Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions
Bibliographic record
Abstract
Four kinetic models are studied as first-order reactions with flotation rate distribution f(k): (i) deterministic nth-order reaction, (ii) second-order with Rectangular f(k), (iii) Rosin–Rammler, and (iv) Fractional kinetics. These models are studied because they are considered as alternatives to the first-order reactions. The first-order representation leads to the same recovery R(t) as in the original domain. The first-order R∞-f(k) are obtained by inspection of the R(t) formulae or by inverse Laplace Transforms. The reaction orders of model (i) are related to the shape parameters of first-order Gamma f(k)s. Higher reaction orders imply rate concentrations at k ≈ 0 in the first-order domain. Model (ii) shows reverse J-shaped first-order f(k)s. Model (iii) under stretched exponentials presents mounded first-order f(k)s, whereas model (iv) with derivative orders lower than 1 shows from reverse J-shaped to mounded first-order f(k)s. Kinetic descriptions that lead to the same R(t) cannot be differentiated between each other. However, the first-order f(k)s can be studied in a comparable domain.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.002 | 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".