Bibliographic record
Abstract
The general solution of the Ornstein–Zernike equation presented by Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is further discussed. By applying the Hilbert transform, the first-order factorization and direct correlation functions (DCF) are generally and analytically obtained, with emphasis on the mean spherical approximation (MSA) for Yukawa fluids. These analytical results are employed to produce a new DCF for hard spheres through integrating with the previous generalized mean spherical approximation [J. Chem. Phys. 103, 7463 (1995)]. The new DCF is of simple analytical form and remedies the deficiencies of its Percus–Yevick version at high densities. Comparisons between the first-order and full MSA solutions are also made. It is shown that the two solutions give very close results for thermodynamic properties in the phase stable region and phase coexistence curves away from the critical point. At unstable states, the first-order MSA looks more advantageous when applications go beyond homogeneous.
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".