Mesoscale Simulation of Grain Growth
Bibliographic record
Abstract
Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".