Influence of the medium's dimensionality on defect-mediated turbulence
Bibliographic record
Abstract
Spatiotemporal chaos in oscillatory and excitable media is often characterized by the presence of phase singularities called defects. Understanding such defect-mediated turbulence and its dependence on the dimensionality of a given system is an important challenge in nonlinear dynamics. This is especially true in the context of ventricular fibrillation in the heart, where the importance of the thickness of the ventricular wall is contentious. Here, we study defect-mediated turbulence arising in two different regimes in a conceptual model of excitable media and investigate how the statistical character of the turbulence changes if the thickness of the medium is changed from (quasi-) two- dimensional to three dimensional. We find that the thickness of the medium does not have a significant influence in, far from onset, fully developed turbulence while there is a clear transition if the system is close to a spiral instability. We provide clear evidence that the observed transition and change in the mechanism that drives the turbulent behavior is purely a consequence of the dimensionality of the medium. Using filament tracking, we further show that the statistical properties in the three-dimensional medium are different from those in turbulent regimes arising from filament instabilities like the negative line tension instability. Simulations also show that the presence of this unique three-dimensional turbulent dynamics is not model specific.
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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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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".