Bifurcations of Asymmetric Vortices in Symmetric Harmonic Traps
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Bibliographic record
Abstract
We show that, under the effect of rotation, symmetric vortices located at the center of a two-dimensional harmonic potential are subject to a pitchfork bifurcation with radial symmetry. This bifurcation leads to the family of asymmetric vortices, which precess constantly along an orbit enclosing the center of symmetry. The radius of the orbit depends monotonically on the difference between the rotation frequency and the eigenfrequency of negative Krein signature associated with the symmetric vortex. We show that both symmetric and asymmetric vortices are spectrally and orbitally stable with respect to small time-dependent perturbations for rotation frequencies exceeding the bifurcation eigenfrequency. At the same time, the symmetric vortex is a local minimizer of energy for supercritical rotation frequencies, whereas the asymmetric vortex corresponds to a saddle point of energy. For subcritical rotation frequencies, the symmetric vortex is a saddle point of the energy.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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 it