On the advective‐diffusive transport in porous media in the presence of time‐dependent velocities
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Bibliographic record
Abstract
This paper develops certain exact closed form solutions to one‐dimensional problems involving both advective and advective‐diffusive transport in a porous medium, particularly in the presence of a Darcy velocity field that is time‐dependent. Such situations can occur when the boundary potential inducing flow in the porous medium is time‐dependent. A particular form chosen is an exponentially decaying time‐dependency in the flow velocity, resulting from a non‐replenishing source. The value of the one‐dimensional solution stems not only from its potential applicability for the calibration of computational schemes used to examine the advection‐diffusion equation in general, but also for the study of the purely advective flow problem with time‐dependent velocity that requires sophisticated adaptive computational schemes to ensure numerical stability at a leading front in the form a discontinuity.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it