Collective behaviour of large number of vortices in the plane
Bibliographic record
Abstract
We investigate the dynamics of N point vortices in the plane, in the limit of large N . We consider relative equilibria , which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in several recent experiments. We show that these solutions and their stability are fully characterized via a related aggregation model which was recently investigated in the context of biological swarms. By using this connection, we give explicit analytical formulae for many of the configurations that have been observed experimentally. These include configurations of vortices of equal strength; the N +1 configurations of N vortices of equal strength and one vortex of much higher strength; and more generally, N + K configurations. We also give examples of configurations that have not been studied experimentally, including N +2 configurations, where N vortices aggregate inside an ellipse. Finally, we introduce an artificial ‘damping’ to the vortex dynamics, in an attempt to explain the phenomenon of crystallization that is often observed in real experiments. The diffusion breaks the conservative structure of vortex dynamics, so that any initial conditions converge to the lattice-like relative equilibrium.
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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".