Padé approximations in inverse homogenization and numerical simulation of electromagnetic fields in composites
Bibliographic record
Abstract
The paper considers rational Padé approximation of the spectral function of composites with fine microstructure and discusses its use in characterization of the microgeometry of composite materials and in numerical simulation of time-domain electromagnetic fields in composites. It is assumed that the scale of the structure is much smaller than the smallest wavelength of the applied field. We use Stieltjes representation of the effective complex permittivity of the composite and derive its Padé approximation. The spectral function in this representation contains all information about the microgeometry of the mixture. Having reconstructed the Padé approximation, we recover information about the composite structure. The resulting time-domain equations governing the electromagnetic fields are of convolution type. We use rational Padé approximation to derive equations for internal variables for time-domain simulation. We show that electromagnetic fields computed using such internal variables, correspond to the fields in S-equivalent composite structures.
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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) | 0.000 | 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 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".