Computer simulation of cavity pair distribution functions of hard spheres in a hard slit pore
Bibliographic record
Abstract
We describe efficient Monte Carlo computer simulation techniques to calculate conditional distribution functions for pairs of hard-sphere (HS) cavities in a hard slit pore of width L, n* (z 1,z 2,r), and use these as an efficient route to calculating the corresponding dimensionless excess chemical potentials μ e (z 1,z 2,r). zi is the distance of an HS centre from a (specified) wall and r is the distance between the cavity centres. This is the first calculation of such functions, which are of interest in their own right and provide data for the testing of theories, in addition to providing data for a simple model for the infinite dilution behaviour of a polyatomic solute in a simple molecularly confined solvent. Results are presented for special cases for the cavity functions n* (z 1,z 2,r) which occur when the spheres are in the same plane, when the line of sphere centres is perpendicular to the walls, and when the spheres are in contact. We compare results obtained using the Kirkwood superposition approximation in conjunction with results obtained from the computer simulation data using the first member of the BGY integral equation hierarchy. The approximation is found to be exact in certain limiting geometrical situations, but in general is quantitatively poor.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".