New numerical method for solving the dynamic population balance equations
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Bibliographic record
Abstract
Abstract A new numerical scheme is proposed for solving general dynamic population balance equations (PBE). The PBE considered can simultaneously include the kinetic processes of nucleation, growth, aggregation and breakage. Using the features of population balance, this method converts the PBE into a succession of algebraic equations which can be solved easily and accurately. The new method is free from stability and dispersion problems of general numerical techniques. Some benchmark problems with analytic solutions were tested. In all cases tested this method gave accurate results with very few computational requirements. For nucleation and size‐independent growth without aggregation and breakage, the numerical method gives exactly the same result as analytic solution. © 2005 American Institute of Chemical Engineers AIChE J, 2005
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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 | 0.001 | 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) | 0.001 | 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 it