Analysis of thermodiffusive cellular instabilities in continuum combustion fronts
Bibliographic record
Abstract
We explore numerically the morphological patterns of thermodiffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the recent model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers. These are studied using a dynamic adaptive mesh refinement technique that allows very large computational domains, thus allowing us to reduce finite-size effects that can affect or even preclude the emergence of these patterns. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip splitting and cell merging, are well described within the framework of thermodiffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as "quasilinear" and characterized by low-amplitude cells that may be strongly affected by the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly nonlinear effects become prominent and large-amplitude, complex cellular and seaweed dendritic morphologies emerge.
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How this classification was reachedexpand
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 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".