Stability Analysis of Metasurfaces Based on Effective Surface Susceptibility State-Space Model
Bibliographic record
Abstract
As a mathematical model of broadband dispersive metasurfaces, the Generalized Sheet Transition Conditions (GSTC) with Lorentz-dispersive material response is formulated as a continuous-time singular system, i.e. a system of differential algebraic equations, which provides a convenient method to investigate the numerical stability of time-domain simulations. This system is transformed to an equivalent regular system which can be represented as a state-space model to methodically solve for the system’s exact time-domain solutions and impulse response, and allowing for an analysis of stability by determining the system’s poles. The system is then time-discretized with various finite-difference formulations, and represented in discrete-time state-space form to analyze the numerical stability, again by determining the numerical poles produced in each formulation. Detailed theoretical formulations and stability predictions are developed for each finite difference formulations, which are then further validated using numerical full-wave simulations. In both the dispersionless and dispersive cases, the analysis focuses on the polarization and the field responses on the 2D surface, by considering only the surface’s effective tangential and normal susceptibility components, to apply the mathematical techniques and establish a stability analysis framework using state-space control theory.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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 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".