Bibliographic record
Abstract
Resonant behavior in bounded domains and under the influence of weakly periodic forcing with magnitude is studied for a general class of one‐dimensional nonlinear wave systems. The model encompasses and provides analogy to numerous physically motivated cases such as acoustic resonators. Through a generalized weakly nonlinear analysis the linear response and associated resonant spectrum may be determined. In the case where the spectrum is sufficiently noncommensurate a single mode response emerges with amplitude . Dependence upon detuning and dissipative effects follow immediately from the subsequent nonlinear balance. In the case where the spectrum is commensurate a multimodal response arises, leading to a coupled system of solvability conditions. The amplitude of the response depends in detail on the commensurate structure, in the case where it is fully commensurate. This is in keeping with the well‐known dichotomy between responses for acoustic waves in open and closed tubes. Through continuous variation of the model system, the nature of the transition between these distinct regimes is then studied and through an appropriate modal truncation the connection is achieved. A numerical example is presented to further illustrate and corroborate the general analysis.
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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 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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".