Bibliographic record
Abstract
ABSTRACT: In a recent asymptotic analysis Peirce (2024) of the nonlocal PKN formulation Adachi and Peirce (2008) for a slender rectangular hydraulic fracture propagating in a permeable elastic medium, two distinct classes of tip asymptotes were identified. These two distinct classes of tip asymptote are the result of different limiting processes that were used to derive the asymptotes. The first class of asymptote, is established by a local analysis in the tip region of the nonlocal PKN model equations. The second class of asymptote, is established by combining the expression for the average fracture aperture and the appropriate plane strain asymptote for the desired mode of propagation. These asymptotes differ by from one another by between 4% - 9%. Since these two classes of limit asymptotes are equally valid, this paper aims to identify which asymptote yields a closer approximation to a fully planar model of a PKN fracture. The fully planar model is assumed to be endowed with the complete multiscale asymptote for a planar a hydraulic fracture in a 3D elastic medium that can propagate and arrest after shut-in, and which combines the competing processes of viscous dissipation, toughness energy release, and fluid leak-off.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".