On the solution of the dynamic population balance model describing emulsification: Evaluation of weighted residual methods
Bibliographic record
Abstract
Abstract Numerical techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau and least‐squares, are evaluated for the solution of transient population balance (PB) models describing liquid–liquid emulsification systems in stirred batch vessels. The numerical solution techniques are compared based on (i) a breakage dominated system with experimental data available, and (ii) a breakage–coalescence test case. Two numerical approaches are studied for the transient term: (i) time‐differencing by a low order finite difference approximation, and (ii) the spectral‐element technique. Both approaches use spectral approximations in the phase space dimension. Based on a residual measure, computational costs, and implementation complexity the combined finite difference–spectral approach is recommended above the spectral‐in‐time‐spectral‐in‐space approach. Within this recommended solution framework, it is not necessary to use a more mathematical complex spectral method than the orthogonal collocation technique.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".