New Single-Source Surface Integral Equations for Scattering on Penetrable Cylinders and Current Flow Modeling in 2-D Conductors
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Bibliographic record
Abstract
The traditional volume electric field integral equation (IE) used for solution of full-wave scattering problems on penetrable scatterers of arbitrary cross section and its magnetostatic counterpart commonly utilized for the resistance and inductance extraction problem are reduced to a novel derivative-free single-source surface IE. The reduction of volume to surface IE is based on representation of the electric field in the cylinder cross section in the form of a single-layer ansatz. Substitution of such surface based electric field representation into the volume IE reduces it to a surface IE with respect to the unknown surface current density. Since the new surface IE enforces exactly the field continuity at the material interfaces, the radiation condition as well as underlying Helmholtz equations both inside and outside the penetrable cylinder, it is rigorously equivalent to the solution of Maxwell's equations. The method of moments discretization of the new IE is shown to produce an error-controllable field approximation. Due to the presence of a product of surface-to-volume and volume-to-surface integral operators, the discretization of the novel surface-volume-surface IE requires both surface and volume meshes.
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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) | 0.000 | 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