Electromagnetic Scattering in Curvilinear Coordinates Using a Generalized Functions Method
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Bibliographic record
Abstract
Abstract A system of equations for calculating the electric field in curvilinear coordinates without imposing external boundary conditions is proposed. First, the system of equations is derived using generalized functions, without imposing external boundary conditions or a coordinate system. Then, in order to demonstrate the use of the system of equations, the derived system is applied to the case of a spherical scatterer, which is then narrowed to the case of a perfect electrically conducting (PEC) sphere. It is shown that for the particular case of a PEC sphere, the resulting field expression agrees with the Stratton‐Chu solution for the Maxwell's equations, confirming that the proposed method can be used to reach a general solution for the electromagnetic field scattered by a PEC sphere, which allows for the calculation of its cross section.
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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 | 0.001 |
| 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) | 0.001 | 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 it