Computation of Fields Via Integration Along Branch Cuts
Bibliographic record
Abstract
This chapter examines how integration along the Sommerfeld integration path can be transformed using Cauchy theorem to integration along the branch cuts. It sets up numerical integration along branch cuts through appropriate parametrization of the paths. The chapter explores the Zenneck surface wave and its role in the overall solution of the Sommerfeld problem of vertical electric dipole (VED) radiation above half-space. It then focuses on the transformation of the surface wave into a leaky wave in the near cut-off regimes. The exploration of the surface waves excited by VED above the half-space dates back to 1909 when Sommerfeld published his original paper. In the solution of this radiation problem the surface wave known as the Zenneck wave may or may not appear as a contribution to the field not only depending on the choice of the physical parameters of the problem but also depending on the choice of the branch cut convention.
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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".