Reduction of Multiply-Nested Dielectric Bodies for Wave Scattering Analysis By Single Source Surface Integral Equations
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Bibliographic record
Abstract
A recursive single source surface integral equation formulation for the problem of electromagnetic wave scattering by multiply-nested bodies yields an equivalent outer surface model that is independent of the material and the illumination in the exterior region, and therefore invariant under rotation and translation. The proposed algorithm is applicable to both far-field and near-field problems, and also gives, through a fast backward recursion, the field values at interior points. Such a reduced model may be duplicated and reused in an assortment of complex scattering problems without repeating the reduction calculation. Thus, the high computational efficiencies realized by the recursive formulation, with respect to the previous, direct, single source surface integral equation formulations, are further enhanced for problems involving some degree of repetition, as in geometry and material optimization of scattering structures under various types of illumination. Numerical examples are included in order to demonstrate the features and the efficiency of the recursive multiply-nested algorithm in comparison to direct, simultaneous solution of all unknowns by the electric field integral equation method.
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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) | 0.000 | 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 it