Improved Formulations of the Superposition Method
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Bibliographic record
Abstract
Abstract Two formulations of an improved superposition method are proposed for studying droplet–droplet hydrodynamic interactions. The formulations make explicit use of the boundary conditions on the surface of the two interacting droplets. The improved formulations are described through a consistent and rigorous consideration of the relationship between the drag force and representation of disturbance flows. It is demonstrated that the improved formulations are much more accurate than the original implementation of the superposition method. Specifically, for the case of Stokes disturbance flows, the relative errors on the drag force can be reduced by one order of magnitude using the improved formulations, when compared with the original formulation, for situations when the lubrication effect is not dominant. Using the improved superposition method, collision efficiencies of small cloud droplets falling in calm air are also computed and compared with previously published results.
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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 | 0.001 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it