Mode Localization and Sensitivity in Weakly Coupled Resonators
Bibliographic record
Abstract
Localization of normal modes in weakly coupled resonators is used in the recent MEMS sensors to achieve orders of magnitude improvement in sensitivity. It is known that the sensitivity (S) of the modal amplitude ratio varies with the strength of the normalized coupling (κ) as S ∝ κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> in the case of two identical coupled oscillators, and as S ∝ κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> in the case of three coupled oscillators with the middle oscillator of a much higher natural frequency. We have recently shown that an asymmetry measure (α) will also affect the sensitivity according to S ∝ α <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . Here, we prove, using an energybased analysis, that in the general case of n ·· 2 uniformly coupled oscillators chained between two terminal oscillators, S ∝ α <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-n</sup> , if the blocked resonance spectra of the embedded oscillators and the end oscillators are well-separated. We further show that coupled asymmetric oscillators will also enhance the operating linear range, besides the increased sensitivity when compared with their symmetric counterparts, in a three coupled oscillators system. Our sensitivity and linear range expressions, not based on a (small) perturbation approach, have a wider range of accuracy. These analytical results are validated through numerical computation in the illustrative cases of three and four cell resonator chains.
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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".