Constant-number Monte Carlo simulation of aggregating and fragmenting particles
Bibliographic record
Abstract
The constant-number Monte Carlo method introduced by Matsoukas and co-workers for simulating particulate systems is applied to the kinetics of aggregating and fragmenting particles. The efficiency of this approach is increased by incorporating a modified version of Gillespie’s full-conditioning algorithm for selecting an aggregation or fragmentation event. After the steps comprising the algorithm are outlined, it is validated by simulations for several aggregation and fragmentation kernels for which the population balance equations can be solved exactly. The results agree very well with the analytical expressions except for those kernels that give rise to a gelation transition, such as the product kernel kij=ij. In this case, the simulation data are accurate below the transition time tg, but deviate significantly above tg. The accuracy of the simulation method in describing gelling kernels, including those of the form kij=(ij)ω, is also investigated. For a strongly gelling kernel, tg is accurately predicted by maxima in the time derivative of the second moment of the particle mass and the time dependence of the number of size classes in the simulation. Gel formation is simulated by setting a threshold size g above which particles have properties of the gel in the Stockmayer or Flory models. The Stockmayer model can be accurately simulated for a value of g that depends on the number of particles in the simulation. Simulation of the Flory model is less successful; results are obtained more efficiently by using the conventional constant-volume Monte Carlo method.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 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".