Guided and standing Bloch waves in periodic elastic strips
Bibliographic record
Abstract
Elastic waveguiding structures are investigated for guides constructed of periodically alternating media thereby forming a striped waveguide. The guide has finite width with either homogeneous traction-free or clamped boundary conditions on the guide walls, or a combination of these. The band spectrum and associated Floquet–Bloch eigensolutions for these in-plane elastic waveguides are identified. Several features of this guiding structure emerge, and are of interest; in some cases a total stop band at zero frequency is identified providing space for low frequency localized modes: such modes also appear when we create defects in the structured waveguide. The dispersion curves often have maxima and minima of the spectral edges far from the edges of the Brillouin zone and these are related to slow sound or standing waves within the structure. Numerical and asymptotic techniques are developed and discussed, the latter are based on weak contrast, and weak geometric changes, or utilize jump conditions in limits where one medium is thin relative to the other. There are technological applications that could utilize this theory and we demonstrate that imaging is possible using anomalous dispersion.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".