Equivalence Principle and Integral Equations in Layered Media
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Bibliographic record
Abstract
Computation of the electromagnetic fields in the presence of the objects embedded in layered media requires solution of the Maxwell equations constrained with appropriate boundary conditions. Two commonly used techniques for evaluation of electromagnetic fields in multilayered structures are the integral equation method and the differential equation methods based on the finite-element and finite-difference discretization. The integral equation method relies on the availability of the layered medium Green's functions which the structure is embedded in and, thus, has ability to localize the unknown quantities to the surfaces of only the conductors and finite dielectric insertions in the layers. In this chapter the authors present detailed derivation of such integral equations formulations suitable for solution of both static and full-wave problems. They review the reciprocity relation, which is key to formulation of the equivalence principle and integral equations for the quasi-electrostatic fields.
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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 | 0.000 |
| 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) | 0.005 | 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