Maxwellian Fields and Geometry, Field Behaviour Near Region Boundaries and Sharp Discontinuities – a Review
Bibliographic record
Abstract
The solution of Maxwell's equation is normally determined subject to boundary conditions, and conducting boundaries have the most influence on the field behaviors, especially near sharp discontinuities, where the transverse field components become singular. It is shown that if the region outside the boundary with curvature discontinuities is mapped onto a region with a smooth boundary the reciprocal of the metric coefficient of the transformation describes exactly the singular behavior of the field components near the surface discontinuities. This is shown first mathematically for a conducting wedge. Then, the problem of a TM scattering by the wedge and a conducting prism is investigated, and shown again the same relationship between the surface currents and the reciprocal of the transformation metric coefficients. This property is used to develop a new integral equation by eliminating the singularity of the surface current in the integral equation. This study also showed that the product of the prism surface current and the metric coefficient of the transformation behaved nearly the same as the surface current on a corresponding circular cylinder, an interesting geometrical relationship.
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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) | 0.001 | 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".