Bounds on the complex permittivity of polycrystalline materials by analytic continuation
Bibliographic record
Abstract
An analytic continuation method for obtaining rigorous bounds on the effective complex permittivity ε * of polycrystalline composite materials is developed. It is assumed that the composite consists of many identical anisotropic crystals, each with a unique orientation. The key step in obtaining the bounds involves deriving an integral representation for ε *, which separates parameter information from geometrical information. Forward bounds are then found using knowledge of the single crystal permittivity tensor and mean crystal orientation. Inverse bounds are also developed, which recover information about the mean crystal orientation from ε *. We apply the polycrystalline bounds to sea ice, a critical component of the climate system. Different ice types, which result from different growth conditions, have different crystal orientation and size statistics. These characteristics significantly influence the fluid transport properties of sea ice, which control many geophysical and biogeochemical processes important to the climate and polar ecosystems. Using a two-scale homogenization scheme, where the single crystal tensor is numerically computed, forward bounds for sea ice are obtained and are in excellent agreement with columnar sea ice data. Furthermore, the inverse bounds are also applied to sea ice, helping to lay the groundwork for determining ice type using remote sensing techniques.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".