Pairwise interactions of ring dark solitons with vortices and other rings: Stationary states, stability features, and nonlinear dynamics
Bibliographic record
Abstract
In the present work, we explore analytically and numerically the coexistence and interactions of ring dark solitons (RDSs) with other RDSs, as well as with vortices. The azimuthal instabilities of the rings are explored via the so-called filament method. As a result of their nonlinear interaction, the vortices are found to play a stabilizing role on the rings, yet their effect is not sufficient to offer complete stabilization of RDSs. Nevertheless, complete stabilization of the relevant configuration can be achieved by the presence of external ring-shaped barrier potentials. Interactions of multiple rings are also explored, and their equilibrium positions (as a result of their own curvature, the external trap, and their tail-tail interactions) are identified. In this case too, stabilization is achieved via multiring external barrier potentials.
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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) | 0.001 | 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".