NUMERICAL ESTIMATION OF CRITICAL CONDITIONS IN THERMAL EXPLOSION PROBLEM FOR A MEDIUM WITH FLUCTUATIONS OF REACTIVITY
Bibliographic record
Abstract
Формулируется задача о тепловом взрыве в среде с флуктуациями реакционной способности, которые задаются через функцию распределения энергии активации. Для дифференциального уравнения, описывающего стационарное распределение температуры в такой среде, предложена вариационная формулировка. С использованием простой пробной функции численно исследуется зависимость величины вариационного функционала от максимальной температуры. Критические условия теплового взрыва соответствуют появлению точки перегиба на этой зависимости. Расчеты показывают, что увеличение дисперсии распределения реакционной способности снижает устойчивость системы за счет уменьшения эффективной энергии активации для процесса тепловыделения. The problem of a thermal explosion in a medium with fluctuations in reactivity, which are specified through the distribution function for the activation energy, is formulated. A variational formulation is proposed for the differential equation describing the stationary temperature distribution in such a medium. Using a simple test function, the dependence of the variational functional on the value of the maximum temperature is numerically investigated. The critical conditions for a thermal explosion correspond to the appearance of an inflection point on this curve. Calculations show that an increase in the dispersion of the reactivity distribution the stability of the system decreases due to shift of the apparent activation energy of the chemical reaction.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".