Resonant oscillation of surface waves in an annular tank
Bibliographic record
Abstract
We consider the resonant oscillation of surface waves in a shallow annular tank. This axisymmetric configuration provides a simple yet nontrivial setting in which to investigate the long-time interplay between geometric and nonlinear effects. Since, unlike the rectangular case, standard analytic approaches based on underlying characteristic structures are no longer applicable, we employ an alternative and more general analytic framework based upon the underlying spectral decomposition of spatial eigenfunctions. In the limit that geometric effects vanish, we show that this reduces to the known forced Korteweg–de Vries (fKdV) equation for the rectangular case. We then apply this approach to the annular configuration both in general and in the limit that the curvature scales with the forcing amplitude. For the latter, we derive an associated hierarchical system of algebraic solvability conditions for the modal amplitudes as a correction to that for the underlying rectangular case. The subsequent solution of these systems in turn provides direct characterization of the geometric effects to this order. In parallel, and in the absence of a simplified long-time balance akin to the fKdV, a general numerical implementation involving the splitting of the elliptic and evolutionary aspects of the full equations for surface waves is developed and implemented. This is used to validate and extend these analytic results and provide further insights into the fundamental ways in which geometric variation impacts resonant behavior.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".