Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique
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Bibliographic record
Abstract
This paper presents the application of a numerical approach known as proper generalized decomposition (PGD) to calculate the per-unit length (PUL) ac resistance of rectangular conductors. PGD has been successfully used in areas such as fluid mechanics and biomedical applications. It solves a partial differential equation (PDE) by decomposing the answer into a set of unknown one-dimensional (1D) functions in an iterative approach until it reaches a predetermined convergence. In this paper, a frequency-dependent meshing scheme is employed in the PGD technique at each frequency to properly take skin and proximity effects into account. One of the main advantages of PGD over traditional numerical approaches such as finite element or finite difference methods is that it confines the answers within a set of one-dimensional functions, which require fewer computational resources. Different examples of single and multiple rectangular conductors are considered to study skin and proximity effects. The PGD results are compared with those obtained using a commercial finite element method (FEM) software to verify the accuracy of the model. This approach can be used in applications such as white box modeling of transformers, EMC analysis, hairpin winding design used in electric vehicles, and busbar simulation.
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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