Computation of Fields Via Integration Along Steepest Descent Path
Bibliographic record
Abstract
In this chapter, the authors consider approach to evaluation of the Sommerfeld integrals (SIs) based on modification of the Sommerfeld integration path (SIP) into a special path, along which the integrand attenuates the most rapidly for any given observation point elevation and radial distance. The steepest descent path (SDP) of the integrand is determined by the exponential factor entering into the SI. While integration along the SDP is arguably the optimal among all possible alternatives from the vantage point of minimizing oscillations of the integrand and providing its fastest convergence. When losses are introduced into the layers defining segments of the SDPs on the four Riemann sheets of the integrand becomes significantly more involved, once again making the SDP approach to evaluation of the SIs notably more difficult to implement than other approaches. Systematic location of the surface wave poles in the general case of lossy layered medium is also complicated.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".