Flow and Solute Transport in Saturated Porous Media: 1. The Continuum Hypothesis
Bibliographic record
Abstract
The continuum hypothesis provides one alternative to dealing with transport phenomena in porous media. If adapted correctly, the continuum approach may be easier than dealing with the system at the microscopic level. However, to adopt the continuum approach to phenomena occurring in porous media, certain conditions and length scale constraints need to be satisfied. Failing to satisfy these conditions may restrict the use of this approach, and other sophisticated methods need to be devised. This article provides an overview of the conditions and length scale constraints needed to be able to adopt the continuum hypothesis. Two types of length scale constraints may be identified. The first type arises when establishing the conditions and requirements for proper upscaling; they are thus essential and hence have to be completely satisfied. They have been collected in four constraints. The second type represents those derived during mathematical manipulations and order of magnitude analysis to neglect higher-order terms. It will be shown that most of the second type of length scale constraints are automatically satisfied once the essential constraints are satisfied.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".