Causal transient propagation in media with classical or power-law loss
Bibliographic record
Abstract
The manner in which transient waves propagate in a medium with classical viscous losses is generally addressed is by determining solutions to the wave equation originally derived by Stokes. Exact solutions are difficult to obtain even for plane waves and simple transient forms and consequently, approximations are generally made. A related problem, of particular interest in relation to ultrasound transmission in soft tissue, is propagation in a medium, whose absorption coefficient obeys power-law frequency dependence, i.e., /spl alpha/ /spl prop/ /spl omega/". By using a recently obtained solution to a causal convolution wave equation, expressions are obtained for one-dimensional transient propagation for n=2 and n=1. Analytical expressions are obtained for a sinusoidal step function source when the effects of dispersion are ignored. When the effects of dispersion are accounted for, it is shown that the propagation can be expressed in terms of Fourier transforms. Examples are used to illustrate the results for both dispersive and non-dispersive media.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".