A Homogenized Energy Model for Hysteresis in Ferroelectric Materials: General Density Formulation
Bibliographic record
Abstract
In this article, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations that can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data.
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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 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".