Bibliographic record
Abstract
In the quest to understand the dynamics of distributed systems on time-dependent spatial domains, we study experimentally the response to domain deformations by Faraday wave patterns – standing waves formed on the free surface of a liquid layer due to its vertical vibration – chosen as a paradigm owing to their historical use in testing new theories and ideas. In our experimental set-up of a vibrating water container with controlled positions of lateral walls and liquid layer depth, the characteristics of the patterns are measured using the Fourier transform profilometry technique, which allows us to reconstruct an accurate time history of the pattern three-dimensional landscape and reveal how it reacts to the domain dynamics on various length and time scales. Analysis of Faraday waves on growing, shrinking and oscillating domains leads to a number of intriguing results. First, the observation of a transverse instability – namely, when a two-dimensional pattern experiences an instability in the direction orthogonal to the direction of the domain deformation – provides a new facet to the stability picture compared to the one-dimensional systems in which the longitudinal (Eckhaus) instability accounts for pattern transformation on time-varying domains. Second, the domain evolution rate is found to be a key factor dictating the patterns observed on the path between the initial and final domain aspect ratios. Its effects range from allowing the formation of complex sequences of patterns to impeding the appearance of any new pattern on the path. Third, the shrinkage–growth process turns out to be generally irreversible on a horizontally evolving domain, but becomes reversible in the case of a time-dependent liquid layer depth, i.e. when the dilution and convective effects of the domain flow are absent. These experimentally observed enigmatic effects of the domain size variations in time are complemented here with appropriate theoretical insights elucidating the dynamics of two-dimensional pattern evolution, which proves to be more intricate compared to one-dimensional systems.
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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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".