Distribution of Reactive Energy Density around Antennas in Time-Harmonic Regime: An Electromagnetic Lagrangian Approach
Bibliographic record
Abstract
In this paper, we present an electromagnetic (EM) Lagrangian approach to quantify the reactive energy density distribution around generic antenna systems operating in the time-harmonic regime. First, we introduce the ‘period-averaged EM Lagrangian density’ for radiating EM fields and present its intrinsic relations with the complex Poynting vector, total EM energy density, complex Helicity density, antenna reactive energy and radiation Q-factor. Furthermore, utilising full-wave MoM (method-of-moments) based MATLAB Antenna Toolbox, we compute contour plots of period-averaged EM Lagrangian density around thin-strip dipoles as well as printed microstrip patch antennas. It is demonstrated that such contour plots can not only distinguish between the capacitive and inductive nature of reactive energy density around multiple antenna systems, but also assist in the visualization of the links of inter-element mutual coupling via reactive fields. Such spatial maps of period-averaged EM Lagrangian density can be potentially useful for engineers working in the design of antenna arrays, MIMO (multiple-input multiple-output) and full-duplex systems, as well as EMI/EMC (Electromagnetic Interference/Compatibility) compliant devices.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".