Computation of response envelopes in a lattice material withspatiotemporal modulations
Bibliographic record
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 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".