Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane
Bibliographic record
Abstract
Scattering of an obliquely incident plane wave by a general-shaped groove engraved on a perfectly conducting plane is rigorously solved. The scattered field is represented by a Fourier-integral representation. To analytically represent the fields in a general-shaped groove, the groove is divided into L number of layers. Fields are then expressed in each layer as summations of 2D spatial harmonic fields with unknown coefficients. Matching the boundary conditions between layers provides a linear set of equations connecting all the unknown harmonic coefficients. Judicious use of Fourier transform on the equations resulting from matching boundary conditions at the groove aperture provides a series representation of the scattered field in the spectral domain with unknown harmonic coefficients of the first layer in the groove. A stable solution is obtained by solving the complete system of equations with an adaptive choice for the number of modes in each layer.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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 | 0.001 |
| 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".