Negative bending mode curvature via Robin boundary conditions
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Bibliographic record
Abstract
We examine the band spectrum, and associated Floquet–Bloch eigensolutions, arising in straight walled acoustic waveguides that have periodic structure along the guide. Homogeneous impedance (Robin) conditions are imposed along the guide walls and we find that in certain circumstances, negative curvature of the lowest (bending) mode can be achieved. This is unexpected, and has not been observed in a variety of physical situations examined by other authors. Further unexpected properties include the existence of the bending mode only on a subset of the Brillouin zone, as well as permitting otherwise unobtainable velocities of energy transmission. We conclude with a discussion of how such boundary conditions might be physically reproduced using effective conditions and homogenization theory, although the methodology to achieve these effective conditions is an open problem.
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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 | 0.000 | 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 | 0.001 |
| 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