Iterative solution to the scattering by hemispherical bosses on a conducting surface
Bibliographic record
Abstract
Analytic solution to the problem of scattering of a plane electromagnetic wave by a system of hemispherical bosses on a perfectly conducting surface has-a variety of engineering applications. For example, the electromagnetic scattering by three-dimensional rough surfaces or partially buried objects can be simulated by a system of spheres [1]. Exact analytic solution to the problem of scattering by a system of hemispherical bosses has been obtained by using the translational addition theorem for vector spherical wave functions [1]. The required computer time and memory to invert the resulting system matrix increases rapidly with the number of hemispherical bosses. In this paper we replace the array of hemispherical bosses by full spheres in the absence of the conducting plane, but with the given incident plane wave and also a supplementary, image plane wave, chosen such that the boundary conditions for the total field are satisfied at all points where the conducting plane is located in the original problem. Next, we apply the iterative solution where it requires the held scattered by each sphere due only to the primary and secondary incident fields, which acts as an incident field on the other spheres [2]. Hence this iterative process continues until the solution converges. Numerical results are plotted for the normalized backscattering cross section patterns for various angles of incidence.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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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) | 0.000 | 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) | 0.002 | 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".