Solitary Waves in an Array of Nonlinear Oscillators With Time-Periodic Damping and Stiffness Coefficients
Bibliographic record
Abstract
Abstract The localized nonlinear responses of a chain of nonlinear pendulums with time-periodic damping and stiffness coefficients are investigated. The existence conditions and stability of the solitary waves are revisited for the aforementioned system. In essence, the parametrically driven discrete Klein-Gordon equation with time-periodic damping coefficient is converted to a damped parametrically driven discrete nonlinear Schrodinger equation using the method of multiple scales. The numerical simulations show how the stability and characteristics of the solitary waves are modified when the periodically modulated damping coefficient, which is either synchronized or asynchronized with the time-periodic stiffness coefficient, is added. In practice, time-periodic damping coefficient can be treated as a new way to tune the characteristic of the solitons (i.e., required threshold of the soliton activation and the period of oscillations) in the nonlinear periodic structures. This modification may provide some insights towards the control of the energy localization phenomena in nonlinear periodic structures with time-varying coefficients for efficient energy transport/management applications.
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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".