Poroelastic acoustic wave trains excited by harmonic line tractions
Bibliographic record
Abstract
A two-dimensional boundary-value problem for a porous half-space with an open boundary, described by the widely recognized Biot's equations of poroelasticity, is considered. Using complex analysis techniques, a general solution is represented as a superposition of contributions from the four different types of motion corresponding to P1, P2, S and Rayleigh waves. Far-field asymptotic solutions for the bulk modes, as well as near-field numerical results, are investigated. Most notably, this analysis reveals the following: (i) a line traction generates three wave trains corresponding to the bulk modes, so that P1, P2 and S modes emerge from corresponding wave trains at a certain distance from the source, (ii) bulk modes propagating along the plane boundary are subjected to geometric attenuation, which is found quantitatively to be x −3/2 , similar to the classical results in perfect elasticity theory, (iii) the Rayleigh wave is found to be predominant at the surface in both the near (due to the negation of the P1 and S wave trains) and the far field (due to geometric attenuation of the bulk modes), and (iv) the recovery of the transition to the classical perfect elasticity asymptotic results validates the asymptotics established herein.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".