Generalization of the integral and differential method for analysis of rate data by means of the fractional calculus
Bibliographic record
Abstract
Abstract The kinetic study of chemical reactions is usually carried out by means of analysis of experimental rate data obtained during the evolution of a reaction in a batch reactor. The methods for analysis of rate data obtained in a batch reactor include the classical integral methods (CIM) and classical differential methods (CDM), which use temporal derivatives of the unit‐order concentration, dC A /dt , in the mass balance equation. The present study proposes these two methods of analysis in a generalized formulation that makes use of non‐integer order temporal derivatives, d α C A /dt α , 0 < α ≤ 1, called generalized integral method (GIM) and generalized differential method (GDM) in the present work. The solutions of the fractional ordinary differential equations (FODE) of GIM are presented using the Laplace transform technique and numerical fractional derivative evaluation methods for GDM application. The proposed generalized methods allow for the determination of the order and the specific reaction rate in the same way as the classical methods, that is, of integer order ( α = 1 ); however, generalized methods have the additional advantage of determining the fractional order of the temporal derivative.
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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 | 0.002 |
| 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".