Buckling of a thin, viscous film in an axisymmetric geometry
Bibliographic record
Abstract
By adapting the Föppl-von Kàrmàn equation, which describes the deformation of a thin elastic membrane, we present an analysis of the buckling pattern of a thin, very viscous fluid layer subject to shear in an axisymmetric geometry. A linear stability analysis yields a differential eigenvalue problem, whose solution, obtained using spectral techniques, yields the most unstable azimuthal wave-number, m⋆. Contrary to the discussion of Slim et al. [J. Fluid Mech. 694, 5–28 (2012)]10.1017/jfm.2011.437, it is argued that the axisymmetric problem shares the same degeneracy as its rectilinear counterpart, i.e., at the onset of instability, m⋆ is indefinitely large. Away from this point, however, a comparison with analogue experimental results is both possible and generally favorable. In this vein, we describe the laboratory apparatus used to make new measurements of m⋆, the phase speed and the wave amplitude; note that no prediction concerning the latter two quantities can be made using the present theory. Experiments reveal a limited range of angular velocities wherein waves of either small or large amplitude may be excited. Transition from one to the other regime does not appear to be associated with a notable change in m⋆.
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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 | 0.001 |
| 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".