Transport Solutions of Biot’s Equations at Subsonic Loads
Bibliographic record
Abstract
The investigation of transport movement in tunnels, transported cargo and fluids in pipelines leads to model problems on the action of moving loads in a continuous medium.A feature of such problems is that the transport speed significantly affects the type of differential equations, which parametrically depend on the ratio of the transport speed to the wave propagation speeds in the medium.Therefore, when solving transport problems, different motion modes arise, which affects the type of transport equations on which the properties of solutions and the choice of methods for constructing them depend.In this case, it becomes necessary to study the effect of transport speed on the surrounding massif depending on its physical and mechanical properties.This paper is devoted to studying the dynamics of a two-component Biot's model under transport loads whose speed does not exceed the speeds of wave propagation in media (subsonic loads).The Green's tensor of transport equations is constructed and, on its basis, their solutions are obtained for any type of transport loads from the class of generalized functions, both regular and singular, concentrated on moving surfaces and lines.Numerical calculations illustrating the wave dynamics of a two-component Biot's model at subsonic speeds of transport loads are carried out.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".