavelength limits.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".