Moving and jumping spot in a two-dimensional reaction–diffusion model
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We consider a single spot solution for the Schnakenberg model in a two-dimensional unit disk in the singularly perturbed limit of a small diffusivity ratio. For large values of the reaction-time constant, this spot can undergo two different types of instabilities, both due to a Hopf bifurcation. The first type induces oscillatory instability in the height of the spot. The second type induces a periodic motion of the spot center. We use formal asymptotics to investigate when these instabilities are triggered, and which one dominates. In the parameter regime where spot motion occurs, we construct a periodic solution consisting of a rotating spot, and compute its radius of rotation and angular velocity. Detailed numerical simulations are performed to validate the asymptotic theory, including rotating spots. More complex, non-circular spot trajectories are also explored numerically.
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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 | 0.000 | 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 | 0.001 |
| 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