Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".