Bibliographic record
Abstract
The reciprocity theorem in elastic materials states that the response of a linear, time-invariant system to an external load remains invariant with respect to interchanging the locations of the input and output. In the presence of nonlinear forces within a material, circumventing the reciprocity invariance requires breaking the mirror symmetry of the medium, thus allowing different wave propagation characteristics in opposite directions along the same transmission path. This work highlights the application of numerical continuation methods for exploring the steady-state nonreciprocal dynamics of nonlinear periodic materials in response to external harmonic drive. Using the archetypal example of coupled oscillators, we apply continuation methods to analyze the influence of nonlinearity and symmetry on the reciprocity invariance. We present symmetry-breaking bifurcations for systems with and without mirror symmetry, and discuss their influence on the nonreciprocal dynamics. Direct computation of the reciprocity bias allows the identification of response regimes in which nonreciprocity manifests itself as a phase shift in the output displacements. Various operating regimes, bifurcations and manifestations of nonreciprocity are identified and discussed throughout the work.
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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 | 0.001 | 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".