Transient propagation in media with classical or power-law loss
Bibliographic record
Abstract
This paper addresses the problem of small-signal transient wave propagation in media whose absorption coefficient obeys power-law frequency dependence, i.e., alpha infinity omega n. Our approach makes use of previously derived relations between the absorption and dispersion based on the Kramers-Kronig relations. This, combined with a recently obtained solution to a causal convolution wave equation enable expressions to be obtained for one-dimensional transient propagation when n is in the range 0 < n < 3. For n = 2, corresponding to no dispersion, straightforward analytical expressions are obtained for a delta-function and a sinusoidal step function sources and these are shown to correspond to relations previously derived. For other values of n, the effects of dispersion are accounted for by using Fourier transforms. Examples are used to illustrate the results for normal and anomalous dispersive media and to examine the question as to the conditions under which the effects of dispersion should be accounted for, especially for wideband ultrasound pulses of the type used in B-mode tissue imaging. It is shown that the product of the attenuation and total propagation path can be used as a criterion for judging whether dispersion needs to be accounted for.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".