A General Expression for the Ordered-Packed Volume Fraction of Hard Spheres of Different Diameters
Bibliographic record
Abstract
An expression is proposed to evaluate the ordered-packed volume fraction of hard spheres of unequal diameters in multicomponent mixtures. This value can be used with different mixing rules and with any one-component hard-sphere equation of state (EOS) meeting the correct close-packed limit. It is shown that the new method improves the results produced by conventional mixing rules for the individual radial distribution functions (RDFs) at contact value of hard-sphere mixtures. Particular attention is given to the case of the large diameter ratio especially when the larger spheres are at low concentration. Based on the observation that, in a binary mixture, the value of the RDF at contact value of the larger spheres approaches the value of the RDF at contact value of a one-component hard-sphere fluid, the proposed expression is used to correct the RDF at contact value of a pure hard-sphere fluid in the Santos et al. mixing rule. The EOS obtained by combining the Ghotbi−Vera one-component EOS with the corrected Santos et al. mixing rule is used to predict different thermodynamic properties, and the results are compared with the computer-simulated data.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".