Dissipative phenomena and acoustic phonons in isothermal crystals: A density-functional theory study
Bibliographic record
Abstract
We derive the nonlinear transport equations for isothermal crystalline solids using a density-functional theory based free energy and the Poisson bracket formalism. The model is comprised of three characteristic time scales: A fast one of sound waves and two slow ones of diffusive phenomena. It also combines long-range elastic features with a density field $\ensuremath{\rho}$ having an atomistic resolution. At the level of linearized hydrodynamics, our results are identical to transport equations obtained from the Mori projection operator treatment when the coupling of mass density and phonons becomes weak. At the linear level, we also show that Fick's law breaks down without dislocations in accordance with Cahn's theory of stress effects on diffusion in solids. In contrast, with no bilinear couplings between the density and the displacement fields, it is possible to use a nonlinear local theory to describe diffusion and elastic effects using just a single scalar field $\ensuremath{\rho}$, which is numerically efficient. We show how a variety of phenomenological phase field crystal models---which have recently demonstrated their power in materials science applications---can be derived, and how their parameters can be related to more microscopic ones.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".