Complex group velocity and energy transport in absorbing media
Bibliographic record
Abstract
Complex group velocity is common in absorbing and active media, yet its precise physical meaning is unclear. While in the case of a nondissipative medium the group velocity of propagating waves Cg=dω/dk is exactly equal to the observable energy velocity (defined as the ratio between the energy flux and the total energy density) Cg=F/E , in a dissipative medium Cg=dω/dk is in general a complex quantity which cannot be associated with the velocity of energy transport. Nevertheless, we find that the complex group velocity may contain information about the energy transport as well as the energy dissipated in the medium. The presented analysis is intended to expound the connection between the complex group velocity and energy transport characteristics for a class of hyperbolic dissipative dynamical systems. Dissipation mechanisms considered herein include viscous and viscoelastic types of damping. Both cases of spatial and temporal decay are discussed. The presented approach stems from the Lagrangian formulation and is illustrated with identities that relate the complex group velocity and energy transport characteristics for the damped Klein-Gordon equation; Maxwell's equations, governing electromagnetic waves in partially conducting media; and Biot's theory, governing acoustic wave propagation in porous solids.
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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".