Integral equation study of the residual chemical potential in infinite‐dilution supercritical solutions
Bibliographic record
Abstract
Abstract A new method for solving the integral equation based on the Ornstein‐Zernike equation for binary mixture is proposed. Then the radial distribution function obtained for both the Percus‐Yevick and the hypernetted chain closure equations are used to calculate the residual chemical potential at infinite‐dilution and at reduced temperatures T* = 2, 1.5 (supercritical isotherms) over a varying range of reduced densities ρ* = 0.1 to 0.6 for various types of the Lennard‐Jones mixture in terms of size ratios D and energy ratios C. To examine the ability of the integral equation approach for the residual chemical potential calculations, the results are compared with the Monte‐Carlo simulation data and the van der Waals I results (Shing et al., 1988). It is seen that at ρ* = 0.1 to 0.5, the deviation of the integral equation results from the MC simulation data is less than the reported statistical fluctuation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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".