Slow manifold for a bimolecular association mechanism
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Bibliographic record
Abstract
Finding the slow manifold for two-variable ordinary differential equation (ODE) models of chemical reactions with a single equilibrium is generally simple. In such planar ODEs the slow manifold is the unique trajectory corresponding to the slow relaxation of the system as it moves towards the equilibrium point. One method of finding the slow manifold is to use direct iteration of a functional equation; another method is to obtain a series solution of the trajectory differential equation of the system. In some cases these two methods agree order-by-order in the singular perturbation parameter controlling the fast relaxation of the intermediate (complex). However, de la Llave has found a model ODE where the series method always diverges. Bimolecular association is an example of a chemical reaction where the series method for finding the slow manifold diverges but the iterative method converges. In this mechanism a complex is formed which can then undergo unimolecular decay, i.e., [reaction: see text]. The kinetics of this reaction are investigated and its properties compared with two other two-step mechanisms where series expansion and iteration methods are equivalent: the Michaelis-Menten mechanism for enzyme kinetics, and the Lindemann-Christiansen mechanism of unimolecular decay in gas kinetics.
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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 it