Effect of discreteness on heterogeneous flames: Propagation limits in regular and random particle arrays
Bibliographic record
Abstract
In a system with discrete heat sources distributed in an inert, heat conducting medium, there exists two asymptotic regimes of flame propagation. When the flame thickness is much greater than the inter-particle spacing, the system approximates a homogeneous medium and the flame can be modeled as a continuum. In the other extreme, when the flame is very thin due to rapid reaction of particles, the heterogeneous flame can no longer be treated as a continuum since discrete effects become dominant. The effects of discreteness are characterized by a strong dependence on the spatial distribution of the sources. The present work investigates the effects of discreteness on flame propagation and demonstrates that these effects result in a propagation limit in the absence of losses. For a system of regularly spaced particles, this limit can be found analytically for one-, two-, and three-dimensional systems, although the flame exhibits a complex dynamic of bifurcations as it approaches this limit. Propagation of a flame beyond this limit is only possible through concentration fluctuations in a system with randomly distributed particles. Two-dimensional numerical simulations with randomly distributed particles show a strong dependence of the propagation limit on the size of the computational domain. A consequence of the random particle distribution is that the flammability limit can only be defined as a probabilistic outcome of the flame propagation simulations.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".