Comparison of Tensor Boundary Conditions With Generalized Sheet Transition Conditions
Bibliographic record
Abstract
This paper compares the tensor boundary conditions (TBCs) with the surface-susceptibility-based generalized sheet transition conditions (GSTCs) for the modeling of metasurfaces and 2-D material allotropes. First, we recall the GSTCs, distinguishing the full-tensor (FT) GSTCs and the tangential-tensor (TT) GSTCs, which correspond to the most general and most reported GSTC forms, respectively. We show, by separating tangential and normal polarizations, that the FT-GSTCs involve 36 independent susceptibility parameters, associated with $3\times 3$ electric, magnetic, electric-to-magnetic, and magnetic-to-electric susceptibility tensors, despite the 2-D nature of the structure. Moreover, we find that suppressing the normal polarizations nontrivially reduces the number of FT-GSTC parameters to 24, which is greater than the 16 parameters of the TT-GSTCs. Then, the paper recalls the TBCs as originally reported in a previous study, called here scalar-parameter (SP) TBCs, and extends them to their tensorial-parameter (TP) counterparts, called the TP TBCs. In both formulations, we derive the equivalent susceptibilities in terms of the TBC parameters. We show that the SP-TBCs involve eight equivalent susceptibility parameters, among which only three are independent, while the TP-TBCs involve 16 independent susceptibility parameters. Next, we compare the two models, with their two respective formulations, in terms of both generality and physicality. We deduce from the number of independent susceptibility parameters the following ranking between the four formulations: 1) FT-GSTCs (36 independent parameters); 2) TT-GSTCs = TP-TBCs (16 independent parameters); 3) SP-TBCs (3 independent parameters), and illustrate with examples the property and functionality limitations of the TT-GSTCs, TP-TBCs, and SP-TBCs due to their parameter restrictions. Finally, we show that while the GSTCs appropriately describe the physics of the problem, the TBCs are discordant with it.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".