Bibliographic record
Abstract
Abstract Benchmarks are provided for the evaluation of the effective coefficient for species diffusion, or electrical/thermal conduction, in structured porous media. The cases considered corresponding to doubly periodic rows of circular cylinders, for which a power series solution has been previously obtained, from complex variable theory. Both inline and staggered geometries are considered for three common configurations: inline-square, rotated-square, and equilateral geometries. From these mathematical solutions, values for the effective conduction/diffusion coefficient are readily constructed. The results are presented in terms of correlations for the ratio of effective-to-bulk conductivity/diffusivity or microstructural parameter, as a function of porosity. It is shown that near identical results with the present analytical analysis are obtained using calculations based on a finite-volume method and also with a previous mathematical analysis for the case of inline-square geometry. The present analytical solutions are also compared with two well-known correlations for random porous media, based on effective medium and percolation theory. It is shown that agreement with the analytical solution is not in general particularly good and depends on the choice of fitting parameters. The present results may be used as canonical data for comparative studies with numerical procedures to enumerate microstructural parameters for arbitrary-shaped occlusions in random geometries.
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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".