Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems
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Bibliographic record
Abstract
We consider the general class of two-component reaction-diffusion systems on afinite domain that admit interface solutions in one of the components, and westudy the dynamics of $n$ interfaces in one dimension. In the limit where thesecond component has large diffusion, we fully characterize the possiblebehaviour of $n$ interfaces. We show that after the transients die out, themotion of $n$ interfaces is described by the motion of a singleinterface on the domain that is $1/n$ the size of the original domain.Depending on parameter regime and initial conditions, one of the followingthree outcomes results: (1) some interfaces collide; (2) all $n$ interfacesreach a symmetric steady state; (3) all $n$ interfaces oscillateindefinitely. In the latter case, the oscillations are described by a simpleharmonic motion with even-numbered interfaces oscillating in phase whileodd-numbered interfaces are oscillating in anti-phase. This extends a recentwork by [McKay, Kolokolnikov, Muir, DCDS B(17), 2012] from two to any numberof interfaces.
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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 | 0.000 | 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 it