Buckling of a soap film spanning a flexible loop resistant to bending and twisting
Bibliographic record
Abstract
A generalization of the Euler–Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler–Lagrange equations are derived in a parametrized setting and a buckling analysis is performed. A pair of dimensionless parameters govern buckling from a flat, circular ground state. While one of these is familiar from the Euler–Plateau problem, the other encompasses information about the ratio of the torsional rigidity to the bending rigidity, the twist density and the size of the loop. For sufficiently small values of the latter parameter, two separate groups of buckling modes are identified. However, for values of that parameter exceeding the critical twist density arising in Michell's study of the stability of a twisted elastic ring, only one group of buckling modes exists. Buckling diagrams indicate that a loop with greater torsional rigidity shows more resistance to transverse buckling. Additionally, a twisted flexible loop spanned by a soap film buckles at a value of the twist density less that the value at which buckling would occur if the soap film were absent.
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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".