The Growth of Ice Crystals by Molecular Diffusion
Bibliographic record
Abstract
Abstract The mass transfer of water molecules by diffusion onto ice particles is best described by their Sherwood number (Sh), a dimensionless quantity, which combines molecular and convective effects and depends on the airflow as represented by the Reynolds number (Re). While Sh (Re > 0) has been previously measured in experiments for typical crystal shapes, the limiting case of pure molecular diffusion (Sh0) for zero flow with Re = 0 is not known well and needs independent determination. The direct numerical solution of the controlling Laplace equation links diffusion with electric fields through the electrostatic analogy. It will be solved for the electrostatic potential V around a crystal-shaped conductor of capacitance C. The results will then be converted by similarity theory. This led to the first numerical determination of Sh0 for hexagonal plates, hexagonal columns, stellar crystals, capped columns, and broad-branched crystals. The new data represent another necessary step in the formulation of an experiment-based theory of the growth of freely falling ice crystals in the atmosphere. A discrete version of Gauss's flux law is developed to compute the flux generated by a crystal-shaped conductor in a finite Cartesian grid box, using a Gauss–Seidel iterative scheme. This method is general and can be applied to compute Sh0 for any rectilinear shapes to any degree of accuracy. The dimensionless mass transfer by molecular diffusion, Sh0, is identical to the diffusion of heat characterized by the Nusselt number Nu0.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| 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 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".