Wave-optical treatment of the shadow cast by a large sphere
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Bibliographic record
Abstract
We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high-frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this treatment, we demonstrate that there is no EM field deep in the shadow, except for the field that is diffracted into the shadow by the edges of the sphere, as anticipated.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| 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