Integral Approximation Method for Calculating Ultrasonic Beam Propagation in Anisotropic Materials
Bibliographic record
Abstract
ConclusionThe theory of elastic plane wave propagation has been applied to the specific case of a convergent acoustic beam inside an anisotropic material. The result of this theoretical analysis is used to determine the general expression for a convergent beam propagating in an anisotropic specimen. By using an asymptotic expansion around points of stationary phase, one can write a simple analytic approximation that has much in common with the geometric ray theory, while also containing useful amplitude information. The approximate result is not restricted to any specific problem since it was derived without concern for boundary conditions. The result is efficiency in computation that would be missing from a fully accurate wave theory. These theoretical results also confirm some previous theoretical and experimental analyses9,16–17 concerning quasi-2D crystals (graphite and HTS materials), and which also may be applied to ferroelastics near the ferroelastic transition, ordered composites, matrix metals, and other materials. Acoustomicroscopical visualisation was achieved using the more favourable features of the propagation of convergent acoustic beams in anisotropic media. The lateral resolution of an acoustic microscope in that case can be reached up to the order of a wavelength in the liquid couplant for any depth inside the material. Because we can achieve high contrast at significant depths, it is possible to use these results as a useful and powerful method to study the bulk structure of materials.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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".