Computation of response envelopes in a lattice material withspatiotemporal modulations
Bibliographic record
Abstract
Abstract: Materials with spatiotemporal modulations possess effective properties that vary in space and time periodically. Because of the wave-like properties of a modulated material, propagation of incident waves through the material depends on their directions of travel. This direction-dependent transmission occurs due to a scattering effect that is caused because of the modulations. If the modulated material is long enough, it can act as a unidirectional wave isolator, preventing waves from propagating in one direction. However, such unidirectional transmission does not occur in very short modulated materials, i.e. two degrees of freedom (2 DOF) systems. In this work, we study nonreciprocal vibration transmission in a discrete onedimensional (1-D) modulated material, with a focus on computing the change in the amplitude and phase of transmitted vibrations along opposite directions. Because the response of a modulated system is not periodic in time, this process requires either brute force computations or asymptotic analysis with a limited range of validity. To overcome this shortcoming, we develop and utilize the envelopes of the steady-state output displacements to investigate nonreciprocity. Furthermore, we highlight the application of envelope equations in identifying nonreciprocal response regimes characterized by a nonreciprocal phase shift in transmitted vibrations. The role of the length of 1-D modulated materials on determining the amplitude difference is highlighted. The analysis method based on envelopes of the steady-state response facilitates future parametric studies on nonreciprocity in discrete modulated materials.
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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".