Numerical Analysis of Phase Nonreciprocity in a Linear Spatiotemporally Modulated System
Bibliographic record
Abstract
Abstract Vibration transmissibility in a material with spatiotemporal modulation can be changed by just inverting the direction of transmission. This asymmetric feature of transmission can occur due to nonreciprocity. Various studies have demonstrated nonreciprocity in modulated materials by calculating or measuring the differences in amplitudes of response in opposite transmission directions. However, equal amplitudes do not indicate reciprocity because amplitude difference is blind to phase shift. In this work, we investigate nonreciprocal phase shifts (with equal transmitted amplitudes) in vibration transmission through a discrete one-dimensional periodic material subject to spatiotemporal modulation of grounding stiffness coefficients; the transmitted vibrations along the opposite directions have the same amplitude but undergo different phase shifts. We focus on the effects of the number of degrees of freedom (DoF) and modulation amplitude on vibration transmission nonreciprocity. We use the averaging method to calculate the steady-state response of the modulated system. Reciprocity bias and output norms are calculated to evaluate the degree of nonreciprocity in opposite transmission directions. Phase nonreciprocity is identified in cases where output norms are equal but reciprocity bias is not zero. While the response of the system is quasiperiodic, its envelope is periodic in time. We therefore use the response envelopes to help us identify response regimes that are characterized by nonreciprocal phase shifts. The analysis method based on the envelope of the steady-state response facilitates future parametric studies on phase nonreciprocity in discrete materials with spatiotemporal modulations.
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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 | 0.001 | 0.003 |
| 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".